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- Committer: Anders Logg
- Date: 2008-06-12 13:24:57 UTC
- mfrom: (2668.16.2 trunk)
- mto: This revision was merged to the branch mainline in revision 2670.
- Revision ID: logg@simula.no-20080612132457-sh7of8y10y5yebj0
Merge work on assembly benchmark by Ilmar
- files added:
- bench/fem/assembly/Elasticity3D.form
- files removed:
- bench/fem/assembly/Advection.form
added
removed
bench/fem/assembly/Advection.h
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// This code conforms with the UFC specification version 1.0
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// and was automatically generated by FFC version 0.4.5.
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//
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// Warning: This code was generated with the option '-l dolfin'
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// and contains DOLFIN-specific wrappers that depend on DOLFIN.
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#ifndef __ADVECTION_H
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#define __ADVECTION_H
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#include <cmath>
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#include <stdexcept>
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#include <fstream>
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#include <ufc.h>
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/// This class defines the interface for a finite element.
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class UFC_AdvectionBilinearForm_finite_element_0: public ufc::finite_element
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{
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public:
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/// Constructor
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UFC_AdvectionBilinearForm_finite_element_0() : ufc::finite_element()
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{
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// Do nothing
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}
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/// Destructor
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virtual ~UFC_AdvectionBilinearForm_finite_element_0()
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{
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// Do nothing
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}
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/// Return a string identifying the finite element
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virtual const char* signature() const
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{
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return "Lagrange finite element of degree 3 on a tetrahedron";
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}
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/// Return the cell shape
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virtual ufc::shape cell_shape() const
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{
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return ufc::tetrahedron;
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}
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/// Return the dimension of the finite element function space
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virtual unsigned int space_dimension() const
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{
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return 20;
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}
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/// Return the rank of the value space
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virtual unsigned int value_rank() const
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{
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return 0;
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}
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/// Return the dimension of the value space for axis i
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virtual unsigned int value_dimension(unsigned int i) const
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{
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return 1;
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}
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/// Evaluate basis function i at given point in cell
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virtual void evaluate_basis(unsigned int i,
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double* values,
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const double* coordinates,
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const ufc::cell& c) const
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{
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// Extract vertex coordinates
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const double * const * element_coordinates = c.coordinates;
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// Compute Jacobian of affine map from reference cell
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const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
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const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
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const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];
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const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
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const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
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const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];
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const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];
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const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];
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const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];
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// Compute sub determinants
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const double d00 = J_11*J_22 - J_12*J_21;
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const double d01 = J_12*J_20 - J_10*J_22;
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const double d02 = J_10*J_21 - J_11*J_20;
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const double d10 = J_02*J_21 - J_01*J_22;
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const double d11 = J_00*J_22 - J_02*J_20;
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const double d12 = J_01*J_20 - J_00*J_21;
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const double d20 = J_01*J_12 - J_02*J_11;
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const double d21 = J_02*J_10 - J_00*J_12;
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const double d22 = J_00*J_11 - J_01*J_10;
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// Compute determinant of Jacobian
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double detJ = J_00*d00 + J_10*d10 + J_20*d20;
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// Compute inverse of Jacobian
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// Compute constants
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const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \
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+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \
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+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);
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const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \
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+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \
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+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);
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const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \
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+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \
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+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);
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// Get coordinates and map to the UFC reference element
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double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;
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double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;
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double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;
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// Map coordinates to the reference cube
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if (std::abs(y + z - 1.0) < 1e-14)
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x = 1.0;
122
else
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x = -2.0 * x/(y + z - 1.0) - 1.0;
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if (std::abs(z - 1.0) < 1e-14)
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y = -1.0;
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else
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y = 2.0 * y/(1.0 - z) - 1.0;
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z = 2.0 * z - 1.0;
129
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// Reset values
131
*values = 0;
132
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// Map degree of freedom to element degree of freedom
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const unsigned int dof = i;
135
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// Generate scalings
137
const double scalings_y_0 = 1;
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const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
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const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);
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const double scalings_y_3 = scalings_y_2*(0.5 - 0.5*y);
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const double scalings_z_0 = 1;
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const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);
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const double scalings_z_2 = scalings_z_1*(0.5 - 0.5*z);
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const double scalings_z_3 = scalings_z_2*(0.5 - 0.5*z);
145
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// Compute psitilde_a
147
const double psitilde_a_0 = 1;
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const double psitilde_a_1 = x;
149
const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;
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const double psitilde_a_3 = 1.66666666666667*x*psitilde_a_2 - 0.666666666666667*psitilde_a_1;
151
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// Compute psitilde_bs
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const double psitilde_bs_0_0 = 1;
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const double psitilde_bs_0_1 = 1.5*y + 0.5;
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const double psitilde_bs_0_2 = 0.111111111111111*psitilde_bs_0_1 + 1.66666666666667*y*psitilde_bs_0_1 - 0.555555555555556*psitilde_bs_0_0;
156
const double psitilde_bs_0_3 = 0.05*psitilde_bs_0_2 + 1.75*y*psitilde_bs_0_2 - 0.7*psitilde_bs_0_1;
157
const double psitilde_bs_1_0 = 1;
158
const double psitilde_bs_1_1 = 2.5*y + 1.5;
159
const double psitilde_bs_1_2 = 0.54*psitilde_bs_1_1 + 2.1*y*psitilde_bs_1_1 - 0.56*psitilde_bs_1_0;
160
const double psitilde_bs_2_0 = 1;
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const double psitilde_bs_2_1 = 3.5*y + 2.5;
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const double psitilde_bs_3_0 = 1;
163
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// Compute psitilde_cs
165
const double psitilde_cs_00_0 = 1;
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const double psitilde_cs_00_1 = 2*z + 1;
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const double psitilde_cs_00_2 = 0.3125*psitilde_cs_00_1 + 1.875*z*psitilde_cs_00_1 - 0.5625*psitilde_cs_00_0;
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const double psitilde_cs_00_3 = 0.155555555555556*psitilde_cs_00_2 + 1.86666666666667*z*psitilde_cs_00_2 - 0.711111111111111*psitilde_cs_00_1;
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const double psitilde_cs_01_0 = 1;
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const double psitilde_cs_01_1 = 3*z + 2;
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const double psitilde_cs_01_2 = 0.777777777777778*psitilde_cs_01_1 + 2.33333333333333*z*psitilde_cs_01_1 - 0.555555555555556*psitilde_cs_01_0;
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const double psitilde_cs_02_0 = 1;
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const double psitilde_cs_02_1 = 4*z + 3;
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const double psitilde_cs_03_0 = 1;
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const double psitilde_cs_10_0 = 1;
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const double psitilde_cs_10_1 = 3*z + 2;
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const double psitilde_cs_10_2 = 0.777777777777778*psitilde_cs_10_1 + 2.33333333333333*z*psitilde_cs_10_1 - 0.555555555555556*psitilde_cs_10_0;
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const double psitilde_cs_11_0 = 1;
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const double psitilde_cs_11_1 = 4*z + 3;
180
const double psitilde_cs_12_0 = 1;
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const double psitilde_cs_20_0 = 1;
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const double psitilde_cs_20_1 = 4*z + 3;
183
const double psitilde_cs_21_0 = 1;
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const double psitilde_cs_30_0 = 1;
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// Compute basisvalues
187
const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
188
const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;
189
const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;
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const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;
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const double basisvalue4 = 5.1234753829798*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_0;
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const double basisvalue5 = 3.96862696659689*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_0;
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const double basisvalue6 = 2.29128784747792*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_0;
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const double basisvalue7 = 3.24037034920393*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_1;
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const double basisvalue8 = 1.87082869338697*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_1;
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const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;
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const double basisvalue10 = 7.93725393319377*psitilde_a_3*scalings_y_3*psitilde_bs_3_0*scalings_z_3*psitilde_cs_30_0;
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const double basisvalue11 = 6.70820393249937*psitilde_a_2*scalings_y_2*psitilde_bs_2_1*scalings_z_3*psitilde_cs_21_0;
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const double basisvalue12 = 5.19615242270663*psitilde_a_1*scalings_y_1*psitilde_bs_1_2*scalings_z_3*psitilde_cs_12_0;
200
const double basisvalue13 = 3*psitilde_a_0*scalings_y_0*psitilde_bs_0_3*scalings_z_3*psitilde_cs_03_0;
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const double basisvalue14 = 5.80947501931113*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_1;
202
const double basisvalue15 = 4.5*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_1;
203
const double basisvalue16 = 2.59807621135332*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_1;
204
const double basisvalue17 = 3.67423461417477*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_2;
205
const double basisvalue18 = 2.12132034355964*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_2;
206
const double basisvalue19 = 1.5*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_3;
207
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// Table(s) of coefficients
209
const static double coefficients0[20][20] = \
210
{{0.0288675134594814, 0.0130410132739326, 0.00752923252421041, 0.00532397137499949, 0.018298126367785, 0.014173667737846, 0.00818317088384972, 0.0115727512471569, 0.0066815310478106, 0.00472455591261533, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197612, -0.0131222664791956, -0.00757614408414157, -0.00535714285714285},
211
{0.0288675134594813, -0.0130410132739325, 0.0075292325242104, 0.00532397137499953, 0.018298126367785, -0.014173667737846, 0.00818317088384972, -0.0115727512471569, 0.0066815310478106, 0.00472455591261534, 0.028347335475692, -0.0239578711874977, 0.0185576872239523, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197613, 0.0131222664791956, -0.00757614408414159, -0.00535714285714286},
212
{0.0288675134594812, 0, -0.0150584650484208, 0.00532397137499948, 0, 0, 0.0245495126515492, 0, -0.0133630620956212, 0.00472455591261538, 0, 0, 0, 0.0428571428571428, 0, 0, -0.0278365308359284, 0, 0.0151522881682832, -0.00535714285714287},
213
{0.0288675134594813, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.028347335475692, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286},
214
{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546474, 0, 0.0267261241912424, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731327, 0.0267857142857143},
215
{0, 0, -0.0225876975726313, 0.127775312999988, 0, 0, 0, 0, 0.0668153104781061, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0, 0.0757614408414158, -0.0535714285714286},
216
{0, 0.097807599554494, -0.0564692439315782, -0.063887656499994, 0.054894379103355, -0.0425210032135381, 0.0245495126515491, 0.0231455024943138, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, -0.0375, 0.021650635094611, -0.0524890659167824, 0.0303045763365663, 0.0267857142857143},
217
{0, -0.0195615199108988, 0.0112938487863157, 0.127775312999988, 0, 0, 0, 0.0578637562357845, -0.0334076552390531, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0.065611332395978, -0.0378807204207079, -0.0535714285714286},
218
{0, 0.097807599554494, -0.0790569415042095, -0.031943828249997, 0.054894379103355, 0.014173667737846, -0.0245495126515491, -0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, -0.0618589574131742, 0.0428571428571429, -0.00691604168965609, -0.0160714285714286, 0.0154647393532935, 0.00874817765279706, 0, -0.00535714285714286},
219
{0, -0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, 0.0566946709513841, 0.0245495126515492, -0.0115727512471569, -0.0467707173346742, 0.0236227795630767, 0, 0, 0.0618589574131742, -0.0642857142857143, 0, -0.0214285714285714, 0.00927884361197613, 0.00437408882639853, 0.00757614408414158, -0.00535714285714285},
220
{0, -0.0978075995544939, -0.0564692439315781, -0.063887656499994, 0.054894379103355, 0.0425210032135381, 0.0245495126515491, -0.0231455024943137, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, 0.0375, 0.021650635094611, 0.0524890659167824, 0.0303045763365663, 0.0267857142857143},
221
{0, 0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, -0.0578637562357845, -0.033407655239053, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, -0.065611332395978, -0.0378807204207079, -0.0535714285714286},
222
{0, -0.097807599554494, -0.0790569415042095, -0.031943828249997, 0.054894379103355, -0.014173667737846, -0.0245495126515492, 0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, 0.0618589574131742, 0.0428571428571429, -0.0069160416896561, 0.0160714285714286, 0.0154647393532935, -0.00874817765279706, 0, -0.00535714285714287},
223
{0, 0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, -0.0566946709513841, 0.0245495126515492, 0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, -0.0618589574131742, -0.0642857142857143, 0, 0.0214285714285714, 0.00927884361197613, -0.00437408882639853, 0.00757614408414157, -0.00535714285714286},
224
{0, -0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.018298126367785, 0.0425210032135381, 0.0409158544192485, 0.0347182537414707, 0.033407655239053, 0.0236227795630767, 0.0850420064270761, 0.0239578711874977, -0.00618589574131741, -0.0107142857142857, 0.0207481250689683, -0.00535714285714284, -0.00927884361197614, -0.00437408882639852, -0.0075761440841416, -0.00535714285714286},
225
{0, 0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.018298126367785, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.0334076552390531, 0.0236227795630767, -0.0850420064270761, 0.0239578711874978, 0.0061858957413174, -0.0107142857142857, 0.0207481250689683, 0.00535714285714285, -0.00927884361197613, 0.00437408882639852, -0.00757614408414159, -0.00535714285714286},
226
{0.259807621135332, 0.117369119465393, 0.0677630927178939, 0.0479157423749955, 0, 0.0850420064270761, -0.0736485379546474, 0.0694365074829413, 0.0400891862868636, -0.0992156741649222, 0, 0, 0, 0, 0, 0.075, -0.0649519052838329, -0.0262445329583912, -0.0151522881682832, 0.0267857142857143},
227
{0.259807621135332, -0.117369119465393, 0.0677630927178938, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546474, -0.0694365074829414, 0.0400891862868636, -0.0992156741649221, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682832, 0.0267857142857143},
228
{0.259807621135332, 0, -0.135526185435788, 0.0479157423749955, -0.10978875820671, 0, 0.0245495126515491, 0, -0.0801783725737273, -0.0992156741649221, 0, 0, 0, 0, -0.0968245836551854, 0, 0.021650635094611, 0, 0.0303045763365663, 0.0267857142857143},
229
{0.259807621135332, 0, 0, -0.143747227124986, -0.10978875820671, 0, -0.122747563257746, 0, 0, 0.0425210032135381, 0, -0.095831484749991, 0, 0.0428571428571429, 0.0138320833793122, 0, 0.0154647393532935, 0, 0, -0.00535714285714284}};
230
231
// Extract relevant coefficients
232
const double coeff0_0 = coefficients0[dof][0];
233
const double coeff0_1 = coefficients0[dof][1];
234
const double coeff0_2 = coefficients0[dof][2];
235
const double coeff0_3 = coefficients0[dof][3];
236
const double coeff0_4 = coefficients0[dof][4];
237
const double coeff0_5 = coefficients0[dof][5];
238
const double coeff0_6 = coefficients0[dof][6];
239
const double coeff0_7 = coefficients0[dof][7];
240
const double coeff0_8 = coefficients0[dof][8];
241
const double coeff0_9 = coefficients0[dof][9];
242
const double coeff0_10 = coefficients0[dof][10];
243
const double coeff0_11 = coefficients0[dof][11];
244
const double coeff0_12 = coefficients0[dof][12];
245
const double coeff0_13 = coefficients0[dof][13];
246
const double coeff0_14 = coefficients0[dof][14];
247
const double coeff0_15 = coefficients0[dof][15];
248
const double coeff0_16 = coefficients0[dof][16];
249
const double coeff0_17 = coefficients0[dof][17];
250
const double coeff0_18 = coefficients0[dof][18];
251
const double coeff0_19 = coefficients0[dof][19];
252
253
// Compute value(s)
254
*values = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2 + coeff0_3*basisvalue3 + coeff0_4*basisvalue4 + coeff0_5*basisvalue5 + coeff0_6*basisvalue6 + coeff0_7*basisvalue7 + coeff0_8*basisvalue8 + coeff0_9*basisvalue9 + coeff0_10*basisvalue10 + coeff0_11*basisvalue11 + coeff0_12*basisvalue12 + coeff0_13*basisvalue13 + coeff0_14*basisvalue14 + coeff0_15*basisvalue15 + coeff0_16*basisvalue16 + coeff0_17*basisvalue17 + coeff0_18*basisvalue18 + coeff0_19*basisvalue19;
255
}
256
257
/// Evaluate all basis functions at given point in cell
258
virtual void evaluate_basis_all(double* values,
259
const double* coordinates,
260
const ufc::cell& c) const
261
{
262
throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");
263
}
264
265
/// Evaluate order n derivatives of basis function i at given point in cell
266
virtual void evaluate_basis_derivatives(unsigned int i,
267
unsigned int n,
268
double* values,
269
const double* coordinates,
270
const ufc::cell& c) const
271
{
272
// Extract vertex coordinates
273
const double * const * element_coordinates = c.coordinates;
274
275
// Compute Jacobian of affine map from reference cell
276
const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
277
const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
278
const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];
279
const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
280
const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
281
const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];
282
const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];
283
const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];
284
const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];
285
286
// Compute sub determinants
287
const double d00 = J_11*J_22 - J_12*J_21;
288
const double d01 = J_12*J_20 - J_10*J_22;
289
const double d02 = J_10*J_21 - J_11*J_20;
290
291
const double d10 = J_02*J_21 - J_01*J_22;
292
const double d11 = J_00*J_22 - J_02*J_20;
293
const double d12 = J_01*J_20 - J_00*J_21;
294
295
const double d20 = J_01*J_12 - J_02*J_11;
296
const double d21 = J_02*J_10 - J_00*J_12;
297
const double d22 = J_00*J_11 - J_01*J_10;
298
299
// Compute determinant of Jacobian
300
double detJ = J_00*d00 + J_10*d10 + J_20*d20;
301
302
// Compute inverse of Jacobian
303
304
// Compute constants
305
const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \
306
+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \
307
+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);
308
309
const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \
310
+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \
311
+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);
312
313
const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \
314
+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \
315
+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);
316
317
// Get coordinates and map to the UFC reference element
318
double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;
319
double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;
320
double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;
321
322
// Map coordinates to the reference cube
323
if (std::abs(y + z - 1.0) < 1e-14)
324
x = 1.0;
325
else
326
x = -2.0 * x/(y + z - 1.0) - 1.0;
327
if (std::abs(z - 1.0) < 1e-14)
328
y = -1.0;
329
else
330
y = 2.0 * y/(1.0 - z) - 1.0;
331
z = 2.0 * z - 1.0;
332
333
// Compute number of derivatives
334
unsigned int num_derivatives = 1;
335
336
for (unsigned int j = 0; j < n; j++)
337
num_derivatives *= 3;
338
339
340
// Declare pointer to two dimensional array that holds combinations of derivatives and initialise
341
unsigned int **combinations = new unsigned int *[num_derivatives];
342
343
for (unsigned int j = 0; j < num_derivatives; j++)
344
{
345
combinations[j] = new unsigned int [n];
346
for (unsigned int k = 0; k < n; k++)
347
combinations[j][k] = 0;
348
}
349
350
// Generate combinations of derivatives
351
for (unsigned int row = 1; row < num_derivatives; row++)
352
{
353
for (unsigned int num = 0; num < row; num++)
354
{
355
for (unsigned int col = n-1; col+1 > 0; col--)
356
{
357
if (combinations[row][col] + 1 > 2)
358
combinations[row][col] = 0;
359
else
360
{
361
combinations[row][col] += 1;
362
break;
363
}
364
}
365
}
366
}
367
368
// Compute inverse of Jacobian
369
const double Jinv[3][3] ={{d00 / detJ, d10 / detJ, d20 / detJ}, {d01 / detJ, d11 / detJ, d21 / detJ}, {d02 / detJ, d12 / detJ, d22 / detJ}};
370
371
// Declare transformation matrix
372
// Declare pointer to two dimensional array and initialise
373
double **transform = new double *[num_derivatives];
374
375
for (unsigned int j = 0; j < num_derivatives; j++)
376
{
377
transform[j] = new double [num_derivatives];
378
for (unsigned int k = 0; k < num_derivatives; k++)
379
transform[j][k] = 1;
380
}
381
382
// Construct transformation matrix
383
for (unsigned int row = 0; row < num_derivatives; row++)
384
{
385
for (unsigned int col = 0; col < num_derivatives; col++)
386
{
387
for (unsigned int k = 0; k < n; k++)
388
transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
389
}
390
}
391
392
// Reset values
393
for (unsigned int j = 0; j < 1*num_derivatives; j++)
394
values[j] = 0;
395
396
// Map degree of freedom to element degree of freedom
397
const unsigned int dof = i;
398
399
// Generate scalings
400
const double scalings_y_0 = 1;
401
const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
402
const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);
403
const double scalings_y_3 = scalings_y_2*(0.5 - 0.5*y);
404
const double scalings_z_0 = 1;
405
const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);
406
const double scalings_z_2 = scalings_z_1*(0.5 - 0.5*z);
407
const double scalings_z_3 = scalings_z_2*(0.5 - 0.5*z);
408
409
// Compute psitilde_a
410
const double psitilde_a_0 = 1;
411
const double psitilde_a_1 = x;
412
const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;
413
const double psitilde_a_3 = 1.66666666666667*x*psitilde_a_2 - 0.666666666666667*psitilde_a_1;
414
415
// Compute psitilde_bs
416
const double psitilde_bs_0_0 = 1;
417
const double psitilde_bs_0_1 = 1.5*y + 0.5;
418
const double psitilde_bs_0_2 = 0.111111111111111*psitilde_bs_0_1 + 1.66666666666667*y*psitilde_bs_0_1 - 0.555555555555556*psitilde_bs_0_0;
419
const double psitilde_bs_0_3 = 0.05*psitilde_bs_0_2 + 1.75*y*psitilde_bs_0_2 - 0.7*psitilde_bs_0_1;
420
const double psitilde_bs_1_0 = 1;
421
const double psitilde_bs_1_1 = 2.5*y + 1.5;
422
const double psitilde_bs_1_2 = 0.54*psitilde_bs_1_1 + 2.1*y*psitilde_bs_1_1 - 0.56*psitilde_bs_1_0;
423
const double psitilde_bs_2_0 = 1;
424
const double psitilde_bs_2_1 = 3.5*y + 2.5;
425
const double psitilde_bs_3_0 = 1;
426
427
// Compute psitilde_cs
428
const double psitilde_cs_00_0 = 1;
429
const double psitilde_cs_00_1 = 2*z + 1;
430
const double psitilde_cs_00_2 = 0.3125*psitilde_cs_00_1 + 1.875*z*psitilde_cs_00_1 - 0.5625*psitilde_cs_00_0;
431
const double psitilde_cs_00_3 = 0.155555555555556*psitilde_cs_00_2 + 1.86666666666667*z*psitilde_cs_00_2 - 0.711111111111111*psitilde_cs_00_1;
432
const double psitilde_cs_01_0 = 1;
433
const double psitilde_cs_01_1 = 3*z + 2;
434
const double psitilde_cs_01_2 = 0.777777777777778*psitilde_cs_01_1 + 2.33333333333333*z*psitilde_cs_01_1 - 0.555555555555556*psitilde_cs_01_0;
435
const double psitilde_cs_02_0 = 1;
436
const double psitilde_cs_02_1 = 4*z + 3;
437
const double psitilde_cs_03_0 = 1;
438
const double psitilde_cs_10_0 = 1;
439
const double psitilde_cs_10_1 = 3*z + 2;
440
const double psitilde_cs_10_2 = 0.777777777777778*psitilde_cs_10_1 + 2.33333333333333*z*psitilde_cs_10_1 - 0.555555555555556*psitilde_cs_10_0;
441
const double psitilde_cs_11_0 = 1;
442
const double psitilde_cs_11_1 = 4*z + 3;
443
const double psitilde_cs_12_0 = 1;
444
const double psitilde_cs_20_0 = 1;
445
const double psitilde_cs_20_1 = 4*z + 3;
446
const double psitilde_cs_21_0 = 1;
447
const double psitilde_cs_30_0 = 1;
448
449
// Compute basisvalues
450
const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
451
const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;
452
const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;
453
const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;
454
const double basisvalue4 = 5.1234753829798*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_0;
455
const double basisvalue5 = 3.96862696659689*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_0;
456
const double basisvalue6 = 2.29128784747792*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_0;
457
const double basisvalue7 = 3.24037034920393*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_1;
458
const double basisvalue8 = 1.87082869338697*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_1;
459
const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;
460
const double basisvalue10 = 7.93725393319377*psitilde_a_3*scalings_y_3*psitilde_bs_3_0*scalings_z_3*psitilde_cs_30_0;
461
const double basisvalue11 = 6.70820393249937*psitilde_a_2*scalings_y_2*psitilde_bs_2_1*scalings_z_3*psitilde_cs_21_0;
462
const double basisvalue12 = 5.19615242270663*psitilde_a_1*scalings_y_1*psitilde_bs_1_2*scalings_z_3*psitilde_cs_12_0;
463
const double basisvalue13 = 3*psitilde_a_0*scalings_y_0*psitilde_bs_0_3*scalings_z_3*psitilde_cs_03_0;
464
const double basisvalue14 = 5.80947501931113*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_1;
465
const double basisvalue15 = 4.5*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_1;
466
const double basisvalue16 = 2.59807621135332*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_1;
467
const double basisvalue17 = 3.67423461417477*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_2;
468
const double basisvalue18 = 2.12132034355964*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_2;
469
const double basisvalue19 = 1.5*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_3;
470
471
// Table(s) of coefficients
472
const static double coefficients0[20][20] = \
473
{{0.0288675134594814, 0.0130410132739326, 0.00752923252421041, 0.00532397137499949, 0.018298126367785, 0.014173667737846, 0.00818317088384972, 0.0115727512471569, 0.0066815310478106, 0.00472455591261533, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197612, -0.0131222664791956, -0.00757614408414157, -0.00535714285714285},
474
{0.0288675134594813, -0.0130410132739325, 0.0075292325242104, 0.00532397137499953, 0.018298126367785, -0.014173667737846, 0.00818317088384972, -0.0115727512471569, 0.0066815310478106, 0.00472455591261534, 0.028347335475692, -0.0239578711874977, 0.0185576872239523, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197613, 0.0131222664791956, -0.00757614408414159, -0.00535714285714286},
475
{0.0288675134594812, 0, -0.0150584650484208, 0.00532397137499948, 0, 0, 0.0245495126515492, 0, -0.0133630620956212, 0.00472455591261538, 0, 0, 0, 0.0428571428571428, 0, 0, -0.0278365308359284, 0, 0.0151522881682832, -0.00535714285714287},
476
{0.0288675134594813, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.028347335475692, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286},
477
{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546474, 0, 0.0267261241912424, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731327, 0.0267857142857143},
478
{0, 0, -0.0225876975726313, 0.127775312999988, 0, 0, 0, 0, 0.0668153104781061, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0, 0.0757614408414158, -0.0535714285714286},
479
{0, 0.097807599554494, -0.0564692439315782, -0.063887656499994, 0.054894379103355, -0.0425210032135381, 0.0245495126515491, 0.0231455024943138, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, -0.0375, 0.021650635094611, -0.0524890659167824, 0.0303045763365663, 0.0267857142857143},
480
{0, -0.0195615199108988, 0.0112938487863157, 0.127775312999988, 0, 0, 0, 0.0578637562357845, -0.0334076552390531, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0.065611332395978, -0.0378807204207079, -0.0535714285714286},
481
{0, 0.097807599554494, -0.0790569415042095, -0.031943828249997, 0.054894379103355, 0.014173667737846, -0.0245495126515491, -0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, -0.0618589574131742, 0.0428571428571429, -0.00691604168965609, -0.0160714285714286, 0.0154647393532935, 0.00874817765279706, 0, -0.00535714285714286},
482
{0, -0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, 0.0566946709513841, 0.0245495126515492, -0.0115727512471569, -0.0467707173346742, 0.0236227795630767, 0, 0, 0.0618589574131742, -0.0642857142857143, 0, -0.0214285714285714, 0.00927884361197613, 0.00437408882639853, 0.00757614408414158, -0.00535714285714285},
483
{0, -0.0978075995544939, -0.0564692439315781, -0.063887656499994, 0.054894379103355, 0.0425210032135381, 0.0245495126515491, -0.0231455024943137, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, 0.0375, 0.021650635094611, 0.0524890659167824, 0.0303045763365663, 0.0267857142857143},
484
{0, 0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, -0.0578637562357845, -0.033407655239053, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, -0.065611332395978, -0.0378807204207079, -0.0535714285714286},
485
{0, -0.097807599554494, -0.0790569415042095, -0.031943828249997, 0.054894379103355, -0.014173667737846, -0.0245495126515492, 0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, 0.0618589574131742, 0.0428571428571429, -0.0069160416896561, 0.0160714285714286, 0.0154647393532935, -0.00874817765279706, 0, -0.00535714285714287},
486
{0, 0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, -0.0566946709513841, 0.0245495126515492, 0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, -0.0618589574131742, -0.0642857142857143, 0, 0.0214285714285714, 0.00927884361197613, -0.00437408882639853, 0.00757614408414157, -0.00535714285714286},
487
{0, -0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.018298126367785, 0.0425210032135381, 0.0409158544192485, 0.0347182537414707, 0.033407655239053, 0.0236227795630767, 0.0850420064270761, 0.0239578711874977, -0.00618589574131741, -0.0107142857142857, 0.0207481250689683, -0.00535714285714284, -0.00927884361197614, -0.00437408882639852, -0.0075761440841416, -0.00535714285714286},
488
{0, 0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.018298126367785, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.0334076552390531, 0.0236227795630767, -0.0850420064270761, 0.0239578711874978, 0.0061858957413174, -0.0107142857142857, 0.0207481250689683, 0.00535714285714285, -0.00927884361197613, 0.00437408882639852, -0.00757614408414159, -0.00535714285714286},
489
{0.259807621135332, 0.117369119465393, 0.0677630927178939, 0.0479157423749955, 0, 0.0850420064270761, -0.0736485379546474, 0.0694365074829413, 0.0400891862868636, -0.0992156741649222, 0, 0, 0, 0, 0, 0.075, -0.0649519052838329, -0.0262445329583912, -0.0151522881682832, 0.0267857142857143},
490
{0.259807621135332, -0.117369119465393, 0.0677630927178938, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546474, -0.0694365074829414, 0.0400891862868636, -0.0992156741649221, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682832, 0.0267857142857143},
491
{0.259807621135332, 0, -0.135526185435788, 0.0479157423749955, -0.10978875820671, 0, 0.0245495126515491, 0, -0.0801783725737273, -0.0992156741649221, 0, 0, 0, 0, -0.0968245836551854, 0, 0.021650635094611, 0, 0.0303045763365663, 0.0267857142857143},
492
{0.259807621135332, 0, 0, -0.143747227124986, -0.10978875820671, 0, -0.122747563257746, 0, 0, 0.0425210032135381, 0, -0.095831484749991, 0, 0.0428571428571429, 0.0138320833793122, 0, 0.0154647393532935, 0, 0, -0.00535714285714284}};
493
494
// Interesting (new) part
495
// Tables of derivatives of the polynomial base (transpose)
496
const static double dmats0[20][20] = \
497
{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
498
{6.32455532033676, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
499
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
500
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
501
{0, 11.2249721603218, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
502
{4.58257569495584, 0, 8.36660026534076, -1.18321595661992, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
503
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
504
{3.74165738677394, 0, 0, 8.69482604771366, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
505
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
506
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
507
{5.49909083394702, 0, -3.3466401061363, -2.36643191323985, 15.4919333848297, 0, 0.692820323027552, 0, 0.565685424949239, 0.400000000000001, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
508
{0, 4.89897948556636, 0, 0, 0, 14.1985914794391, 0, -0.828078671210832, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
509
{3.6, 0, 8.76356092008266, -1.54919333848297, 0, 0, 9.52470471983253, 0, -1.48131215963608, 0.261861468283191, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
510
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
511
{0, 4.24264068711929, 0, 0, 0, 0, 0, 14.3427433120127, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
512
{3.11769145362398, 0, 3.16227766016838, 4.91934955049954, 0, 0, 0, 0, 10.690449676497, -2.41897262725906, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
513
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
514
{2.54558441227157, 0, 0, 7.66811580507233, 0, 0, 0, 0, 0, 10.3691851174526, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
515
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
516
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};
517
518
const static double dmats1[20][20] = \
519
{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
520
{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
521
{5.47722557505166, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
522
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
523
{2.9580398915498, 5.61248608016091, -1.08012344973464, -0.763762615825973, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
524
{2.29128784747791, 7.24568837309472, 4.18330013267038, -0.59160797830996, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
525
{-2.64575131106459, 0, 9.66091783079296, 0.683130051063974, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
526
{1.87082869338697, 0, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
527
{3.24037034920393, 0, 0, 7.52994023880668, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
528
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
529
{2.7495454169735, 5.79655069847578, -1.67332005306815, -1.18321595661992, 7.74596669241483, -1.2, 0.346410161513777, -0.979795897113271, 0.282842712474621, 0.2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
530
{2.32379000772445, 2.44948974278318, 2.82842712474619, -1, 9.16515138991168, 7.09929573971954, -2.04939015319192, -0.414039335605415, -0.478091443733757, 0.169030850945705, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
531
{1.80000000000001, -5.69209978830308, 4.38178046004132, -0.774596669241485, 0, 10.998181667894, 4.76235235991626, 0.962140470884726, -0.740656079818042, 0.130930734141596, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
532
{5.19615242270664, 0, -3.16227766016837, -2.23606797749979, 0, 0, 13.7477270848675, 0, 0.53452248382485, 0.377964473009228, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
533
{2.01246117974981, 2.12132034355964, -0.408248290463862, 3.17542648054294, 0, 0, 0, 7.17137165600636, -1.38013111868471, -1.56144011671765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
534
{1.55884572681199, 2.73861278752583, 1.58113883008419, 2.45967477524977, 0, 0, 0, 9.25820099772551, 5.34522483824849, -1.20948631362953, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
535
{-1.79999999999999, 0, 3.65148371670111, -2.84018778721878, 0, 0, 0, 0, 12.3442679969674, 1.39659449751035, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
536
{1.27279220613578, 0, 0, 3.83405790253616, 0, 0, 0, 0, 0, 5.18459255872629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
537
{2.20454076850486, 0, 0, 6.6407830863536, 0, 0, 0, 0, 0, 8.97997772825746, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
538
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};
539
540
const static double dmats2[20][20] = \
541
{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
542
{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
543
{1.82574185835055, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
544
{5.16397779494322, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
545
{2.9580398915498, 5.61248608016091, -1.08012344973464, -0.763762615825973, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
546
{2.29128784747792, 1.44913767461894, 4.18330013267038, -0.591607978309959, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
547
{1.32287565553229, 0, 3.86436713231718, -0.341565025531987, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
548
{1.87082869338696, 7.09929573971954, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
549
{1.08012344973464, 0, 7.09929573971954, 2.50998007960222, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
550
{-3.81881307912987, 0, 0, 8.87411967464942, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
551
{2.7495454169735, 5.79655069847578, -1.67332005306815, -1.18321595661992, 7.74596669241483, -1.19999999999999, 0.346410161513777, -0.979795897113271, 0.28284271247462, 0.2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
552
{2.32379000772445, 2.44948974278318, 2.82842712474619, -1, 1.30930734141595, 7.09929573971954, -2.04939015319192, -0.414039335605416, -0.478091443733756, 0.169030850945703, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
553
{1.8, 0.632455532033674, 4.38178046004133, -0.774596669241483, 0, 3.14233761939829, 4.76235235991626, -0.106904496764969, -0.740656079818041, 0.130930734141595, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
554
{1.03923048454133, 0, 3.16227766016838, -0.447213595499959, 0, 0, 5.8918830363718, 0, -0.53452248382485, 0.0755928946018456, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
555
{2.01246117974981, 2.12132034355965, -0.408248290463862, 3.17542648054294, 9.07114735222145, 0, 0, 7.17137165600636, -1.38013111868471, -1.56144011671765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
556
{1.55884572681199, 0.547722557505166, 1.58113883008419, 2.45967477524977, 0, 9.07114735222145, 0, 1.8516401995451, 5.34522483824849, -1.20948631362953, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
557
{0.9, 0, 1.46059348668044, 1.42009389360939, 0, 0, 9.07114735222146, 0, 4.93770719878694, -0.698297248755176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
558
{1.27279220613579, -6.26099033699941, 0, 3.83405790253616, 0, 0, 0, 10.5830052442584, 0, 5.18459255872629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
559
{0.734846922834956, 0, -6.26099033699941, 2.21359436211787, 0, 0, 0, 0, 10.5830052442584, 2.99332590941915, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
560
{5.7157676649773, 0, 0, -4.69574275274955, 0, 0, 0, 0, 0, 12.69960629311, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};
561
562
// Compute reference derivatives
563
// Declare pointer to array of derivatives on FIAT element
564
double *derivatives = new double [num_derivatives];
565
566
// Declare coefficients
567
double coeff0_0 = 0;
568
double coeff0_1 = 0;
569
double coeff0_2 = 0;
570
double coeff0_3 = 0;
571
double coeff0_4 = 0;
572
double coeff0_5 = 0;
573
double coeff0_6 = 0;
574
double coeff0_7 = 0;
575
double coeff0_8 = 0;
576
double coeff0_9 = 0;
577
double coeff0_10 = 0;
578
double coeff0_11 = 0;
579
double coeff0_12 = 0;
580
double coeff0_13 = 0;
581
double coeff0_14 = 0;
582
double coeff0_15 = 0;
583
double coeff0_16 = 0;
584
double coeff0_17 = 0;
585
double coeff0_18 = 0;
586
double coeff0_19 = 0;
587
588
// Declare new coefficients
589
double new_coeff0_0 = 0;
590
double new_coeff0_1 = 0;
591
double new_coeff0_2 = 0;
592
double new_coeff0_3 = 0;
593
double new_coeff0_4 = 0;
594
double new_coeff0_5 = 0;
595
double new_coeff0_6 = 0;
596
double new_coeff0_7 = 0;
597
double new_coeff0_8 = 0;
598
double new_coeff0_9 = 0;
599
double new_coeff0_10 = 0;
600
double new_coeff0_11 = 0;
601
double new_coeff0_12 = 0;
602
double new_coeff0_13 = 0;
603
double new_coeff0_14 = 0;
604
double new_coeff0_15 = 0;
605
double new_coeff0_16 = 0;
606
double new_coeff0_17 = 0;
607
double new_coeff0_18 = 0;
608
double new_coeff0_19 = 0;
609
610
// Loop possible derivatives
611
for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
612
{
613
// Get values from coefficients array
614
new_coeff0_0 = coefficients0[dof][0];
615
new_coeff0_1 = coefficients0[dof][1];
616
new_coeff0_2 = coefficients0[dof][2];
617
new_coeff0_3 = coefficients0[dof][3];
618
new_coeff0_4 = coefficients0[dof][4];
619
new_coeff0_5 = coefficients0[dof][5];
620
new_coeff0_6 = coefficients0[dof][6];
621
new_coeff0_7 = coefficients0[dof][7];
622
new_coeff0_8 = coefficients0[dof][8];
623
new_coeff0_9 = coefficients0[dof][9];
624
new_coeff0_10 = coefficients0[dof][10];
625
new_coeff0_11 = coefficients0[dof][11];
626
new_coeff0_12 = coefficients0[dof][12];
627
new_coeff0_13 = coefficients0[dof][13];
628
new_coeff0_14 = coefficients0[dof][14];
629
new_coeff0_15 = coefficients0[dof][15];
630
new_coeff0_16 = coefficients0[dof][16];
631
new_coeff0_17 = coefficients0[dof][17];
632
new_coeff0_18 = coefficients0[dof][18];
633
new_coeff0_19 = coefficients0[dof][19];
634
635
// Loop derivative order
636
for (unsigned int j = 0; j < n; j++)
637
{
638
// Update old coefficients
639
coeff0_0 = new_coeff0_0;
640
coeff0_1 = new_coeff0_1;
641
coeff0_2 = new_coeff0_2;
642
coeff0_3 = new_coeff0_3;
643
coeff0_4 = new_coeff0_4;
644
coeff0_5 = new_coeff0_5;
645
coeff0_6 = new_coeff0_6;
646
coeff0_7 = new_coeff0_7;
647
coeff0_8 = new_coeff0_8;
648
coeff0_9 = new_coeff0_9;
649
coeff0_10 = new_coeff0_10;
650
coeff0_11 = new_coeff0_11;
651
coeff0_12 = new_coeff0_12;
652
coeff0_13 = new_coeff0_13;
653
coeff0_14 = new_coeff0_14;
654
coeff0_15 = new_coeff0_15;
655
coeff0_16 = new_coeff0_16;
656
coeff0_17 = new_coeff0_17;
657
coeff0_18 = new_coeff0_18;
658
coeff0_19 = new_coeff0_19;
659
660
if(combinations[deriv_num][j] == 0)
661
{
662
new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0] + coeff0_3*dmats0[3][0] + coeff0_4*dmats0[4][0] + coeff0_5*dmats0[5][0] + coeff0_6*dmats0[6][0] + coeff0_7*dmats0[7][0] + coeff0_8*dmats0[8][0] + coeff0_9*dmats0[9][0] + coeff0_10*dmats0[10][0] + coeff0_11*dmats0[11][0] + coeff0_12*dmats0[12][0] + coeff0_13*dmats0[13][0] + coeff0_14*dmats0[14][0] + coeff0_15*dmats0[15][0] + coeff0_16*dmats0[16][0] + coeff0_17*dmats0[17][0] + coeff0_18*dmats0[18][0] + coeff0_19*dmats0[19][0];
663
new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1] + coeff0_3*dmats0[3][1] + coeff0_4*dmats0[4][1] + coeff0_5*dmats0[5][1] + coeff0_6*dmats0[6][1] + coeff0_7*dmats0[7][1] + coeff0_8*dmats0[8][1] + coeff0_9*dmats0[9][1] + coeff0_10*dmats0[10][1] + coeff0_11*dmats0[11][1] + coeff0_12*dmats0[12][1] + coeff0_13*dmats0[13][1] + coeff0_14*dmats0[14][1] + coeff0_15*dmats0[15][1] + coeff0_16*dmats0[16][1] + coeff0_17*dmats0[17][1] + coeff0_18*dmats0[18][1] + coeff0_19*dmats0[19][1];
664
new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2] + coeff0_3*dmats0[3][2] + coeff0_4*dmats0[4][2] + coeff0_5*dmats0[5][2] + coeff0_6*dmats0[6][2] + coeff0_7*dmats0[7][2] + coeff0_8*dmats0[8][2] + coeff0_9*dmats0[9][2] + coeff0_10*dmats0[10][2] + coeff0_11*dmats0[11][2] + coeff0_12*dmats0[12][2] + coeff0_13*dmats0[13][2] + coeff0_14*dmats0[14][2] + coeff0_15*dmats0[15][2] + coeff0_16*dmats0[16][2] + coeff0_17*dmats0[17][2] + coeff0_18*dmats0[18][2] + coeff0_19*dmats0[19][2];
665
new_coeff0_3 = coeff0_0*dmats0[0][3] + coeff0_1*dmats0[1][3] + coeff0_2*dmats0[2][3] + coeff0_3*dmats0[3][3] + coeff0_4*dmats0[4][3] + coeff0_5*dmats0[5][3] + coeff0_6*dmats0[6][3] + coeff0_7*dmats0[7][3] + coeff0_8*dmats0[8][3] + coeff0_9*dmats0[9][3] + coeff0_10*dmats0[10][3] + coeff0_11*dmats0[11][3] + coeff0_12*dmats0[12][3] + coeff0_13*dmats0[13][3] + coeff0_14*dmats0[14][3] + coeff0_15*dmats0[15][3] + coeff0_16*dmats0[16][3] + coeff0_17*dmats0[17][3] + coeff0_18*dmats0[18][3] + coeff0_19*dmats0[19][3];
666
new_coeff0_4 = coeff0_0*dmats0[0][4] + coeff0_1*dmats0[1][4] + coeff0_2*dmats0[2][4] + coeff0_3*dmats0[3][4] + coeff0_4*dmats0[4][4] + coeff0_5*dmats0[5][4] + coeff0_6*dmats0[6][4] + coeff0_7*dmats0[7][4] + coeff0_8*dmats0[8][4] + coeff0_9*dmats0[9][4] + coeff0_10*dmats0[10][4] + coeff0_11*dmats0[11][4] + coeff0_12*dmats0[12][4] + coeff0_13*dmats0[13][4] + coeff0_14*dmats0[14][4] + coeff0_15*dmats0[15][4] + coeff0_16*dmats0[16][4] + coeff0_17*dmats0[17][4] + coeff0_18*dmats0[18][4] + coeff0_19*dmats0[19][4];
667
new_coeff0_5 = coeff0_0*dmats0[0][5] + coeff0_1*dmats0[1][5] + coeff0_2*dmats0[2][5] + coeff0_3*dmats0[3][5] + coeff0_4*dmats0[4][5] + coeff0_5*dmats0[5][5] + coeff0_6*dmats0[6][5] + coeff0_7*dmats0[7][5] + coeff0_8*dmats0[8][5] + coeff0_9*dmats0[9][5] + coeff0_10*dmats0[10][5] + coeff0_11*dmats0[11][5] + coeff0_12*dmats0[12][5] + coeff0_13*dmats0[13][5] + coeff0_14*dmats0[14][5] + coeff0_15*dmats0[15][5] + coeff0_16*dmats0[16][5] + coeff0_17*dmats0[17][5] + coeff0_18*dmats0[18][5] + coeff0_19*dmats0[19][5];
668
new_coeff0_6 = coeff0_0*dmats0[0][6] + coeff0_1*dmats0[1][6] + coeff0_2*dmats0[2][6] + coeff0_3*dmats0[3][6] + coeff0_4*dmats0[4][6] + coeff0_5*dmats0[5][6] + coeff0_6*dmats0[6][6] + coeff0_7*dmats0[7][6] + coeff0_8*dmats0[8][6] + coeff0_9*dmats0[9][6] + coeff0_10*dmats0[10][6] + coeff0_11*dmats0[11][6] + coeff0_12*dmats0[12][6] + coeff0_13*dmats0[13][6] + coeff0_14*dmats0[14][6] + coeff0_15*dmats0[15][6] + coeff0_16*dmats0[16][6] + coeff0_17*dmats0[17][6] + coeff0_18*dmats0[18][6] + coeff0_19*dmats0[19][6];
669
new_coeff0_7 = coeff0_0*dmats0[0][7] + coeff0_1*dmats0[1][7] + coeff0_2*dmats0[2][7] + coeff0_3*dmats0[3][7] + coeff0_4*dmats0[4][7] + coeff0_5*dmats0[5][7] + coeff0_6*dmats0[6][7] + coeff0_7*dmats0[7][7] + coeff0_8*dmats0[8][7] + coeff0_9*dmats0[9][7] + coeff0_10*dmats0[10][7] + coeff0_11*dmats0[11][7] + coeff0_12*dmats0[12][7] + coeff0_13*dmats0[13][7] + coeff0_14*dmats0[14][7] + coeff0_15*dmats0[15][7] + coeff0_16*dmats0[16][7] + coeff0_17*dmats0[17][7] + coeff0_18*dmats0[18][7] + coeff0_19*dmats0[19][7];
670
new_coeff0_8 = coeff0_0*dmats0[0][8] + coeff0_1*dmats0[1][8] + coeff0_2*dmats0[2][8] + coeff0_3*dmats0[3][8] + coeff0_4*dmats0[4][8] + coeff0_5*dmats0[5][8] + coeff0_6*dmats0[6][8] + coeff0_7*dmats0[7][8] + coeff0_8*dmats0[8][8] + coeff0_9*dmats0[9][8] + coeff0_10*dmats0[10][8] + coeff0_11*dmats0[11][8] + coeff0_12*dmats0[12][8] + coeff0_13*dmats0[13][8] + coeff0_14*dmats0[14][8] + coeff0_15*dmats0[15][8] + coeff0_16*dmats0[16][8] + coeff0_17*dmats0[17][8] + coeff0_18*dmats0[18][8] + coeff0_19*dmats0[19][8];
671
new_coeff0_9 = coeff0_0*dmats0[0][9] + coeff0_1*dmats0[1][9] + coeff0_2*dmats0[2][9] + coeff0_3*dmats0[3][9] + coeff0_4*dmats0[4][9] + coeff0_5*dmats0[5][9] + coeff0_6*dmats0[6][9] + coeff0_7*dmats0[7][9] + coeff0_8*dmats0[8][9] + coeff0_9*dmats0[9][9] + coeff0_10*dmats0[10][9] + coeff0_11*dmats0[11][9] + coeff0_12*dmats0[12][9] + coeff0_13*dmats0[13][9] + coeff0_14*dmats0[14][9] + coeff0_15*dmats0[15][9] + coeff0_16*dmats0[16][9] + coeff0_17*dmats0[17][9] + coeff0_18*dmats0[18][9] + coeff0_19*dmats0[19][9];
672
new_coeff0_10 = coeff0_0*dmats0[0][10] + coeff0_1*dmats0[1][10] + coeff0_2*dmats0[2][10] + coeff0_3*dmats0[3][10] + coeff0_4*dmats0[4][10] + coeff0_5*dmats0[5][10] + coeff0_6*dmats0[6][10] + coeff0_7*dmats0[7][10] + coeff0_8*dmats0[8][10] + coeff0_9*dmats0[9][10] + coeff0_10*dmats0[10][10] + coeff0_11*dmats0[11][10] + coeff0_12*dmats0[12][10] + coeff0_13*dmats0[13][10] + coeff0_14*dmats0[14][10] + coeff0_15*dmats0[15][10] + coeff0_16*dmats0[16][10] + coeff0_17*dmats0[17][10] + coeff0_18*dmats0[18][10] + coeff0_19*dmats0[19][10];
673
new_coeff0_11 = coeff0_0*dmats0[0][11] + coeff0_1*dmats0[1][11] + coeff0_2*dmats0[2][11] + coeff0_3*dmats0[3][11] + coeff0_4*dmats0[4][11] + coeff0_5*dmats0[5][11] + coeff0_6*dmats0[6][11] + coeff0_7*dmats0[7][11] + coeff0_8*dmats0[8][11] + coeff0_9*dmats0[9][11] + coeff0_10*dmats0[10][11] + coeff0_11*dmats0[11][11] + coeff0_12*dmats0[12][11] + coeff0_13*dmats0[13][11] + coeff0_14*dmats0[14][11] + coeff0_15*dmats0[15][11] + coeff0_16*dmats0[16][11] + coeff0_17*dmats0[17][11] + coeff0_18*dmats0[18][11] + coeff0_19*dmats0[19][11];
674
new_coeff0_12 = coeff0_0*dmats0[0][12] + coeff0_1*dmats0[1][12] + coeff0_2*dmats0[2][12] + coeff0_3*dmats0[3][12] + coeff0_4*dmats0[4][12] + coeff0_5*dmats0[5][12] + coeff0_6*dmats0[6][12] + coeff0_7*dmats0[7][12] + coeff0_8*dmats0[8][12] + coeff0_9*dmats0[9][12] + coeff0_10*dmats0[10][12] + coeff0_11*dmats0[11][12] + coeff0_12*dmats0[12][12] + coeff0_13*dmats0[13][12] + coeff0_14*dmats0[14][12] + coeff0_15*dmats0[15][12] + coeff0_16*dmats0[16][12] + coeff0_17*dmats0[17][12] + coeff0_18*dmats0[18][12] + coeff0_19*dmats0[19][12];
675
new_coeff0_13 = coeff0_0*dmats0[0][13] + coeff0_1*dmats0[1][13] + coeff0_2*dmats0[2][13] + coeff0_3*dmats0[3][13] + coeff0_4*dmats0[4][13] + coeff0_5*dmats0[5][13] + coeff0_6*dmats0[6][13] + coeff0_7*dmats0[7][13] + coeff0_8*dmats0[8][13] + coeff0_9*dmats0[9][13] + coeff0_10*dmats0[10][13] + coeff0_11*dmats0[11][13] + coeff0_12*dmats0[12][13] + coeff0_13*dmats0[13][13] + coeff0_14*dmats0[14][13] + coeff0_15*dmats0[15][13] + coeff0_16*dmats0[16][13] + coeff0_17*dmats0[17][13] + coeff0_18*dmats0[18][13] + coeff0_19*dmats0[19][13];
676
new_coeff0_14 = coeff0_0*dmats0[0][14] + coeff0_1*dmats0[1][14] + coeff0_2*dmats0[2][14] + coeff0_3*dmats0[3][14] + coeff0_4*dmats0[4][14] + coeff0_5*dmats0[5][14] + coeff0_6*dmats0[6][14] + coeff0_7*dmats0[7][14] + coeff0_8*dmats0[8][14] + coeff0_9*dmats0[9][14] + coeff0_10*dmats0[10][14] + coeff0_11*dmats0[11][14] + coeff0_12*dmats0[12][14] + coeff0_13*dmats0[13][14] + coeff0_14*dmats0[14][14] + coeff0_15*dmats0[15][14] + coeff0_16*dmats0[16][14] + coeff0_17*dmats0[17][14] + coeff0_18*dmats0[18][14] + coeff0_19*dmats0[19][14];
677
new_coeff0_15 = coeff0_0*dmats0[0][15] + coeff0_1*dmats0[1][15] + coeff0_2*dmats0[2][15] + coeff0_3*dmats0[3][15] + coeff0_4*dmats0[4][15] + coeff0_5*dmats0[5][15] + coeff0_6*dmats0[6][15] + coeff0_7*dmats0[7][15] + coeff0_8*dmats0[8][15] + coeff0_9*dmats0[9][15] + coeff0_10*dmats0[10][15] + coeff0_11*dmats0[11][15] + coeff0_12*dmats0[12][15] + coeff0_13*dmats0[13][15] + coeff0_14*dmats0[14][15] + coeff0_15*dmats0[15][15] + coeff0_16*dmats0[16][15] + coeff0_17*dmats0[17][15] + coeff0_18*dmats0[18][15] + coeff0_19*dmats0[19][15];
678
new_coeff0_16 = coeff0_0*dmats0[0][16] + coeff0_1*dmats0[1][16] + coeff0_2*dmats0[2][16] + coeff0_3*dmats0[3][16] + coeff0_4*dmats0[4][16] + coeff0_5*dmats0[5][16] + coeff0_6*dmats0[6][16] + coeff0_7*dmats0[7][16] + coeff0_8*dmats0[8][16] + coeff0_9*dmats0[9][16] + coeff0_10*dmats0[10][16] + coeff0_11*dmats0[11][16] + coeff0_12*dmats0[12][16] + coeff0_13*dmats0[13][16] + coeff0_14*dmats0[14][16] + coeff0_15*dmats0[15][16] + coeff0_16*dmats0[16][16] + coeff0_17*dmats0[17][16] + coeff0_18*dmats0[18][16] + coeff0_19*dmats0[19][16];
679
new_coeff0_17 = coeff0_0*dmats0[0][17] + coeff0_1*dmats0[1][17] + coeff0_2*dmats0[2][17] + coeff0_3*dmats0[3][17] + coeff0_4*dmats0[4][17] + coeff0_5*dmats0[5][17] + coeff0_6*dmats0[6][17] + coeff0_7*dmats0[7][17] + coeff0_8*dmats0[8][17] + coeff0_9*dmats0[9][17] + coeff0_10*dmats0[10][17] + coeff0_11*dmats0[11][17] + coeff0_12*dmats0[12][17] + coeff0_13*dmats0[13][17] + coeff0_14*dmats0[14][17] + coeff0_15*dmats0[15][17] + coeff0_16*dmats0[16][17] + coeff0_17*dmats0[17][17] + coeff0_18*dmats0[18][17] + coeff0_19*dmats0[19][17];
680
new_coeff0_18 = coeff0_0*dmats0[0][18] + coeff0_1*dmats0[1][18] + coeff0_2*dmats0[2][18] + coeff0_3*dmats0[3][18] + coeff0_4*dmats0[4][18] + coeff0_5*dmats0[5][18] + coeff0_6*dmats0[6][18] + coeff0_7*dmats0[7][18] + coeff0_8*dmats0[8][18] + coeff0_9*dmats0[9][18] + coeff0_10*dmats0[10][18] + coeff0_11*dmats0[11][18] + coeff0_12*dmats0[12][18] + coeff0_13*dmats0[13][18] + coeff0_14*dmats0[14][18] + coeff0_15*dmats0[15][18] + coeff0_16*dmats0[16][18] + coeff0_17*dmats0[17][18] + coeff0_18*dmats0[18][18] + coeff0_19*dmats0[19][18];
681
new_coeff0_19 = coeff0_0*dmats0[0][19] + coeff0_1*dmats0[1][19] + coeff0_2*dmats0[2][19] + coeff0_3*dmats0[3][19] + coeff0_4*dmats0[4][19] + coeff0_5*dmats0[5][19] + coeff0_6*dmats0[6][19] + coeff0_7*dmats0[7][19] + coeff0_8*dmats0[8][19] + coeff0_9*dmats0[9][19] + coeff0_10*dmats0[10][19] + coeff0_11*dmats0[11][19] + coeff0_12*dmats0[12][19] + coeff0_13*dmats0[13][19] + coeff0_14*dmats0[14][19] + coeff0_15*dmats0[15][19] + coeff0_16*dmats0[16][19] + coeff0_17*dmats0[17][19] + coeff0_18*dmats0[18][19] + coeff0_19*dmats0[19][19];
682
}
683
if(combinations[deriv_num][j] == 1)
684
{
685
new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0] + coeff0_3*dmats1[3][0] + coeff0_4*dmats1[4][0] + coeff0_5*dmats1[5][0] + coeff0_6*dmats1[6][0] + coeff0_7*dmats1[7][0] + coeff0_8*dmats1[8][0] + coeff0_9*dmats1[9][0] + coeff0_10*dmats1[10][0] + coeff0_11*dmats1[11][0] + coeff0_12*dmats1[12][0] + coeff0_13*dmats1[13][0] + coeff0_14*dmats1[14][0] + coeff0_15*dmats1[15][0] + coeff0_16*dmats1[16][0] + coeff0_17*dmats1[17][0] + coeff0_18*dmats1[18][0] + coeff0_19*dmats1[19][0];
686
new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1] + coeff0_3*dmats1[3][1] + coeff0_4*dmats1[4][1] + coeff0_5*dmats1[5][1] + coeff0_6*dmats1[6][1] + coeff0_7*dmats1[7][1] + coeff0_8*dmats1[8][1] + coeff0_9*dmats1[9][1] + coeff0_10*dmats1[10][1] + coeff0_11*dmats1[11][1] + coeff0_12*dmats1[12][1] + coeff0_13*dmats1[13][1] + coeff0_14*dmats1[14][1] + coeff0_15*dmats1[15][1] + coeff0_16*dmats1[16][1] + coeff0_17*dmats1[17][1] + coeff0_18*dmats1[18][1] + coeff0_19*dmats1[19][1];
687
new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2] + coeff0_3*dmats1[3][2] + coeff0_4*dmats1[4][2] + coeff0_5*dmats1[5][2] + coeff0_6*dmats1[6][2] + coeff0_7*dmats1[7][2] + coeff0_8*dmats1[8][2] + coeff0_9*dmats1[9][2] + coeff0_10*dmats1[10][2] + coeff0_11*dmats1[11][2] + coeff0_12*dmats1[12][2] + coeff0_13*dmats1[13][2] + coeff0_14*dmats1[14][2] + coeff0_15*dmats1[15][2] + coeff0_16*dmats1[16][2] + coeff0_17*dmats1[17][2] + coeff0_18*dmats1[18][2] + coeff0_19*dmats1[19][2];
688
new_coeff0_3 = coeff0_0*dmats1[0][3] + coeff0_1*dmats1[1][3] + coeff0_2*dmats1[2][3] + coeff0_3*dmats1[3][3] + coeff0_4*dmats1[4][3] + coeff0_5*dmats1[5][3] + coeff0_6*dmats1[6][3] + coeff0_7*dmats1[7][3] + coeff0_8*dmats1[8][3] + coeff0_9*dmats1[9][3] + coeff0_10*dmats1[10][3] + coeff0_11*dmats1[11][3] + coeff0_12*dmats1[12][3] + coeff0_13*dmats1[13][3] + coeff0_14*dmats1[14][3] + coeff0_15*dmats1[15][3] + coeff0_16*dmats1[16][3] + coeff0_17*dmats1[17][3] + coeff0_18*dmats1[18][3] + coeff0_19*dmats1[19][3];
689
new_coeff0_4 = coeff0_0*dmats1[0][4] + coeff0_1*dmats1[1][4] + coeff0_2*dmats1[2][4] + coeff0_3*dmats1[3][4] + coeff0_4*dmats1[4][4] + coeff0_5*dmats1[5][4] + coeff0_6*dmats1[6][4] + coeff0_7*dmats1[7][4] + coeff0_8*dmats1[8][4] + coeff0_9*dmats1[9][4] + coeff0_10*dmats1[10][4] + coeff0_11*dmats1[11][4] + coeff0_12*dmats1[12][4] + coeff0_13*dmats1[13][4] + coeff0_14*dmats1[14][4] + coeff0_15*dmats1[15][4] + coeff0_16*dmats1[16][4] + coeff0_17*dmats1[17][4] + coeff0_18*dmats1[18][4] + coeff0_19*dmats1[19][4];
690
new_coeff0_5 = coeff0_0*dmats1[0][5] + coeff0_1*dmats1[1][5] + coeff0_2*dmats1[2][5] + coeff0_3*dmats1[3][5] + coeff0_4*dmats1[4][5] + coeff0_5*dmats1[5][5] + coeff0_6*dmats1[6][5] + coeff0_7*dmats1[7][5] + coeff0_8*dmats1[8][5] + coeff0_9*dmats1[9][5] + coeff0_10*dmats1[10][5] + coeff0_11*dmats1[11][5] + coeff0_12*dmats1[12][5] + coeff0_13*dmats1[13][5] + coeff0_14*dmats1[14][5] + coeff0_15*dmats1[15][5] + coeff0_16*dmats1[16][5] + coeff0_17*dmats1[17][5] + coeff0_18*dmats1[18][5] + coeff0_19*dmats1[19][5];
691
new_coeff0_6 = coeff0_0*dmats1[0][6] + coeff0_1*dmats1[1][6] + coeff0_2*dmats1[2][6] + coeff0_3*dmats1[3][6] + coeff0_4*dmats1[4][6] + coeff0_5*dmats1[5][6] + coeff0_6*dmats1[6][6] + coeff0_7*dmats1[7][6] + coeff0_8*dmats1[8][6] + coeff0_9*dmats1[9][6] + coeff0_10*dmats1[10][6] + coeff0_11*dmats1[11][6] + coeff0_12*dmats1[12][6] + coeff0_13*dmats1[13][6] + coeff0_14*dmats1[14][6] + coeff0_15*dmats1[15][6] + coeff0_16*dmats1[16][6] + coeff0_17*dmats1[17][6] + coeff0_18*dmats1[18][6] + coeff0_19*dmats1[19][6];
692
new_coeff0_7 = coeff0_0*dmats1[0][7] + coeff0_1*dmats1[1][7] + coeff0_2*dmats1[2][7] + coeff0_3*dmats1[3][7] + coeff0_4*dmats1[4][7] + coeff0_5*dmats1[5][7] + coeff0_6*dmats1[6][7] + coeff0_7*dmats1[7][7] + coeff0_8*dmats1[8][7] + coeff0_9*dmats1[9][7] + coeff0_10*dmats1[10][7] + coeff0_11*dmats1[11][7] + coeff0_12*dmats1[12][7] + coeff0_13*dmats1[13][7] + coeff0_14*dmats1[14][7] + coeff0_15*dmats1[15][7] + coeff0_16*dmats1[16][7] + coeff0_17*dmats1[17][7] + coeff0_18*dmats1[18][7] + coeff0_19*dmats1[19][7];
693
new_coeff0_8 = coeff0_0*dmats1[0][8] + coeff0_1*dmats1[1][8] + coeff0_2*dmats1[2][8] + coeff0_3*dmats1[3][8] + coeff0_4*dmats1[4][8] + coeff0_5*dmats1[5][8] + coeff0_6*dmats1[6][8] + coeff0_7*dmats1[7][8] + coeff0_8*dmats1[8][8] + coeff0_9*dmats1[9][8] + coeff0_10*dmats1[10][8] + coeff0_11*dmats1[11][8] + coeff0_12*dmats1[12][8] + coeff0_13*dmats1[13][8] + coeff0_14*dmats1[14][8] + coeff0_15*dmats1[15][8] + coeff0_16*dmats1[16][8] + coeff0_17*dmats1[17][8] + coeff0_18*dmats1[18][8] + coeff0_19*dmats1[19][8];
694
new_coeff0_9 = coeff0_0*dmats1[0][9] + coeff0_1*dmats1[1][9] + coeff0_2*dmats1[2][9] + coeff0_3*dmats1[3][9] + coeff0_4*dmats1[4][9] + coeff0_5*dmats1[5][9] + coeff0_6*dmats1[6][9] + coeff0_7*dmats1[7][9] + coeff0_8*dmats1[8][9] + coeff0_9*dmats1[9][9] + coeff0_10*dmats1[10][9] + coeff0_11*dmats1[11][9] + coeff0_12*dmats1[12][9] + coeff0_13*dmats1[13][9] + coeff0_14*dmats1[14][9] + coeff0_15*dmats1[15][9] + coeff0_16*dmats1[16][9] + coeff0_17*dmats1[17][9] + coeff0_18*dmats1[18][9] + coeff0_19*dmats1[19][9];
695
new_coeff0_10 = coeff0_0*dmats1[0][10] + coeff0_1*dmats1[1][10] + coeff0_2*dmats1[2][10] + coeff0_3*dmats1[3][10] + coeff0_4*dmats1[4][10] + coeff0_5*dmats1[5][10] + coeff0_6*dmats1[6][10] + coeff0_7*dmats1[7][10] + coeff0_8*dmats1[8][10] + coeff0_9*dmats1[9][10] + coeff0_10*dmats1[10][10] + coeff0_11*dmats1[11][10] + coeff0_12*dmats1[12][10] + coeff0_13*dmats1[13][10] + coeff0_14*dmats1[14][10] + coeff0_15*dmats1[15][10] + coeff0_16*dmats1[16][10] + coeff0_17*dmats1[17][10] + coeff0_18*dmats1[18][10] + coeff0_19*dmats1[19][10];
696
new_coeff0_11 = coeff0_0*dmats1[0][11] + coeff0_1*dmats1[1][11] + coeff0_2*dmats1[2][11] + coeff0_3*dmats1[3][11] + coeff0_4*dmats1[4][11] + coeff0_5*dmats1[5][11] + coeff0_6*dmats1[6][11] + coeff0_7*dmats1[7][11] + coeff0_8*dmats1[8][11] + coeff0_9*dmats1[9][11] + coeff0_10*dmats1[10][11] + coeff0_11*dmats1[11][11] + coeff0_12*dmats1[12][11] + coeff0_13*dmats1[13][11] + coeff0_14*dmats1[14][11] + coeff0_15*dmats1[15][11] + coeff0_16*dmats1[16][11] + coeff0_17*dmats1[17][11] + coeff0_18*dmats1[18][11] + coeff0_19*dmats1[19][11];
697
new_coeff0_12 = coeff0_0*dmats1[0][12] + coeff0_1*dmats1[1][12] + coeff0_2*dmats1[2][12] + coeff0_3*dmats1[3][12] + coeff0_4*dmats1[4][12] + coeff0_5*dmats1[5][12] + coeff0_6*dmats1[6][12] + coeff0_7*dmats1[7][12] + coeff0_8*dmats1[8][12] + coeff0_9*dmats1[9][12] + coeff0_10*dmats1[10][12] + coeff0_11*dmats1[11][12] + coeff0_12*dmats1[12][12] + coeff0_13*dmats1[13][12] + coeff0_14*dmats1[14][12] + coeff0_15*dmats1[15][12] + coeff0_16*dmats1[16][12] + coeff0_17*dmats1[17][12] + coeff0_18*dmats1[18][12] + coeff0_19*dmats1[19][12];
698
new_coeff0_13 = coeff0_0*dmats1[0][13] + coeff0_1*dmats1[1][13] + coeff0_2*dmats1[2][13] + coeff0_3*dmats1[3][13] + coeff0_4*dmats1[4][13] + coeff0_5*dmats1[5][13] + coeff0_6*dmats1[6][13] + coeff0_7*dmats1[7][13] + coeff0_8*dmats1[8][13] + coeff0_9*dmats1[9][13] + coeff0_10*dmats1[10][13] + coeff0_11*dmats1[11][13] + coeff0_12*dmats1[12][13] + coeff0_13*dmats1[13][13] + coeff0_14*dmats1[14][13] + coeff0_15*dmats1[15][13] + coeff0_16*dmats1[16][13] + coeff0_17*dmats1[17][13] + coeff0_18*dmats1[18][13] + coeff0_19*dmats1[19][13];
699
new_coeff0_14 = coeff0_0*dmats1[0][14] + coeff0_1*dmats1[1][14] + coeff0_2*dmats1[2][14] + coeff0_3*dmats1[3][14] + coeff0_4*dmats1[4][14] + coeff0_5*dmats1[5][14] + coeff0_6*dmats1[6][14] + coeff0_7*dmats1[7][14] + coeff0_8*dmats1[8][14] + coeff0_9*dmats1[9][14] + coeff0_10*dmats1[10][14] + coeff0_11*dmats1[11][14] + coeff0_12*dmats1[12][14] + coeff0_13*dmats1[13][14] + coeff0_14*dmats1[14][14] + coeff0_15*dmats1[15][14] + coeff0_16*dmats1[16][14] + coeff0_17*dmats1[17][14] + coeff0_18*dmats1[18][14] + coeff0_19*dmats1[19][14];
700
new_coeff0_15 = coeff0_0*dmats1[0][15] + coeff0_1*dmats1[1][15] + coeff0_2*dmats1[2][15] + coeff0_3*dmats1[3][15] + coeff0_4*dmats1[4][15] + coeff0_5*dmats1[5][15] + coeff0_6*dmats1[6][15] + coeff0_7*dmats1[7][15] + coeff0_8*dmats1[8][15] + coeff0_9*dmats1[9][15] + coeff0_10*dmats1[10][15] + coeff0_11*dmats1[11][15] + coeff0_12*dmats1[12][15] + coeff0_13*dmats1[13][15] + coeff0_14*dmats1[14][15] + coeff0_15*dmats1[15][15] + coeff0_16*dmats1[16][15] + coeff0_17*dmats1[17][15] + coeff0_18*dmats1[18][15] + coeff0_19*dmats1[19][15];
701
new_coeff0_16 = coeff0_0*dmats1[0][16] + coeff0_1*dmats1[1][16] + coeff0_2*dmats1[2][16] + coeff0_3*dmats1[3][16] + coeff0_4*dmats1[4][16] + coeff0_5*dmats1[5][16] + coeff0_6*dmats1[6][16] + coeff0_7*dmats1[7][16] + coeff0_8*dmats1[8][16] + coeff0_9*dmats1[9][16] + coeff0_10*dmats1[10][16] + coeff0_11*dmats1[11][16] + coeff0_12*dmats1[12][16] + coeff0_13*dmats1[13][16] + coeff0_14*dmats1[14][16] + coeff0_15*dmats1[15][16] + coeff0_16*dmats1[16][16] + coeff0_17*dmats1[17][16] + coeff0_18*dmats1[18][16] + coeff0_19*dmats1[19][16];
702
new_coeff0_17 = coeff0_0*dmats1[0][17] + coeff0_1*dmats1[1][17] + coeff0_2*dmats1[2][17] + coeff0_3*dmats1[3][17] + coeff0_4*dmats1[4][17] + coeff0_5*dmats1[5][17] + coeff0_6*dmats1[6][17] + coeff0_7*dmats1[7][17] + coeff0_8*dmats1[8][17] + coeff0_9*dmats1[9][17] + coeff0_10*dmats1[10][17] + coeff0_11*dmats1[11][17] + coeff0_12*dmats1[12][17] + coeff0_13*dmats1[13][17] + coeff0_14*dmats1[14][17] + coeff0_15*dmats1[15][17] + coeff0_16*dmats1[16][17] + coeff0_17*dmats1[17][17] + coeff0_18*dmats1[18][17] + coeff0_19*dmats1[19][17];
703
new_coeff0_18 = coeff0_0*dmats1[0][18] + coeff0_1*dmats1[1][18] + coeff0_2*dmats1[2][18] + coeff0_3*dmats1[3][18] + coeff0_4*dmats1[4][18] + coeff0_5*dmats1[5][18] + coeff0_6*dmats1[6][18] + coeff0_7*dmats1[7][18] + coeff0_8*dmats1[8][18] + coeff0_9*dmats1[9][18] + coeff0_10*dmats1[10][18] + coeff0_11*dmats1[11][18] + coeff0_12*dmats1[12][18] + coeff0_13*dmats1[13][18] + coeff0_14*dmats1[14][18] + coeff0_15*dmats1[15][18] + coeff0_16*dmats1[16][18] + coeff0_17*dmats1[17][18] + coeff0_18*dmats1[18][18] + coeff0_19*dmats1[19][18];
704
new_coeff0_19 = coeff0_0*dmats1[0][19] + coeff0_1*dmats1[1][19] + coeff0_2*dmats1[2][19] + coeff0_3*dmats1[3][19] + coeff0_4*dmats1[4][19] + coeff0_5*dmats1[5][19] + coeff0_6*dmats1[6][19] + coeff0_7*dmats1[7][19] + coeff0_8*dmats1[8][19] + coeff0_9*dmats1[9][19] + coeff0_10*dmats1[10][19] + coeff0_11*dmats1[11][19] + coeff0_12*dmats1[12][19] + coeff0_13*dmats1[13][19] + coeff0_14*dmats1[14][19] + coeff0_15*dmats1[15][19] + coeff0_16*dmats1[16][19] + coeff0_17*dmats1[17][19] + coeff0_18*dmats1[18][19] + coeff0_19*dmats1[19][19];
705
}
706
if(combinations[deriv_num][j] == 2)
707
{
708
new_coeff0_0 = coeff0_0*dmats2[0][0] + coeff0_1*dmats2[1][0] + coeff0_2*dmats2[2][0] + coeff0_3*dmats2[3][0] + coeff0_4*dmats2[4][0] + coeff0_5*dmats2[5][0] + coeff0_6*dmats2[6][0] + coeff0_7*dmats2[7][0] + coeff0_8*dmats2[8][0] + coeff0_9*dmats2[9][0] + coeff0_10*dmats2[10][0] + coeff0_11*dmats2[11][0] + coeff0_12*dmats2[12][0] + coeff0_13*dmats2[13][0] + coeff0_14*dmats2[14][0] + coeff0_15*dmats2[15][0] + coeff0_16*dmats2[16][0] + coeff0_17*dmats2[17][0] + coeff0_18*dmats2[18][0] + coeff0_19*dmats2[19][0];
709
new_coeff0_1 = coeff0_0*dmats2[0][1] + coeff0_1*dmats2[1][1] + coeff0_2*dmats2[2][1] + coeff0_3*dmats2[3][1] + coeff0_4*dmats2[4][1] + coeff0_5*dmats2[5][1] + coeff0_6*dmats2[6][1] + coeff0_7*dmats2[7][1] + coeff0_8*dmats2[8][1] + coeff0_9*dmats2[9][1] + coeff0_10*dmats2[10][1] + coeff0_11*dmats2[11][1] + coeff0_12*dmats2[12][1] + coeff0_13*dmats2[13][1] + coeff0_14*dmats2[14][1] + coeff0_15*dmats2[15][1] + coeff0_16*dmats2[16][1] + coeff0_17*dmats2[17][1] + coeff0_18*dmats2[18][1] + coeff0_19*dmats2[19][1];
710
new_coeff0_2 = coeff0_0*dmats2[0][2] + coeff0_1*dmats2[1][2] + coeff0_2*dmats2[2][2] + coeff0_3*dmats2[3][2] + coeff0_4*dmats2[4][2] + coeff0_5*dmats2[5][2] + coeff0_6*dmats2[6][2] + coeff0_7*dmats2[7][2] + coeff0_8*dmats2[8][2] + coeff0_9*dmats2[9][2] + coeff0_10*dmats2[10][2] + coeff0_11*dmats2[11][2] + coeff0_12*dmats2[12][2] + coeff0_13*dmats2[13][2] + coeff0_14*dmats2[14][2] + coeff0_15*dmats2[15][2] + coeff0_16*dmats2[16][2] + coeff0_17*dmats2[17][2] + coeff0_18*dmats2[18][2] + coeff0_19*dmats2[19][2];
711
new_coeff0_3 = coeff0_0*dmats2[0][3] + coeff0_1*dmats2[1][3] + coeff0_2*dmats2[2][3] + coeff0_3*dmats2[3][3] + coeff0_4*dmats2[4][3] + coeff0_5*dmats2[5][3] + coeff0_6*dmats2[6][3] + coeff0_7*dmats2[7][3] + coeff0_8*dmats2[8][3] + coeff0_9*dmats2[9][3] + coeff0_10*dmats2[10][3] + coeff0_11*dmats2[11][3] + coeff0_12*dmats2[12][3] + coeff0_13*dmats2[13][3] + coeff0_14*dmats2[14][3] + coeff0_15*dmats2[15][3] + coeff0_16*dmats2[16][3] + coeff0_17*dmats2[17][3] + coeff0_18*dmats2[18][3] + coeff0_19*dmats2[19][3];
712
new_coeff0_4 = coeff0_0*dmats2[0][4] + coeff0_1*dmats2[1][4] + coeff0_2*dmats2[2][4] + coeff0_3*dmats2[3][4] + coeff0_4*dmats2[4][4] + coeff0_5*dmats2[5][4] + coeff0_6*dmats2[6][4] + coeff0_7*dmats2[7][4] + coeff0_8*dmats2[8][4] + coeff0_9*dmats2[9][4] + coeff0_10*dmats2[10][4] + coeff0_11*dmats2[11][4] + coeff0_12*dmats2[12][4] + coeff0_13*dmats2[13][4] + coeff0_14*dmats2[14][4] + coeff0_15*dmats2[15][4] + coeff0_16*dmats2[16][4] + coeff0_17*dmats2[17][4] + coeff0_18*dmats2[18][4] + coeff0_19*dmats2[19][4];
713
new_coeff0_5 = coeff0_0*dmats2[0][5] + coeff0_1*dmats2[1][5] + coeff0_2*dmats2[2][5] + coeff0_3*dmats2[3][5] + coeff0_4*dmats2[4][5] + coeff0_5*dmats2[5][5] + coeff0_6*dmats2[6][5] + coeff0_7*dmats2[7][5] + coeff0_8*dmats2[8][5] + coeff0_9*dmats2[9][5] + coeff0_10*dmats2[10][5] + coeff0_11*dmats2[11][5] + coeff0_12*dmats2[12][5] + coeff0_13*dmats2[13][5] + coeff0_14*dmats2[14][5] + coeff0_15*dmats2[15][5] + coeff0_16*dmats2[16][5] + coeff0_17*dmats2[17][5] + coeff0_18*dmats2[18][5] + coeff0_19*dmats2[19][5];
714
new_coeff0_6 = coeff0_0*dmats2[0][6] + coeff0_1*dmats2[1][6] + coeff0_2*dmats2[2][6] + coeff0_3*dmats2[3][6] + coeff0_4*dmats2[4][6] + coeff0_5*dmats2[5][6] + coeff0_6*dmats2[6][6] + coeff0_7*dmats2[7][6] + coeff0_8*dmats2[8][6] + coeff0_9*dmats2[9][6] + coeff0_10*dmats2[10][6] + coeff0_11*dmats2[11][6] + coeff0_12*dmats2[12][6] + coeff0_13*dmats2[13][6] + coeff0_14*dmats2[14][6] + coeff0_15*dmats2[15][6] + coeff0_16*dmats2[16][6] + coeff0_17*dmats2[17][6] + coeff0_18*dmats2[18][6] + coeff0_19*dmats2[19][6];
715
new_coeff0_7 = coeff0_0*dmats2[0][7] + coeff0_1*dmats2[1][7] + coeff0_2*dmats2[2][7] + coeff0_3*dmats2[3][7] + coeff0_4*dmats2[4][7] + coeff0_5*dmats2[5][7] + coeff0_6*dmats2[6][7] + coeff0_7*dmats2[7][7] + coeff0_8*dmats2[8][7] + coeff0_9*dmats2[9][7] + coeff0_10*dmats2[10][7] + coeff0_11*dmats2[11][7] + coeff0_12*dmats2[12][7] + coeff0_13*dmats2[13][7] + coeff0_14*dmats2[14][7] + coeff0_15*dmats2[15][7] + coeff0_16*dmats2[16][7] + coeff0_17*dmats2[17][7] + coeff0_18*dmats2[18][7] + coeff0_19*dmats2[19][7];
716
new_coeff0_8 = coeff0_0*dmats2[0][8] + coeff0_1*dmats2[1][8] + coeff0_2*dmats2[2][8] + coeff0_3*dmats2[3][8] + coeff0_4*dmats2[4][8] + coeff0_5*dmats2[5][8] + coeff0_6*dmats2[6][8] + coeff0_7*dmats2[7][8] + coeff0_8*dmats2[8][8] + coeff0_9*dmats2[9][8] + coeff0_10*dmats2[10][8] + coeff0_11*dmats2[11][8] + coeff0_12*dmats2[12][8] + coeff0_13*dmats2[13][8] + coeff0_14*dmats2[14][8] + coeff0_15*dmats2[15][8] + coeff0_16*dmats2[16][8] + coeff0_17*dmats2[17][8] + coeff0_18*dmats2[18][8] + coeff0_19*dmats2[19][8];
717
new_coeff0_9 = coeff0_0*dmats2[0][9] + coeff0_1*dmats2[1][9] + coeff0_2*dmats2[2][9] + coeff0_3*dmats2[3][9] + coeff0_4*dmats2[4][9] + coeff0_5*dmats2[5][9] + coeff0_6*dmats2[6][9] + coeff0_7*dmats2[7][9] + coeff0_8*dmats2[8][9] + coeff0_9*dmats2[9][9] + coeff0_10*dmats2[10][9] + coeff0_11*dmats2[11][9] + coeff0_12*dmats2[12][9] + coeff0_13*dmats2[13][9] + coeff0_14*dmats2[14][9] + coeff0_15*dmats2[15][9] + coeff0_16*dmats2[16][9] + coeff0_17*dmats2[17][9] + coeff0_18*dmats2[18][9] + coeff0_19*dmats2[19][9];
718
new_coeff0_10 = coeff0_0*dmats2[0][10] + coeff0_1*dmats2[1][10] + coeff0_2*dmats2[2][10] + coeff0_3*dmats2[3][10] + coeff0_4*dmats2[4][10] + coeff0_5*dmats2[5][10] + coeff0_6*dmats2[6][10] + coeff0_7*dmats2[7][10] + coeff0_8*dmats2[8][10] + coeff0_9*dmats2[9][10] + coeff0_10*dmats2[10][10] + coeff0_11*dmats2[11][10] + coeff0_12*dmats2[12][10] + coeff0_13*dmats2[13][10] + coeff0_14*dmats2[14][10] + coeff0_15*dmats2[15][10] + coeff0_16*dmats2[16][10] + coeff0_17*dmats2[17][10] + coeff0_18*dmats2[18][10] + coeff0_19*dmats2[19][10];
719
new_coeff0_11 = coeff0_0*dmats2[0][11] + coeff0_1*dmats2[1][11] + coeff0_2*dmats2[2][11] + coeff0_3*dmats2[3][11] + coeff0_4*dmats2[4][11] + coeff0_5*dmats2[5][11] + coeff0_6*dmats2[6][11] + coeff0_7*dmats2[7][11] + coeff0_8*dmats2[8][11] + coeff0_9*dmats2[9][11] + coeff0_10*dmats2[10][11] + coeff0_11*dmats2[11][11] + coeff0_12*dmats2[12][11] + coeff0_13*dmats2[13][11] + coeff0_14*dmats2[14][11] + coeff0_15*dmats2[15][11] + coeff0_16*dmats2[16][11] + coeff0_17*dmats2[17][11] + coeff0_18*dmats2[18][11] + coeff0_19*dmats2[19][11];
720
new_coeff0_12 = coeff0_0*dmats2[0][12] + coeff0_1*dmats2[1][12] + coeff0_2*dmats2[2][12] + coeff0_3*dmats2[3][12] + coeff0_4*dmats2[4][12] + coeff0_5*dmats2[5][12] + coeff0_6*dmats2[6][12] + coeff0_7*dmats2[7][12] + coeff0_8*dmats2[8][12] + coeff0_9*dmats2[9][12] + coeff0_10*dmats2[10][12] + coeff0_11*dmats2[11][12] + coeff0_12*dmats2[12][12] + coeff0_13*dmats2[13][12] + coeff0_14*dmats2[14][12] + coeff0_15*dmats2[15][12] + coeff0_16*dmats2[16][12] + coeff0_17*dmats2[17][12] + coeff0_18*dmats2[18][12] + coeff0_19*dmats2[19][12];
721
new_coeff0_13 = coeff0_0*dmats2[0][13] + coeff0_1*dmats2[1][13] + coeff0_2*dmats2[2][13] + coeff0_3*dmats2[3][13] + coeff0_4*dmats2[4][13] + coeff0_5*dmats2[5][13] + coeff0_6*dmats2[6][13] + coeff0_7*dmats2[7][13] + coeff0_8*dmats2[8][13] + coeff0_9*dmats2[9][13] + coeff0_10*dmats2[10][13] + coeff0_11*dmats2[11][13] + coeff0_12*dmats2[12][13] + coeff0_13*dmats2[13][13] + coeff0_14*dmats2[14][13] + coeff0_15*dmats2[15][13] + coeff0_16*dmats2[16][13] + coeff0_17*dmats2[17][13] + coeff0_18*dmats2[18][13] + coeff0_19*dmats2[19][13];
722
new_coeff0_14 = coeff0_0*dmats2[0][14] + coeff0_1*dmats2[1][14] + coeff0_2*dmats2[2][14] + coeff0_3*dmats2[3][14] + coeff0_4*dmats2[4][14] + coeff0_5*dmats2[5][14] + coeff0_6*dmats2[6][14] + coeff0_7*dmats2[7][14] + coeff0_8*dmats2[8][14] + coeff0_9*dmats2[9][14] + coeff0_10*dmats2[10][14] + coeff0_11*dmats2[11][14] + coeff0_12*dmats2[12][14] + coeff0_13*dmats2[13][14] + coeff0_14*dmats2[14][14] + coeff0_15*dmats2[15][14] + coeff0_16*dmats2[16][14] + coeff0_17*dmats2[17][14] + coeff0_18*dmats2[18][14] + coeff0_19*dmats2[19][14];
723
new_coeff0_15 = coeff0_0*dmats2[0][15] + coeff0_1*dmats2[1][15] + coeff0_2*dmats2[2][15] + coeff0_3*dmats2[3][15] + coeff0_4*dmats2[4][15] + coeff0_5*dmats2[5][15] + coeff0_6*dmats2[6][15] + coeff0_7*dmats2[7][15] + coeff0_8*dmats2[8][15] + coeff0_9*dmats2[9][15] + coeff0_10*dmats2[10][15] + coeff0_11*dmats2[11][15] + coeff0_12*dmats2[12][15] + coeff0_13*dmats2[13][15] + coeff0_14*dmats2[14][15] + coeff0_15*dmats2[15][15] + coeff0_16*dmats2[16][15] + coeff0_17*dmats2[17][15] + coeff0_18*dmats2[18][15] + coeff0_19*dmats2[19][15];
724
new_coeff0_16 = coeff0_0*dmats2[0][16] + coeff0_1*dmats2[1][16] + coeff0_2*dmats2[2][16] + coeff0_3*dmats2[3][16] + coeff0_4*dmats2[4][16] + coeff0_5*dmats2[5][16] + coeff0_6*dmats2[6][16] + coeff0_7*dmats2[7][16] + coeff0_8*dmats2[8][16] + coeff0_9*dmats2[9][16] + coeff0_10*dmats2[10][16] + coeff0_11*dmats2[11][16] + coeff0_12*dmats2[12][16] + coeff0_13*dmats2[13][16] + coeff0_14*dmats2[14][16] + coeff0_15*dmats2[15][16] + coeff0_16*dmats2[16][16] + coeff0_17*dmats2[17][16] + coeff0_18*dmats2[18][16] + coeff0_19*dmats2[19][16];
725
new_coeff0_17 = coeff0_0*dmats2[0][17] + coeff0_1*dmats2[1][17] + coeff0_2*dmats2[2][17] + coeff0_3*dmats2[3][17] + coeff0_4*dmats2[4][17] + coeff0_5*dmats2[5][17] + coeff0_6*dmats2[6][17] + coeff0_7*dmats2[7][17] + coeff0_8*dmats2[8][17] + coeff0_9*dmats2[9][17] + coeff0_10*dmats2[10][17] + coeff0_11*dmats2[11][17] + coeff0_12*dmats2[12][17] + coeff0_13*dmats2[13][17] + coeff0_14*dmats2[14][17] + coeff0_15*dmats2[15][17] + coeff0_16*dmats2[16][17] + coeff0_17*dmats2[17][17] + coeff0_18*dmats2[18][17] + coeff0_19*dmats2[19][17];
726
new_coeff0_18 = coeff0_0*dmats2[0][18] + coeff0_1*dmats2[1][18] + coeff0_2*dmats2[2][18] + coeff0_3*dmats2[3][18] + coeff0_4*dmats2[4][18] + coeff0_5*dmats2[5][18] + coeff0_6*dmats2[6][18] + coeff0_7*dmats2[7][18] + coeff0_8*dmats2[8][18] + coeff0_9*dmats2[9][18] + coeff0_10*dmats2[10][18] + coeff0_11*dmats2[11][18] + coeff0_12*dmats2[12][18] + coeff0_13*dmats2[13][18] + coeff0_14*dmats2[14][18] + coeff0_15*dmats2[15][18] + coeff0_16*dmats2[16][18] + coeff0_17*dmats2[17][18] + coeff0_18*dmats2[18][18] + coeff0_19*dmats2[19][18];
727
new_coeff0_19 = coeff0_0*dmats2[0][19] + coeff0_1*dmats2[1][19] + coeff0_2*dmats2[2][19] + coeff0_3*dmats2[3][19] + coeff0_4*dmats2[4][19] + coeff0_5*dmats2[5][19] + coeff0_6*dmats2[6][19] + coeff0_7*dmats2[7][19] + coeff0_8*dmats2[8][19] + coeff0_9*dmats2[9][19] + coeff0_10*dmats2[10][19] + coeff0_11*dmats2[11][19] + coeff0_12*dmats2[12][19] + coeff0_13*dmats2[13][19] + coeff0_14*dmats2[14][19] + coeff0_15*dmats2[15][19] + coeff0_16*dmats2[16][19] + coeff0_17*dmats2[17][19] + coeff0_18*dmats2[18][19] + coeff0_19*dmats2[19][19];
728
}
729
730
}
731
// Compute derivatives on reference element as dot product of coefficients and basisvalues
732
derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2 + new_coeff0_3*basisvalue3 + new_coeff0_4*basisvalue4 + new_coeff0_5*basisvalue5 + new_coeff0_6*basisvalue6 + new_coeff0_7*basisvalue7 + new_coeff0_8*basisvalue8 + new_coeff0_9*basisvalue9 + new_coeff0_10*basisvalue10 + new_coeff0_11*basisvalue11 + new_coeff0_12*basisvalue12 + new_coeff0_13*basisvalue13 + new_coeff0_14*basisvalue14 + new_coeff0_15*basisvalue15 + new_coeff0_16*basisvalue16 + new_coeff0_17*basisvalue17 + new_coeff0_18*basisvalue18 + new_coeff0_19*basisvalue19;
733
}
734
735
// Transform derivatives back to physical element
736
for (unsigned int row = 0; row < num_derivatives; row++)
737
{
738
for (unsigned int col = 0; col < num_derivatives; col++)
739
{
740
values[row] += transform[row][col]*derivatives[col];
741
}
742
}
743
// Delete pointer to array of derivatives on FIAT element
744
delete [] derivatives;
745
746
// Delete pointer to array of combinations of derivatives and transform
747
for (unsigned int row = 0; row < num_derivatives; row++)
748
{
749
delete [] combinations[row];
750
delete [] transform[row];
751
}
752
753
delete [] combinations;
754
delete [] transform;
755
}
756
757
/// Evaluate order n derivatives of all basis functions at given point in cell
758
virtual void evaluate_basis_derivatives_all(unsigned int n,
759
double* values,
760
const double* coordinates,
761
const ufc::cell& c) const
762
{
763
throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");
764
}
765
766
/// Evaluate linear functional for dof i on the function f
767
virtual double evaluate_dof(unsigned int i,
768
const ufc::function& f,
769
const ufc::cell& c) const
770
{
771
// The reference points, direction and weights:
772
const static double X[20][1][3] = {{{0, 0, 0}}, {{1, 0, 0}}, {{0, 1, 0}}, {{0, 0, 1}}, {{0, 0.666666666666667, 0.333333333333333}}, {{0, 0.333333333333333, 0.666666666666667}}, {{0.666666666666667, 0, 0.333333333333333}}, {{0.333333333333333, 0, 0.666666666666667}}, {{0.666666666666667, 0.333333333333333, 0}}, {{0.333333333333333, 0.666666666666667, 0}}, {{0, 0, 0.333333333333333}}, {{0, 0, 0.666666666666667}}, {{0, 0.333333333333333, 0}}, {{0, 0.666666666666667, 0}}, {{0.333333333333333, 0, 0}}, {{0.666666666666667, 0, 0}}, {{0.333333333333333, 0.333333333333333, 0.333333333333333}}, {{0, 0.333333333333333, 0.333333333333333}}, {{0.333333333333333, 0, 0.333333333333333}}, {{0.333333333333333, 0.333333333333333, 0}}};
773
const static double W[20][1] = {{1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}};
774
const static double D[20][1][1] = {{{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}};
775
776
const double * const * x = c.coordinates;
777
double result = 0.0;
778
// Iterate over the points:
779
// Evaluate basis functions for affine mapping
780
const double w0 = 1.0 - X[i][0][0] - X[i][0][1] - X[i][0][2];
781
const double w1 = X[i][0][0];
782
const double w2 = X[i][0][1];
783
const double w3 = X[i][0][2];
784
785
// Compute affine mapping y = F(X)
786
double y[3];
787
y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0] + w3*x[3][0];
788
y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1] + w3*x[3][1];
789
y[2] = w0*x[0][2] + w1*x[1][2] + w2*x[2][2] + w3*x[3][2];
790
791
// Evaluate function at physical points
792
double values[1];
793
f.evaluate(values, y, c);
794
795
// Map function values using appropriate mapping
796
// Affine map: Do nothing
797
798
// Note that we do not map the weights (yet).
799
800
// Take directional components
801
for(int k = 0; k < 1; k++)
802
result += values[k]*D[i][0][k];
803
// Multiply by weights
804
result *= W[i][0];
805
806
return result;
807
}
808
809
/// Evaluate linear functionals for all dofs on the function f
810
virtual void evaluate_dofs(double* values,
811
const ufc::function& f,
812
const ufc::cell& c) const
813
{
814
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
815
}
816
817
/// Interpolate vertex values from dof values
818
virtual void interpolate_vertex_values(double* vertex_values,
819
const double* dof_values,
820
const ufc::cell& c) const
821
{
822
// Evaluate at vertices and use affine mapping
823
vertex_values[0] = dof_values[0];
824
vertex_values[1] = dof_values[1];
825
vertex_values[2] = dof_values[2];
826
vertex_values[3] = dof_values[3];
827
}
828
829
/// Return the number of sub elements (for a mixed element)
830
virtual unsigned int num_sub_elements() const
831
{
832
return 1;
833
}
834
835
/// Create a new finite element for sub element i (for a mixed element)
836
virtual ufc::finite_element* create_sub_element(unsigned int i) const
837
{
838
return new UFC_AdvectionBilinearForm_finite_element_0();
839
}
840
841
};
842
843
/// This class defines the interface for a finite element.
844
845
class UFC_AdvectionBilinearForm_finite_element_1: public ufc::finite_element
846
{
847
public:
848
849
/// Constructor
850
UFC_AdvectionBilinearForm_finite_element_1() : ufc::finite_element()
851
{
852
// Do nothing
853
}
854
855
/// Destructor
856
virtual ~UFC_AdvectionBilinearForm_finite_element_1()
857
{
858
// Do nothing
859
}
860
861
/// Return a string identifying the finite element
862
virtual const char* signature() const
863
{
864
return "Lagrange finite element of degree 3 on a tetrahedron";
865
}
866
867
/// Return the cell shape
868
virtual ufc::shape cell_shape() const
869
{
870
return ufc::tetrahedron;
871
}
872
873
/// Return the dimension of the finite element function space
874
virtual unsigned int space_dimension() const
875
{
876
return 20;
877
}
878
879
/// Return the rank of the value space
880
virtual unsigned int value_rank() const
881
{
882
return 0;
883
}
884
885
/// Return the dimension of the value space for axis i
886
virtual unsigned int value_dimension(unsigned int i) const
887
{
888
return 1;
889
}
890
891
/// Evaluate basis function i at given point in cell
892
virtual void evaluate_basis(unsigned int i,
893
double* values,
894
const double* coordinates,
895
const ufc::cell& c) const
896
{
897
// Extract vertex coordinates
898
const double * const * element_coordinates = c.coordinates;
899
900
// Compute Jacobian of affine map from reference cell
901
const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
902
const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
903
const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];
904
const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
905
const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
906
const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];
907
const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];
908
const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];
909
const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];
910
911
// Compute sub determinants
912
const double d00 = J_11*J_22 - J_12*J_21;
913
const double d01 = J_12*J_20 - J_10*J_22;
914
const double d02 = J_10*J_21 - J_11*J_20;
915
916
const double d10 = J_02*J_21 - J_01*J_22;
917
const double d11 = J_00*J_22 - J_02*J_20;
918
const double d12 = J_01*J_20 - J_00*J_21;
919
920
const double d20 = J_01*J_12 - J_02*J_11;
921
const double d21 = J_02*J_10 - J_00*J_12;
922
const double d22 = J_00*J_11 - J_01*J_10;
923
924
// Compute determinant of Jacobian
925
double detJ = J_00*d00 + J_10*d10 + J_20*d20;
926
927
// Compute inverse of Jacobian
928
929
// Compute constants
930
const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \
931
+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \
932
+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);
933
934
const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \
935
+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \
936
+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);
937
938
const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \
939
+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \
940
+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);
941
942
// Get coordinates and map to the UFC reference element
943
double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;
944
double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;
945
double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;
946
947
// Map coordinates to the reference cube
948
if (std::abs(y + z - 1.0) < 1e-14)
949
x = 1.0;
950
else
951
x = -2.0 * x/(y + z - 1.0) - 1.0;
952
if (std::abs(z - 1.0) < 1e-14)
953
y = -1.0;
954
else
955
y = 2.0 * y/(1.0 - z) - 1.0;
956
z = 2.0 * z - 1.0;
957
958
// Reset values
959
*values = 0;
960
961
// Map degree of freedom to element degree of freedom
962
const unsigned int dof = i;
963
964
// Generate scalings
965
const double scalings_y_0 = 1;
966
const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
967
const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);
968
const double scalings_y_3 = scalings_y_2*(0.5 - 0.5*y);
969
const double scalings_z_0 = 1;
970
const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);
971
const double scalings_z_2 = scalings_z_1*(0.5 - 0.5*z);
972
const double scalings_z_3 = scalings_z_2*(0.5 - 0.5*z);
973
974
// Compute psitilde_a
975
const double psitilde_a_0 = 1;
976
const double psitilde_a_1 = x;
977
const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;
978
const double psitilde_a_3 = 1.66666666666667*x*psitilde_a_2 - 0.666666666666667*psitilde_a_1;
979
980
// Compute psitilde_bs
981
const double psitilde_bs_0_0 = 1;
982
const double psitilde_bs_0_1 = 1.5*y + 0.5;
983
const double psitilde_bs_0_2 = 0.111111111111111*psitilde_bs_0_1 + 1.66666666666667*y*psitilde_bs_0_1 - 0.555555555555556*psitilde_bs_0_0;
984
const double psitilde_bs_0_3 = 0.05*psitilde_bs_0_2 + 1.75*y*psitilde_bs_0_2 - 0.7*psitilde_bs_0_1;
985
const double psitilde_bs_1_0 = 1;
986
const double psitilde_bs_1_1 = 2.5*y + 1.5;
987
const double psitilde_bs_1_2 = 0.54*psitilde_bs_1_1 + 2.1*y*psitilde_bs_1_1 - 0.56*psitilde_bs_1_0;
988
const double psitilde_bs_2_0 = 1;
989
const double psitilde_bs_2_1 = 3.5*y + 2.5;
990
const double psitilde_bs_3_0 = 1;
991
992
// Compute psitilde_cs
993
const double psitilde_cs_00_0 = 1;
994
const double psitilde_cs_00_1 = 2*z + 1;
995
const double psitilde_cs_00_2 = 0.3125*psitilde_cs_00_1 + 1.875*z*psitilde_cs_00_1 - 0.5625*psitilde_cs_00_0;
996
const double psitilde_cs_00_3 = 0.155555555555556*psitilde_cs_00_2 + 1.86666666666667*z*psitilde_cs_00_2 - 0.711111111111111*psitilde_cs_00_1;
997
const double psitilde_cs_01_0 = 1;
998
const double psitilde_cs_01_1 = 3*z + 2;
999
const double psitilde_cs_01_2 = 0.777777777777778*psitilde_cs_01_1 + 2.33333333333333*z*psitilde_cs_01_1 - 0.555555555555556*psitilde_cs_01_0;
1000
const double psitilde_cs_02_0 = 1;
1001
const double psitilde_cs_02_1 = 4*z + 3;
1002
const double psitilde_cs_03_0 = 1;
1003
const double psitilde_cs_10_0 = 1;
1004
const double psitilde_cs_10_1 = 3*z + 2;
1005
const double psitilde_cs_10_2 = 0.777777777777778*psitilde_cs_10_1 + 2.33333333333333*z*psitilde_cs_10_1 - 0.555555555555556*psitilde_cs_10_0;
1006
const double psitilde_cs_11_0 = 1;
1007
const double psitilde_cs_11_1 = 4*z + 3;
1008
const double psitilde_cs_12_0 = 1;
1009
const double psitilde_cs_20_0 = 1;
1010
const double psitilde_cs_20_1 = 4*z + 3;
1011
const double psitilde_cs_21_0 = 1;
1012
const double psitilde_cs_30_0 = 1;
1013
1014
// Compute basisvalues
1015
const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
1016
const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;
1017
const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;
1018
const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;
1019
const double basisvalue4 = 5.1234753829798*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_0;
1020
const double basisvalue5 = 3.96862696659689*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_0;
1021
const double basisvalue6 = 2.29128784747792*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_0;
1022
const double basisvalue7 = 3.24037034920393*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_1;
1023
const double basisvalue8 = 1.87082869338697*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_1;
1024
const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;
1025
const double basisvalue10 = 7.93725393319377*psitilde_a_3*scalings_y_3*psitilde_bs_3_0*scalings_z_3*psitilde_cs_30_0;
1026
const double basisvalue11 = 6.70820393249937*psitilde_a_2*scalings_y_2*psitilde_bs_2_1*scalings_z_3*psitilde_cs_21_0;
1027
const double basisvalue12 = 5.19615242270663*psitilde_a_1*scalings_y_1*psitilde_bs_1_2*scalings_z_3*psitilde_cs_12_0;
1028
const double basisvalue13 = 3*psitilde_a_0*scalings_y_0*psitilde_bs_0_3*scalings_z_3*psitilde_cs_03_0;
1029
const double basisvalue14 = 5.80947501931113*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_1;
1030
const double basisvalue15 = 4.5*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_1;
1031
const double basisvalue16 = 2.59807621135332*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_1;
1032
const double basisvalue17 = 3.67423461417477*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_2;
1033
const double basisvalue18 = 2.12132034355964*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_2;
1034
const double basisvalue19 = 1.5*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_3;
1035
1036
// Table(s) of coefficients
1037
const static double coefficients0[20][20] = \
1038
{{0.0288675134594814, 0.0130410132739326, 0.00752923252421041, 0.00532397137499949, 0.018298126367785, 0.014173667737846, 0.00818317088384972, 0.0115727512471569, 0.0066815310478106, 0.00472455591261533, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197612, -0.0131222664791956, -0.00757614408414157, -0.00535714285714285},
1039
{0.0288675134594813, -0.0130410132739325, 0.0075292325242104, 0.00532397137499953, 0.018298126367785, -0.014173667737846, 0.00818317088384972, -0.0115727512471569, 0.0066815310478106, 0.00472455591261534, 0.028347335475692, -0.0239578711874977, 0.0185576872239523, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197613, 0.0131222664791956, -0.00757614408414159, -0.00535714285714286},
1040
{0.0288675134594812, 0, -0.0150584650484208, 0.00532397137499948, 0, 0, 0.0245495126515492, 0, -0.0133630620956212, 0.00472455591261538, 0, 0, 0, 0.0428571428571428, 0, 0, -0.0278365308359284, 0, 0.0151522881682832, -0.00535714285714287},
1041
{0.0288675134594813, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.028347335475692, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286},
1042
{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546474, 0, 0.0267261241912424, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731327, 0.0267857142857143},
1043
{0, 0, -0.0225876975726313, 0.127775312999988, 0, 0, 0, 0, 0.0668153104781061, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0, 0.0757614408414158, -0.0535714285714286},
1044
{0, 0.097807599554494, -0.0564692439315782, -0.063887656499994, 0.054894379103355, -0.0425210032135381, 0.0245495126515491, 0.0231455024943138, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, -0.0375, 0.021650635094611, -0.0524890659167824, 0.0303045763365663, 0.0267857142857143},
1045
{0, -0.0195615199108988, 0.0112938487863157, 0.127775312999988, 0, 0, 0, 0.0578637562357845, -0.0334076552390531, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0.065611332395978, -0.0378807204207079, -0.0535714285714286},
1046
{0, 0.097807599554494, -0.0790569415042095, -0.031943828249997, 0.054894379103355, 0.014173667737846, -0.0245495126515491, -0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, -0.0618589574131742, 0.0428571428571429, -0.00691604168965609, -0.0160714285714286, 0.0154647393532935, 0.00874817765279706, 0, -0.00535714285714286},
1047
{0, -0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, 0.0566946709513841, 0.0245495126515492, -0.0115727512471569, -0.0467707173346742, 0.0236227795630767, 0, 0, 0.0618589574131742, -0.0642857142857143, 0, -0.0214285714285714, 0.00927884361197613, 0.00437408882639853, 0.00757614408414158, -0.00535714285714285},
1048
{0, -0.0978075995544939, -0.0564692439315781, -0.063887656499994, 0.054894379103355, 0.0425210032135381, 0.0245495126515491, -0.0231455024943137, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, 0.0375, 0.021650635094611, 0.0524890659167824, 0.0303045763365663, 0.0267857142857143},
1049
{0, 0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, -0.0578637562357845, -0.033407655239053, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, -0.065611332395978, -0.0378807204207079, -0.0535714285714286},
1050
{0, -0.097807599554494, -0.0790569415042095, -0.031943828249997, 0.054894379103355, -0.014173667737846, -0.0245495126515492, 0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, 0.0618589574131742, 0.0428571428571429, -0.0069160416896561, 0.0160714285714286, 0.0154647393532935, -0.00874817765279706, 0, -0.00535714285714287},
1051
{0, 0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, -0.0566946709513841, 0.0245495126515492, 0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, -0.0618589574131742, -0.0642857142857143, 0, 0.0214285714285714, 0.00927884361197613, -0.00437408882639853, 0.00757614408414157, -0.00535714285714286},
1052
{0, -0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.018298126367785, 0.0425210032135381, 0.0409158544192485, 0.0347182537414707, 0.033407655239053, 0.0236227795630767, 0.0850420064270761, 0.0239578711874977, -0.00618589574131741, -0.0107142857142857, 0.0207481250689683, -0.00535714285714284, -0.00927884361197614, -0.00437408882639852, -0.0075761440841416, -0.00535714285714286},
1053
{0, 0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.018298126367785, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.0334076552390531, 0.0236227795630767, -0.0850420064270761, 0.0239578711874978, 0.0061858957413174, -0.0107142857142857, 0.0207481250689683, 0.00535714285714285, -0.00927884361197613, 0.00437408882639852, -0.00757614408414159, -0.00535714285714286},
1054
{0.259807621135332, 0.117369119465393, 0.0677630927178939, 0.0479157423749955, 0, 0.0850420064270761, -0.0736485379546474, 0.0694365074829413, 0.0400891862868636, -0.0992156741649222, 0, 0, 0, 0, 0, 0.075, -0.0649519052838329, -0.0262445329583912, -0.0151522881682832, 0.0267857142857143},
1055
{0.259807621135332, -0.117369119465393, 0.0677630927178938, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546474, -0.0694365074829414, 0.0400891862868636, -0.0992156741649221, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682832, 0.0267857142857143},
1056
{0.259807621135332, 0, -0.135526185435788, 0.0479157423749955, -0.10978875820671, 0, 0.0245495126515491, 0, -0.0801783725737273, -0.0992156741649221, 0, 0, 0, 0, -0.0968245836551854, 0, 0.021650635094611, 0, 0.0303045763365663, 0.0267857142857143},
1057
{0.259807621135332, 0, 0, -0.143747227124986, -0.10978875820671, 0, -0.122747563257746, 0, 0, 0.0425210032135381, 0, -0.095831484749991, 0, 0.0428571428571429, 0.0138320833793122, 0, 0.0154647393532935, 0, 0, -0.00535714285714284}};
1058
1059
// Extract relevant coefficients
1060
const double coeff0_0 = coefficients0[dof][0];
1061
const double coeff0_1 = coefficients0[dof][1];
1062
const double coeff0_2 = coefficients0[dof][2];
1063
const double coeff0_3 = coefficients0[dof][3];
1064
const double coeff0_4 = coefficients0[dof][4];
1065
const double coeff0_5 = coefficients0[dof][5];
1066
const double coeff0_6 = coefficients0[dof][6];
1067
const double coeff0_7 = coefficients0[dof][7];
1068
const double coeff0_8 = coefficients0[dof][8];
1069
const double coeff0_9 = coefficients0[dof][9];
1070
const double coeff0_10 = coefficients0[dof][10];
1071
const double coeff0_11 = coefficients0[dof][11];
1072
const double coeff0_12 = coefficients0[dof][12];
1073
const double coeff0_13 = coefficients0[dof][13];
1074
const double coeff0_14 = coefficients0[dof][14];
1075
const double coeff0_15 = coefficients0[dof][15];
1076
const double coeff0_16 = coefficients0[dof][16];
1077
const double coeff0_17 = coefficients0[dof][17];
1078
const double coeff0_18 = coefficients0[dof][18];
1079
const double coeff0_19 = coefficients0[dof][19];
1080
1081
// Compute value(s)
1082
*values = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2 + coeff0_3*basisvalue3 + coeff0_4*basisvalue4 + coeff0_5*basisvalue5 + coeff0_6*basisvalue6 + coeff0_7*basisvalue7 + coeff0_8*basisvalue8 + coeff0_9*basisvalue9 + coeff0_10*basisvalue10 + coeff0_11*basisvalue11 + coeff0_12*basisvalue12 + coeff0_13*basisvalue13 + coeff0_14*basisvalue14 + coeff0_15*basisvalue15 + coeff0_16*basisvalue16 + coeff0_17*basisvalue17 + coeff0_18*basisvalue18 + coeff0_19*basisvalue19;
1083
}
1084
1085
/// Evaluate all basis functions at given point in cell
1086
virtual void evaluate_basis_all(double* values,
1087
const double* coordinates,
1088
const ufc::cell& c) const
1089
{
1090
throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");
1091
}
1092
1093
/// Evaluate order n derivatives of basis function i at given point in cell
1094
virtual void evaluate_basis_derivatives(unsigned int i,
1095
unsigned int n,
1096
double* values,
1097
const double* coordinates,
1098
const ufc::cell& c) const
1099
{
1100
// Extract vertex coordinates
1101
const double * const * element_coordinates = c.coordinates;
1102
1103
// Compute Jacobian of affine map from reference cell
1104
const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
1105
const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
1106
const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];
1107
const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
1108
const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
1109
const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];
1110
const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];
1111
const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];
1112
const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];
1113
1114
// Compute sub determinants
1115
const double d00 = J_11*J_22 - J_12*J_21;
1116
const double d01 = J_12*J_20 - J_10*J_22;
1117
const double d02 = J_10*J_21 - J_11*J_20;
1118
1119
const double d10 = J_02*J_21 - J_01*J_22;
1120
const double d11 = J_00*J_22 - J_02*J_20;
1121
const double d12 = J_01*J_20 - J_00*J_21;
1122
1123
const double d20 = J_01*J_12 - J_02*J_11;
1124
const double d21 = J_02*J_10 - J_00*J_12;
1125
const double d22 = J_00*J_11 - J_01*J_10;
1126
1127
// Compute determinant of Jacobian
1128
double detJ = J_00*d00 + J_10*d10 + J_20*d20;
1129
1130
// Compute inverse of Jacobian
1131
1132
// Compute constants
1133
const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \
1134
+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \
1135
+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);
1136
1137
const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \
1138
+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \
1139
+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);
1140
1141
const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \
1142
+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \
1143
+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);
1144
1145
// Get coordinates and map to the UFC reference element
1146
double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;
1147
double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;
1148
double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;
1149
1150
// Map coordinates to the reference cube
1151
if (std::abs(y + z - 1.0) < 1e-14)
1152
x = 1.0;
1153
else
1154
x = -2.0 * x/(y + z - 1.0) - 1.0;
1155
if (std::abs(z - 1.0) < 1e-14)
1156
y = -1.0;
1157
else
1158
y = 2.0 * y/(1.0 - z) - 1.0;
1159
z = 2.0 * z - 1.0;
1160
1161
// Compute number of derivatives
1162
unsigned int num_derivatives = 1;
1163
1164
for (unsigned int j = 0; j < n; j++)
1165
num_derivatives *= 3;
1166
1167
1168
// Declare pointer to two dimensional array that holds combinations of derivatives and initialise
1169
unsigned int **combinations = new unsigned int *[num_derivatives];
1170
1171
for (unsigned int j = 0; j < num_derivatives; j++)
1172
{
1173
combinations[j] = new unsigned int [n];
1174
for (unsigned int k = 0; k < n; k++)
1175
combinations[j][k] = 0;
1176
}
1177
1178
// Generate combinations of derivatives
1179
for (unsigned int row = 1; row < num_derivatives; row++)
1180
{
1181
for (unsigned int num = 0; num < row; num++)
1182
{
1183
for (unsigned int col = n-1; col+1 > 0; col--)
1184
{
1185
if (combinations[row][col] + 1 > 2)
1186
combinations[row][col] = 0;
1187
else
1188
{
1189
combinations[row][col] += 1;
1190
break;
1191
}
1192
}
1193
}
1194
}
1195
1196
// Compute inverse of Jacobian
1197
const double Jinv[3][3] ={{d00 / detJ, d10 / detJ, d20 / detJ}, {d01 / detJ, d11 / detJ, d21 / detJ}, {d02 / detJ, d12 / detJ, d22 / detJ}};
1198
1199
// Declare transformation matrix
1200
// Declare pointer to two dimensional array and initialise
1201
double **transform = new double *[num_derivatives];
1202
1203
for (unsigned int j = 0; j < num_derivatives; j++)
1204
{
1205
transform[j] = new double [num_derivatives];
1206
for (unsigned int k = 0; k < num_derivatives; k++)
1207
transform[j][k] = 1;
1208
}
1209
1210
// Construct transformation matrix
1211
for (unsigned int row = 0; row < num_derivatives; row++)
1212
{
1213
for (unsigned int col = 0; col < num_derivatives; col++)
1214
{
1215
for (unsigned int k = 0; k < n; k++)
1216
transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
1217
}
1218
}
1219
1220
// Reset values
1221
for (unsigned int j = 0; j < 1*num_derivatives; j++)
1222
values[j] = 0;
1223
1224
// Map degree of freedom to element degree of freedom
1225
const unsigned int dof = i;
1226
1227
// Generate scalings
1228
const double scalings_y_0 = 1;
1229
const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
1230
const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);
1231
const double scalings_y_3 = scalings_y_2*(0.5 - 0.5*y);
1232
const double scalings_z_0 = 1;
1233
const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);
1234
const double scalings_z_2 = scalings_z_1*(0.5 - 0.5*z);
1235
const double scalings_z_3 = scalings_z_2*(0.5 - 0.5*z);
1236
1237
// Compute psitilde_a
1238
const double psitilde_a_0 = 1;
1239
const double psitilde_a_1 = x;
1240
const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;
1241
const double psitilde_a_3 = 1.66666666666667*x*psitilde_a_2 - 0.666666666666667*psitilde_a_1;
1242
1243
// Compute psitilde_bs
1244
const double psitilde_bs_0_0 = 1;
1245
const double psitilde_bs_0_1 = 1.5*y + 0.5;
1246
const double psitilde_bs_0_2 = 0.111111111111111*psitilde_bs_0_1 + 1.66666666666667*y*psitilde_bs_0_1 - 0.555555555555556*psitilde_bs_0_0;
1247
const double psitilde_bs_0_3 = 0.05*psitilde_bs_0_2 + 1.75*y*psitilde_bs_0_2 - 0.7*psitilde_bs_0_1;
1248
const double psitilde_bs_1_0 = 1;
1249
const double psitilde_bs_1_1 = 2.5*y + 1.5;
1250
const double psitilde_bs_1_2 = 0.54*psitilde_bs_1_1 + 2.1*y*psitilde_bs_1_1 - 0.56*psitilde_bs_1_0;
1251
const double psitilde_bs_2_0 = 1;
1252
const double psitilde_bs_2_1 = 3.5*y + 2.5;
1253
const double psitilde_bs_3_0 = 1;
1254
1255
// Compute psitilde_cs
1256
const double psitilde_cs_00_0 = 1;
1257
const double psitilde_cs_00_1 = 2*z + 1;
1258
const double psitilde_cs_00_2 = 0.3125*psitilde_cs_00_1 + 1.875*z*psitilde_cs_00_1 - 0.5625*psitilde_cs_00_0;
1259
const double psitilde_cs_00_3 = 0.155555555555556*psitilde_cs_00_2 + 1.86666666666667*z*psitilde_cs_00_2 - 0.711111111111111*psitilde_cs_00_1;
1260
const double psitilde_cs_01_0 = 1;
1261
const double psitilde_cs_01_1 = 3*z + 2;
1262
const double psitilde_cs_01_2 = 0.777777777777778*psitilde_cs_01_1 + 2.33333333333333*z*psitilde_cs_01_1 - 0.555555555555556*psitilde_cs_01_0;
1263
const double psitilde_cs_02_0 = 1;
1264
const double psitilde_cs_02_1 = 4*z + 3;
1265
const double psitilde_cs_03_0 = 1;
1266
const double psitilde_cs_10_0 = 1;
1267
const double psitilde_cs_10_1 = 3*z + 2;
1268
const double psitilde_cs_10_2 = 0.777777777777778*psitilde_cs_10_1 + 2.33333333333333*z*psitilde_cs_10_1 - 0.555555555555556*psitilde_cs_10_0;
1269
const double psitilde_cs_11_0 = 1;
1270
const double psitilde_cs_11_1 = 4*z + 3;
1271
const double psitilde_cs_12_0 = 1;
1272
const double psitilde_cs_20_0 = 1;
1273
const double psitilde_cs_20_1 = 4*z + 3;
1274
const double psitilde_cs_21_0 = 1;
1275
const double psitilde_cs_30_0 = 1;
1276
1277
// Compute basisvalues
1278
const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
1279
const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;
1280
const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;
1281
const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;
1282
const double basisvalue4 = 5.1234753829798*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_0;
1283
const double basisvalue5 = 3.96862696659689*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_0;
1284
const double basisvalue6 = 2.29128784747792*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_0;
1285
const double basisvalue7 = 3.24037034920393*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_1;
1286
const double basisvalue8 = 1.87082869338697*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_1;
1287
const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;
1288
const double basisvalue10 = 7.93725393319377*psitilde_a_3*scalings_y_3*psitilde_bs_3_0*scalings_z_3*psitilde_cs_30_0;
1289
const double basisvalue11 = 6.70820393249937*psitilde_a_2*scalings_y_2*psitilde_bs_2_1*scalings_z_3*psitilde_cs_21_0;
1290
const double basisvalue12 = 5.19615242270663*psitilde_a_1*scalings_y_1*psitilde_bs_1_2*scalings_z_3*psitilde_cs_12_0;
1291
const double basisvalue13 = 3*psitilde_a_0*scalings_y_0*psitilde_bs_0_3*scalings_z_3*psitilde_cs_03_0;
1292
const double basisvalue14 = 5.80947501931113*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_1;
1293
const double basisvalue15 = 4.5*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_1;
1294
const double basisvalue16 = 2.59807621135332*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_1;
1295
const double basisvalue17 = 3.67423461417477*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_2;
1296
const double basisvalue18 = 2.12132034355964*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_2;
1297
const double basisvalue19 = 1.5*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_3;
1298
1299
// Table(s) of coefficients
1300
const static double coefficients0[20][20] = \
1301
{{0.0288675134594814, 0.0130410132739326, 0.00752923252421041, 0.00532397137499949, 0.018298126367785, 0.014173667737846, 0.00818317088384972, 0.0115727512471569, 0.0066815310478106, 0.00472455591261533, -0.028347335475692, -0.0239578711874978, -0.0185576872239523, -0.0107142857142857, -0.0207481250689683, -0.0160714285714286, -0.00927884361197612, -0.0131222664791956, -0.00757614408414157, -0.00535714285714285},
1302
{0.0288675134594813, -0.0130410132739325, 0.0075292325242104, 0.00532397137499953, 0.018298126367785, -0.014173667737846, 0.00818317088384972, -0.0115727512471569, 0.0066815310478106, 0.00472455591261534, 0.028347335475692, -0.0239578711874977, 0.0185576872239523, -0.0107142857142857, -0.0207481250689683, 0.0160714285714286, -0.00927884361197613, 0.0131222664791956, -0.00757614408414159, -0.00535714285714286},
1303
{0.0288675134594812, 0, -0.0150584650484208, 0.00532397137499948, 0, 0, 0.0245495126515492, 0, -0.0133630620956212, 0.00472455591261538, 0, 0, 0, 0.0428571428571428, 0, 0, -0.0278365308359284, 0, 0.0151522881682832, -0.00535714285714287},
1304
{0.0288675134594813, 0, 0, -0.0159719141249985, 0, 0, 0, 0, 0, 0.028347335475692, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0535714285714286},
1305
{0, 0, 0.112938487863156, -0.063887656499994, 0, 0, 0.0736485379546474, 0, 0.0267261241912424, -0.0236227795630767, 0, 0, 0, 0, 0, 0, 0.0649519052838329, 0, -0.0606091526731327, 0.0267857142857143},
1306
{0, 0, -0.0225876975726313, 0.127775312999988, 0, 0, 0, 0, 0.0668153104781061, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0, 0.0757614408414158, -0.0535714285714286},
1307
{0, 0.097807599554494, -0.0564692439315782, -0.063887656499994, 0.054894379103355, -0.0425210032135381, 0.0245495126515491, 0.0231455024943138, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, -0.0375, 0.021650635094611, -0.0524890659167824, 0.0303045763365663, 0.0267857142857143},
1308
{0, -0.0195615199108988, 0.0112938487863157, 0.127775312999988, 0, 0, 0, 0.0578637562357845, -0.0334076552390531, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, 0.065611332395978, -0.0378807204207079, -0.0535714285714286},
1309
{0, 0.097807599554494, -0.0790569415042095, -0.031943828249997, 0.054894379103355, 0.014173667737846, -0.0245495126515491, -0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, -0.0618589574131742, 0.0428571428571429, -0.00691604168965609, -0.0160714285714286, 0.0154647393532935, 0.00874817765279706, 0, -0.00535714285714286},
1310
{0, -0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, 0.0566946709513841, 0.0245495126515492, -0.0115727512471569, -0.0467707173346742, 0.0236227795630767, 0, 0, 0.0618589574131742, -0.0642857142857143, 0, -0.0214285714285714, 0.00927884361197613, 0.00437408882639853, 0.00757614408414158, -0.00535714285714285},
1311
{0, -0.0978075995544939, -0.0564692439315781, -0.063887656499994, 0.054894379103355, 0.0425210032135381, 0.0245495126515491, -0.0231455024943137, -0.0133630620956212, -0.0236227795630767, 0, 0, 0, 0, 0.0484122918275927, 0.0375, 0.021650635094611, 0.0524890659167824, 0.0303045763365663, 0.0267857142857143},
1312
{0, 0.0195615199108988, 0.0112938487863156, 0.127775312999988, 0, 0, 0, -0.0578637562357845, -0.033407655239053, 0.0472455591261534, 0, 0, 0, 0, 0, 0, 0, -0.065611332395978, -0.0378807204207079, -0.0535714285714286},
1313
{0, -0.097807599554494, -0.0790569415042095, -0.031943828249997, 0.054894379103355, -0.014173667737846, -0.0245495126515492, 0.0462910049886276, 0.0133630620956212, 0.0236227795630767, 0, 0.0479157423749955, 0.0618589574131742, 0.0428571428571429, -0.0069160416896561, 0.0160714285714286, 0.0154647393532935, -0.00874817765279706, 0, -0.00535714285714287},
1314
{0, 0.0195615199108988, 0.124232336649472, -0.031943828249997, 0, -0.0566946709513841, 0.0245495126515492, 0.0115727512471569, -0.0467707173346743, 0.0236227795630767, 0, 0, -0.0618589574131742, -0.0642857142857143, 0, 0.0214285714285714, 0.00927884361197613, -0.00437408882639853, 0.00757614408414157, -0.00535714285714286},
1315
{0, -0.117369119465393, -0.0451753951452625, -0.031943828249997, -0.018298126367785, 0.0425210032135381, 0.0409158544192485, 0.0347182537414707, 0.033407655239053, 0.0236227795630767, 0.0850420064270761, 0.0239578711874977, -0.00618589574131741, -0.0107142857142857, 0.0207481250689683, -0.00535714285714284, -0.00927884361197614, -0.00437408882639852, -0.0075761440841416, -0.00535714285714286},
1316
{0, 0.117369119465393, -0.0451753951452626, -0.031943828249997, -0.018298126367785, -0.0425210032135381, 0.0409158544192486, -0.0347182537414707, 0.0334076552390531, 0.0236227795630767, -0.0850420064270761, 0.0239578711874978, 0.0061858957413174, -0.0107142857142857, 0.0207481250689683, 0.00535714285714285, -0.00927884361197613, 0.00437408882639852, -0.00757614408414159, -0.00535714285714286},
1317
{0.259807621135332, 0.117369119465393, 0.0677630927178939, 0.0479157423749955, 0, 0.0850420064270761, -0.0736485379546474, 0.0694365074829413, 0.0400891862868636, -0.0992156741649222, 0, 0, 0, 0, 0, 0.075, -0.0649519052838329, -0.0262445329583912, -0.0151522881682832, 0.0267857142857143},
1318
{0.259807621135332, -0.117369119465393, 0.0677630927178938, 0.0479157423749955, 0, -0.0850420064270761, -0.0736485379546474, -0.0694365074829414, 0.0400891862868636, -0.0992156741649221, 0, 0, 0, 0, 0, -0.075, -0.0649519052838329, 0.0262445329583912, -0.0151522881682832, 0.0267857142857143},
1319
{0.259807621135332, 0, -0.135526185435788, 0.0479157423749955, -0.10978875820671, 0, 0.0245495126515491, 0, -0.0801783725737273, -0.0992156741649221, 0, 0, 0, 0, -0.0968245836551854, 0, 0.021650635094611, 0, 0.0303045763365663, 0.0267857142857143},
1320
{0.259807621135332, 0, 0, -0.143747227124986, -0.10978875820671, 0, -0.122747563257746, 0, 0, 0.0425210032135381, 0, -0.095831484749991, 0, 0.0428571428571429, 0.0138320833793122, 0, 0.0154647393532935, 0, 0, -0.00535714285714284}};
1321
1322
// Interesting (new) part
1323
// Tables of derivatives of the polynomial base (transpose)
1324
const static double dmats0[20][20] = \
1325
{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1326
{6.32455532033676, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1327
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1328
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1329
{0, 11.2249721603218, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1330
{4.58257569495584, 0, 8.36660026534076, -1.18321595661992, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1331
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1332
{3.74165738677394, 0, 0, 8.69482604771366, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1333
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1334
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1335
{5.49909083394702, 0, -3.3466401061363, -2.36643191323985, 15.4919333848297, 0, 0.692820323027552, 0, 0.565685424949239, 0.400000000000001, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1336
{0, 4.89897948556636, 0, 0, 0, 14.1985914794391, 0, -0.828078671210832, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1337
{3.6, 0, 8.76356092008266, -1.54919333848297, 0, 0, 9.52470471983253, 0, -1.48131215963608, 0.261861468283191, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1338
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1339
{0, 4.24264068711929, 0, 0, 0, 0, 0, 14.3427433120127, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1340
{3.11769145362398, 0, 3.16227766016838, 4.91934955049954, 0, 0, 0, 0, 10.690449676497, -2.41897262725906, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1341
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1342
{2.54558441227157, 0, 0, 7.66811580507233, 0, 0, 0, 0, 0, 10.3691851174526, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1343
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1344
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};
1345
1346
const static double dmats1[20][20] = \
1347
{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1348
{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1349
{5.47722557505166, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1350
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1351
{2.9580398915498, 5.61248608016091, -1.08012344973464, -0.763762615825973, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1352
{2.29128784747791, 7.24568837309472, 4.18330013267038, -0.59160797830996, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1353
{-2.64575131106459, 0, 9.66091783079296, 0.683130051063974, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1354
{1.87082869338697, 0, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1355
{3.24037034920393, 0, 0, 7.52994023880668, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1356
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1357
{2.7495454169735, 5.79655069847578, -1.67332005306815, -1.18321595661992, 7.74596669241483, -1.2, 0.346410161513777, -0.979795897113271, 0.282842712474621, 0.2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1358
{2.32379000772445, 2.44948974278318, 2.82842712474619, -1, 9.16515138991168, 7.09929573971954, -2.04939015319192, -0.414039335605415, -0.478091443733757, 0.169030850945705, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1359
{1.80000000000001, -5.69209978830308, 4.38178046004132, -0.774596669241485, 0, 10.998181667894, 4.76235235991626, 0.962140470884726, -0.740656079818042, 0.130930734141596, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1360
{5.19615242270664, 0, -3.16227766016837, -2.23606797749979, 0, 0, 13.7477270848675, 0, 0.53452248382485, 0.377964473009228, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1361
{2.01246117974981, 2.12132034355964, -0.408248290463862, 3.17542648054294, 0, 0, 0, 7.17137165600636, -1.38013111868471, -1.56144011671765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1362
{1.55884572681199, 2.73861278752583, 1.58113883008419, 2.45967477524977, 0, 0, 0, 9.25820099772551, 5.34522483824849, -1.20948631362953, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1363
{-1.79999999999999, 0, 3.65148371670111, -2.84018778721878, 0, 0, 0, 0, 12.3442679969674, 1.39659449751035, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1364
{1.27279220613578, 0, 0, 3.83405790253616, 0, 0, 0, 0, 0, 5.18459255872629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1365
{2.20454076850486, 0, 0, 6.6407830863536, 0, 0, 0, 0, 0, 8.97997772825746, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1366
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};
1367
1368
const static double dmats2[20][20] = \
1369
{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1370
{3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1371
{1.82574185835055, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1372
{5.16397779494322, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1373
{2.9580398915498, 5.61248608016091, -1.08012344973464, -0.763762615825973, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1374
{2.29128784747792, 1.44913767461894, 4.18330013267038, -0.591607978309959, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1375
{1.32287565553229, 0, 3.86436713231718, -0.341565025531987, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1376
{1.87082869338696, 7.09929573971954, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1377
{1.08012344973464, 0, 7.09929573971954, 2.50998007960222, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1378
{-3.81881307912987, 0, 0, 8.87411967464942, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1379
{2.7495454169735, 5.79655069847578, -1.67332005306815, -1.18321595661992, 7.74596669241483, -1.19999999999999, 0.346410161513777, -0.979795897113271, 0.28284271247462, 0.2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1380
{2.32379000772445, 2.44948974278318, 2.82842712474619, -1, 1.30930734141595, 7.09929573971954, -2.04939015319192, -0.414039335605416, -0.478091443733756, 0.169030850945703, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1381
{1.8, 0.632455532033674, 4.38178046004133, -0.774596669241483, 0, 3.14233761939829, 4.76235235991626, -0.106904496764969, -0.740656079818041, 0.130930734141595, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1382
{1.03923048454133, 0, 3.16227766016838, -0.447213595499959, 0, 0, 5.8918830363718, 0, -0.53452248382485, 0.0755928946018456, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1383
{2.01246117974981, 2.12132034355965, -0.408248290463862, 3.17542648054294, 9.07114735222145, 0, 0, 7.17137165600636, -1.38013111868471, -1.56144011671765, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1384
{1.55884572681199, 0.547722557505166, 1.58113883008419, 2.45967477524977, 0, 9.07114735222145, 0, 1.8516401995451, 5.34522483824849, -1.20948631362953, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1385
{0.9, 0, 1.46059348668044, 1.42009389360939, 0, 0, 9.07114735222146, 0, 4.93770719878694, -0.698297248755176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1386
{1.27279220613579, -6.26099033699941, 0, 3.83405790253616, 0, 0, 0, 10.5830052442584, 0, 5.18459255872629, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1387
{0.734846922834956, 0, -6.26099033699941, 2.21359436211787, 0, 0, 0, 0, 10.5830052442584, 2.99332590941915, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
1388
{5.7157676649773, 0, 0, -4.69574275274955, 0, 0, 0, 0, 0, 12.69960629311, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};
1389
1390
// Compute reference derivatives
1391
// Declare pointer to array of derivatives on FIAT element
1392
double *derivatives = new double [num_derivatives];
1393
1394
// Declare coefficients
1395
double coeff0_0 = 0;
1396
double coeff0_1 = 0;
1397
double coeff0_2 = 0;
1398
double coeff0_3 = 0;
1399
double coeff0_4 = 0;
1400
double coeff0_5 = 0;
1401
double coeff0_6 = 0;
1402
double coeff0_7 = 0;
1403
double coeff0_8 = 0;
1404
double coeff0_9 = 0;
1405
double coeff0_10 = 0;
1406
double coeff0_11 = 0;
1407
double coeff0_12 = 0;
1408
double coeff0_13 = 0;
1409
double coeff0_14 = 0;
1410
double coeff0_15 = 0;
1411
double coeff0_16 = 0;
1412
double coeff0_17 = 0;
1413
double coeff0_18 = 0;
1414
double coeff0_19 = 0;
1415
1416
// Declare new coefficients
1417
double new_coeff0_0 = 0;
1418
double new_coeff0_1 = 0;
1419
double new_coeff0_2 = 0;
1420
double new_coeff0_3 = 0;
1421
double new_coeff0_4 = 0;
1422
double new_coeff0_5 = 0;
1423
double new_coeff0_6 = 0;
1424
double new_coeff0_7 = 0;
1425
double new_coeff0_8 = 0;
1426
double new_coeff0_9 = 0;
1427
double new_coeff0_10 = 0;
1428
double new_coeff0_11 = 0;
1429
double new_coeff0_12 = 0;
1430
double new_coeff0_13 = 0;
1431
double new_coeff0_14 = 0;
1432
double new_coeff0_15 = 0;
1433
double new_coeff0_16 = 0;
1434
double new_coeff0_17 = 0;
1435
double new_coeff0_18 = 0;
1436
double new_coeff0_19 = 0;
1437
1438
// Loop possible derivatives
1439
for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
1440
{
1441
// Get values from coefficients array
1442
new_coeff0_0 = coefficients0[dof][0];
1443
new_coeff0_1 = coefficients0[dof][1];
1444
new_coeff0_2 = coefficients0[dof][2];
1445
new_coeff0_3 = coefficients0[dof][3];
1446
new_coeff0_4 = coefficients0[dof][4];
1447
new_coeff0_5 = coefficients0[dof][5];
1448
new_coeff0_6 = coefficients0[dof][6];
1449
new_coeff0_7 = coefficients0[dof][7];
1450
new_coeff0_8 = coefficients0[dof][8];
1451
new_coeff0_9 = coefficients0[dof][9];
1452
new_coeff0_10 = coefficients0[dof][10];
1453
new_coeff0_11 = coefficients0[dof][11];
1454
new_coeff0_12 = coefficients0[dof][12];
1455
new_coeff0_13 = coefficients0[dof][13];
1456
new_coeff0_14 = coefficients0[dof][14];
1457
new_coeff0_15 = coefficients0[dof][15];
1458
new_coeff0_16 = coefficients0[dof][16];
1459
new_coeff0_17 = coefficients0[dof][17];
1460
new_coeff0_18 = coefficients0[dof][18];
1461
new_coeff0_19 = coefficients0[dof][19];
1462
1463
// Loop derivative order
1464
for (unsigned int j = 0; j < n; j++)
1465
{
1466
// Update old coefficients
1467
coeff0_0 = new_coeff0_0;
1468
coeff0_1 = new_coeff0_1;
1469
coeff0_2 = new_coeff0_2;
1470
coeff0_3 = new_coeff0_3;
1471
coeff0_4 = new_coeff0_4;
1472
coeff0_5 = new_coeff0_5;
1473
coeff0_6 = new_coeff0_6;
1474
coeff0_7 = new_coeff0_7;
1475
coeff0_8 = new_coeff0_8;
1476
coeff0_9 = new_coeff0_9;
1477
coeff0_10 = new_coeff0_10;
1478
coeff0_11 = new_coeff0_11;
1479
coeff0_12 = new_coeff0_12;
1480
coeff0_13 = new_coeff0_13;
1481
coeff0_14 = new_coeff0_14;
1482
coeff0_15 = new_coeff0_15;
1483
coeff0_16 = new_coeff0_16;
1484
coeff0_17 = new_coeff0_17;
1485
coeff0_18 = new_coeff0_18;
1486
coeff0_19 = new_coeff0_19;
1487
1488
if(combinations[deriv_num][j] == 0)
1489
{
1490
new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0] + coeff0_3*dmats0[3][0] + coeff0_4*dmats0[4][0] + coeff0_5*dmats0[5][0] + coeff0_6*dmats0[6][0] + coeff0_7*dmats0[7][0] + coeff0_8*dmats0[8][0] + coeff0_9*dmats0[9][0] + coeff0_10*dmats0[10][0] + coeff0_11*dmats0[11][0] + coeff0_12*dmats0[12][0] + coeff0_13*dmats0[13][0] + coeff0_14*dmats0[14][0] + coeff0_15*dmats0[15][0] + coeff0_16*dmats0[16][0] + coeff0_17*dmats0[17][0] + coeff0_18*dmats0[18][0] + coeff0_19*dmats0[19][0];
1491
new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1] + coeff0_3*dmats0[3][1] + coeff0_4*dmats0[4][1] + coeff0_5*dmats0[5][1] + coeff0_6*dmats0[6][1] + coeff0_7*dmats0[7][1] + coeff0_8*dmats0[8][1] + coeff0_9*dmats0[9][1] + coeff0_10*dmats0[10][1] + coeff0_11*dmats0[11][1] + coeff0_12*dmats0[12][1] + coeff0_13*dmats0[13][1] + coeff0_14*dmats0[14][1] + coeff0_15*dmats0[15][1] + coeff0_16*dmats0[16][1] + coeff0_17*dmats0[17][1] + coeff0_18*dmats0[18][1] + coeff0_19*dmats0[19][1];
1492
new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2] + coeff0_3*dmats0[3][2] + coeff0_4*dmats0[4][2] + coeff0_5*dmats0[5][2] + coeff0_6*dmats0[6][2] + coeff0_7*dmats0[7][2] + coeff0_8*dmats0[8][2] + coeff0_9*dmats0[9][2] + coeff0_10*dmats0[10][2] + coeff0_11*dmats0[11][2] + coeff0_12*dmats0[12][2] + coeff0_13*dmats0[13][2] + coeff0_14*dmats0[14][2] + coeff0_15*dmats0[15][2] + coeff0_16*dmats0[16][2] + coeff0_17*dmats0[17][2] + coeff0_18*dmats0[18][2] + coeff0_19*dmats0[19][2];
1493
new_coeff0_3 = coeff0_0*dmats0[0][3] + coeff0_1*dmats0[1][3] + coeff0_2*dmats0[2][3] + coeff0_3*dmats0[3][3] + coeff0_4*dmats0[4][3] + coeff0_5*dmats0[5][3] + coeff0_6*dmats0[6][3] + coeff0_7*dmats0[7][3] + coeff0_8*dmats0[8][3] + coeff0_9*dmats0[9][3] + coeff0_10*dmats0[10][3] + coeff0_11*dmats0[11][3] + coeff0_12*dmats0[12][3] + coeff0_13*dmats0[13][3] + coeff0_14*dmats0[14][3] + coeff0_15*dmats0[15][3] + coeff0_16*dmats0[16][3] + coeff0_17*dmats0[17][3] + coeff0_18*dmats0[18][3] + coeff0_19*dmats0[19][3];
1494
new_coeff0_4 = coeff0_0*dmats0[0][4] + coeff0_1*dmats0[1][4] + coeff0_2*dmats0[2][4] + coeff0_3*dmats0[3][4] + coeff0_4*dmats0[4][4] + coeff0_5*dmats0[5][4] + coeff0_6*dmats0[6][4] + coeff0_7*dmats0[7][4] + coeff0_8*dmats0[8][4] + coeff0_9*dmats0[9][4] + coeff0_10*dmats0[10][4] + coeff0_11*dmats0[11][4] + coeff0_12*dmats0[12][4] + coeff0_13*dmats0[13][4] + coeff0_14*dmats0[14][4] + coeff0_15*dmats0[15][4] + coeff0_16*dmats0[16][4] + coeff0_17*dmats0[17][4] + coeff0_18*dmats0[18][4] + coeff0_19*dmats0[19][4];
1495
new_coeff0_5 = coeff0_0*dmats0[0][5] + coeff0_1*dmats0[1][5] + coeff0_2*dmats0[2][5] + coeff0_3*dmats0[3][5] + coeff0_4*dmats0[4][5] + coeff0_5*dmats0[5][5] + coeff0_6*dmats0[6][5] + coeff0_7*dmats0[7][5] + coeff0_8*dmats0[8][5] + coeff0_9*dmats0[9][5] + coeff0_10*dmats0[10][5] + coeff0_11*dmats0[11][5] + coeff0_12*dmats0[12][5] + coeff0_13*dmats0[13][5] + coeff0_14*dmats0[14][5] + coeff0_15*dmats0[15][5] + coeff0_16*dmats0[16][5] + coeff0_17*dmats0[17][5] + coeff0_18*dmats0[18][5] + coeff0_19*dmats0[19][5];
1496
new_coeff0_6 = coeff0_0*dmats0[0][6] + coeff0_1*dmats0[1][6] + coeff0_2*dmats0[2][6] + coeff0_3*dmats0[3][6] + coeff0_4*dmats0[4][6] + coeff0_5*dmats0[5][6] + coeff0_6*dmats0[6][6] + coeff0_7*dmats0[7][6] + coeff0_8*dmats0[8][6] + coeff0_9*dmats0[9][6] + coeff0_10*dmats0[10][6] + coeff0_11*dmats0[11][6] + coeff0_12*dmats0[12][6] + coeff0_13*dmats0[13][6] + coeff0_14*dmats0[14][6] + coeff0_15*dmats0[15][6] + coeff0_16*dmats0[16][6] + coeff0_17*dmats0[17][6] + coeff0_18*dmats0[18][6] + coeff0_19*dmats0[19][6];
1497
new_coeff0_7 = coeff0_0*dmats0[0][7] + coeff0_1*dmats0[1][7] + coeff0_2*dmats0[2][7] + coeff0_3*dmats0[3][7] + coeff0_4*dmats0[4][7] + coeff0_5*dmats0[5][7] + coeff0_6*dmats0[6][7] + coeff0_7*dmats0[7][7] + coeff0_8*dmats0[8][7] + coeff0_9*dmats0[9][7] + coeff0_10*dmats0[10][7] + coeff0_11*dmats0[11][7] + coeff0_12*dmats0[12][7] + coeff0_13*dmats0[13][7] + coeff0_14*dmats0[14][7] + coeff0_15*dmats0[15][7] + coeff0_16*dmats0[16][7] + coeff0_17*dmats0[17][7] + coeff0_18*dmats0[18][7] + coeff0_19*dmats0[19][7];
1498
new_coeff0_8 = coeff0_0*dmats0[0][8] + coeff0_1*dmats0[1][8] + coeff0_2*dmats0[2][8] + coeff0_3*dmats0[3][8] + coeff0_4*dmats0[4][8] + coeff0_5*dmats0[5][8] + coeff0_6*dmats0[6][8] + coeff0_7*dmats0[7][8] + coeff0_8*dmats0[8][8] + coeff0_9*dmats0[9][8] + coeff0_10*dmats0[10][8] + coeff0_11*dmats0[11][8] + coeff0_12*dmats0[12][8] + coeff0_13*dmats0[13][8] + coeff0_14*dmats0[14][8] + coeff0_15*dmats0[15][8] + coeff0_16*dmats0[16][8] + coeff0_17*dmats0[17][8] + coeff0_18*dmats0[18][8] + coeff0_19*dmats0[19][8];
1499
new_coeff0_9 = coeff0_0*dmats0[0][9] + coeff0_1*dmats0[1][9] + coeff0_2*dmats0[2][9] + coeff0_3*dmats0[3][9] + coeff0_4*dmats0[4][9] + coeff0_5*dmats0[5][9] + coeff0_6*dmats0[6][9] + coeff0_7*dmats0[7][9] + coeff0_8*dmats0[8][9] + coeff0_9*dmats0[9][9] + coeff0_10*dmats0[10][9] + coeff0_11*dmats0[11][9] + coeff0_12*dmats0[12][9] + coeff0_13*dmats0[13][9] + coeff0_14*dmats0[14][9] + coeff0_15*dmats0[15][9] + coeff0_16*dmats0[16][9] + coeff0_17*dmats0[17][9] + coeff0_18*dmats0[18][9] + coeff0_19*dmats0[19][9];
1500
new_coeff0_10 = coeff0_0*dmats0[0][10] + coeff0_1*dmats0[1][10] + coeff0_2*dmats0[2][10] + coeff0_3*dmats0[3][10] + coeff0_4*dmats0[4][10] + coeff0_5*dmats0[5][10] + coeff0_6*dmats0[6][10] + coeff0_7*dmats0[7][10] + coeff0_8*dmats0[8][10] + coeff0_9*dmats0[9][10] + coeff0_10*dmats0[10][10] + coeff0_11*dmats0[11][10] + coeff0_12*dmats0[12][10] + coeff0_13*dmats0[13][10] + coeff0_14*dmats0[14][10] + coeff0_15*dmats0[15][10] + coeff0_16*dmats0[16][10] + coeff0_17*dmats0[17][10] + coeff0_18*dmats0[18][10] + coeff0_19*dmats0[19][10];
1501
new_coeff0_11 = coeff0_0*dmats0[0][11] + coeff0_1*dmats0[1][11] + coeff0_2*dmats0[2][11] + coeff0_3*dmats0[3][11] + coeff0_4*dmats0[4][11] + coeff0_5*dmats0[5][11] + coeff0_6*dmats0[6][11] + coeff0_7*dmats0[7][11] + coeff0_8*dmats0[8][11] + coeff0_9*dmats0[9][11] + coeff0_10*dmats0[10][11] + coeff0_11*dmats0[11][11] + coeff0_12*dmats0[12][11] + coeff0_13*dmats0[13][11] + coeff0_14*dmats0[14][11] + coeff0_15*dmats0[15][11] + coeff0_16*dmats0[16][11] + coeff0_17*dmats0[17][11] + coeff0_18*dmats0[18][11] + coeff0_19*dmats0[19][11];
1502
new_coeff0_12 = coeff0_0*dmats0[0][12] + coeff0_1*dmats0[1][12] + coeff0_2*dmats0[2][12] + coeff0_3*dmats0[3][12] + coeff0_4*dmats0[4][12] + coeff0_5*dmats0[5][12] + coeff0_6*dmats0[6][12] + coeff0_7*dmats0[7][12] + coeff0_8*dmats0[8][12] + coeff0_9*dmats0[9][12] + coeff0_10*dmats0[10][12] + coeff0_11*dmats0[11][12] + coeff0_12*dmats0[12][12] + coeff0_13*dmats0[13][12] + coeff0_14*dmats0[14][12] + coeff0_15*dmats0[15][12] + coeff0_16*dmats0[16][12] + coeff0_17*dmats0[17][12] + coeff0_18*dmats0[18][12] + coeff0_19*dmats0[19][12];
1503
new_coeff0_13 = coeff0_0*dmats0[0][13] + coeff0_1*dmats0[1][13] + coeff0_2*dmats0[2][13] + coeff0_3*dmats0[3][13] + coeff0_4*dmats0[4][13] + coeff0_5*dmats0[5][13] + coeff0_6*dmats0[6][13] + coeff0_7*dmats0[7][13] + coeff0_8*dmats0[8][13] + coeff0_9*dmats0[9][13] + coeff0_10*dmats0[10][13] + coeff0_11*dmats0[11][13] + coeff0_12*dmats0[12][13] + coeff0_13*dmats0[13][13] + coeff0_14*dmats0[14][13] + coeff0_15*dmats0[15][13] + coeff0_16*dmats0[16][13] + coeff0_17*dmats0[17][13] + coeff0_18*dmats0[18][13] + coeff0_19*dmats0[19][13];
1504
new_coeff0_14 = coeff0_0*dmats0[0][14] + coeff0_1*dmats0[1][14] + coeff0_2*dmats0[2][14] + coeff0_3*dmats0[3][14] + coeff0_4*dmats0[4][14] + coeff0_5*dmats0[5][14] + coeff0_6*dmats0[6][14] + coeff0_7*dmats0[7][14] + coeff0_8*dmats0[8][14] + coeff0_9*dmats0[9][14] + coeff0_10*dmats0[10][14] + coeff0_11*dmats0[11][14] + coeff0_12*dmats0[12][14] + coeff0_13*dmats0[13][14] + coeff0_14*dmats0[14][14] + coeff0_15*dmats0[15][14] + coeff0_16*dmats0[16][14] + coeff0_17*dmats0[17][14] + coeff0_18*dmats0[18][14] + coeff0_19*dmats0[19][14];
1505
new_coeff0_15 = coeff0_0*dmats0[0][15] + coeff0_1*dmats0[1][15] + coeff0_2*dmats0[2][15] + coeff0_3*dmats0[3][15] + coeff0_4*dmats0[4][15] + coeff0_5*dmats0[5][15] + coeff0_6*dmats0[6][15] + coeff0_7*dmats0[7][15] + coeff0_8*dmats0[8][15] + coeff0_9*dmats0[9][15] + coeff0_10*dmats0[10][15] + coeff0_11*dmats0[11][15] + coeff0_12*dmats0[12][15] + coeff0_13*dmats0[13][15] + coeff0_14*dmats0[14][15] + coeff0_15*dmats0[15][15] + coeff0_16*dmats0[16][15] + coeff0_17*dmats0[17][15] + coeff0_18*dmats0[18][15] + coeff0_19*dmats0[19][15];
1506
new_coeff0_16 = coeff0_0*dmats0[0][16] + coeff0_1*dmats0[1][16] + coeff0_2*dmats0[2][16] + coeff0_3*dmats0[3][16] + coeff0_4*dmats0[4][16] + coeff0_5*dmats0[5][16] + coeff0_6*dmats0[6][16] + coeff0_7*dmats0[7][16] + coeff0_8*dmats0[8][16] + coeff0_9*dmats0[9][16] + coeff0_10*dmats0[10][16] + coeff0_11*dmats0[11][16] + coeff0_12*dmats0[12][16] + coeff0_13*dmats0[13][16] + coeff0_14*dmats0[14][16] + coeff0_15*dmats0[15][16] + coeff0_16*dmats0[16][16] + coeff0_17*dmats0[17][16] + coeff0_18*dmats0[18][16] + coeff0_19*dmats0[19][16];
1507
new_coeff0_17 = coeff0_0*dmats0[0][17] + coeff0_1*dmats0[1][17] + coeff0_2*dmats0[2][17] + coeff0_3*dmats0[3][17] + coeff0_4*dmats0[4][17] + coeff0_5*dmats0[5][17] + coeff0_6*dmats0[6][17] + coeff0_7*dmats0[7][17] + coeff0_8*dmats0[8][17] + coeff0_9*dmats0[9][17] + coeff0_10*dmats0[10][17] + coeff0_11*dmats0[11][17] + coeff0_12*dmats0[12][17] + coeff0_13*dmats0[13][17] + coeff0_14*dmats0[14][17] + coeff0_15*dmats0[15][17] + coeff0_16*dmats0[16][17] + coeff0_17*dmats0[17][17] + coeff0_18*dmats0[18][17] + coeff0_19*dmats0[19][17];
1508
new_coeff0_18 = coeff0_0*dmats0[0][18] + coeff0_1*dmats0[1][18] + coeff0_2*dmats0[2][18] + coeff0_3*dmats0[3][18] + coeff0_4*dmats0[4][18] + coeff0_5*dmats0[5][18] + coeff0_6*dmats0[6][18] + coeff0_7*dmats0[7][18] + coeff0_8*dmats0[8][18] + coeff0_9*dmats0[9][18] + coeff0_10*dmats0[10][18] + coeff0_11*dmats0[11][18] + coeff0_12*dmats0[12][18] + coeff0_13*dmats0[13][18] + coeff0_14*dmats0[14][18] + coeff0_15*dmats0[15][18] + coeff0_16*dmats0[16][18] + coeff0_17*dmats0[17][18] + coeff0_18*dmats0[18][18] + coeff0_19*dmats0[19][18];
1509
new_coeff0_19 = coeff0_0*dmats0[0][19] + coeff0_1*dmats0[1][19] + coeff0_2*dmats0[2][19] + coeff0_3*dmats0[3][19] + coeff0_4*dmats0[4][19] + coeff0_5*dmats0[5][19] + coeff0_6*dmats0[6][19] + coeff0_7*dmats0[7][19] + coeff0_8*dmats0[8][19] + coeff0_9*dmats0[9][19] + coeff0_10*dmats0[10][19] + coeff0_11*dmats0[11][19] + coeff0_12*dmats0[12][19] + coeff0_13*dmats0[13][19] + coeff0_14*dmats0[14][19] + coeff0_15*dmats0[15][19] + coeff0_16*dmats0[16][19] + coeff0_17*dmats0[17][19] + coeff0_18*dmats0[18][19] + coeff0_19*dmats0[19][19];
1510
}
1511
if(combinations[deriv_num][j] == 1)
1512
{
1513
new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0] + coeff0_3*dmats1[3][0] + coeff0_4*dmats1[4][0] + coeff0_5*dmats1[5][0] + coeff0_6*dmats1[6][0] + coeff0_7*dmats1[7][0] + coeff0_8*dmats1[8][0] + coeff0_9*dmats1[9][0] + coeff0_10*dmats1[10][0] + coeff0_11*dmats1[11][0] + coeff0_12*dmats1[12][0] + coeff0_13*dmats1[13][0] + coeff0_14*dmats1[14][0] + coeff0_15*dmats1[15][0] + coeff0_16*dmats1[16][0] + coeff0_17*dmats1[17][0] + coeff0_18*dmats1[18][0] + coeff0_19*dmats1[19][0];
1514
new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1] + coeff0_3*dmats1[3][1] + coeff0_4*dmats1[4][1] + coeff0_5*dmats1[5][1] + coeff0_6*dmats1[6][1] + coeff0_7*dmats1[7][1] + coeff0_8*dmats1[8][1] + coeff0_9*dmats1[9][1] + coeff0_10*dmats1[10][1] + coeff0_11*dmats1[11][1] + coeff0_12*dmats1[12][1] + coeff0_13*dmats1[13][1] + coeff0_14*dmats1[14][1] + coeff0_15*dmats1[15][1] + coeff0_16*dmats1[16][1] + coeff0_17*dmats1[17][1] + coeff0_18*dmats1[18][1] + coeff0_19*dmats1[19][1];
1515
new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2] + coeff0_3*dmats1[3][2] + coeff0_4*dmats1[4][2] + coeff0_5*dmats1[5][2] + coeff0_6*dmats1[6][2] + coeff0_7*dmats1[7][2] + coeff0_8*dmats1[8][2] + coeff0_9*dmats1[9][2] + coeff0_10*dmats1[10][2] + coeff0_11*dmats1[11][2] + coeff0_12*dmats1[12][2] + coeff0_13*dmats1[13][2] + coeff0_14*dmats1[14][2] + coeff0_15*dmats1[15][2] + coeff0_16*dmats1[16][2] + coeff0_17*dmats1[17][2] + coeff0_18*dmats1[18][2] + coeff0_19*dmats1[19][2];
1516
new_coeff0_3 = coeff0_0*dmats1[0][3] + coeff0_1*dmats1[1][3] + coeff0_2*dmats1[2][3] + coeff0_3*dmats1[3][3] + coeff0_4*dmats1[4][3] + coeff0_5*dmats1[5][3] + coeff0_6*dmats1[6][3] + coeff0_7*dmats1[7][3] + coeff0_8*dmats1[8][3] + coeff0_9*dmats1[9][3] + coeff0_10*dmats1[10][3] + coeff0_11*dmats1[11][3] + coeff0_12*dmats1[12][3] + coeff0_13*dmats1[13][3] + coeff0_14*dmats1[14][3] + coeff0_15*dmats1[15][3] + coeff0_16*dmats1[16][3] + coeff0_17*dmats1[17][3] + coeff0_18*dmats1[18][3] + coeff0_19*dmats1[19][3];
1517
new_coeff0_4 = coeff0_0*dmats1[0][4] + coeff0_1*dmats1[1][4] + coeff0_2*dmats1[2][4] + coeff0_3*dmats1[3][4] + coeff0_4*dmats1[4][4] + coeff0_5*dmats1[5][4] + coeff0_6*dmats1[6][4] + coeff0_7*dmats1[7][4] + coeff0_8*dmats1[8][4] + coeff0_9*dmats1[9][4] + coeff0_10*dmats1[10][4] + coeff0_11*dmats1[11][4] + coeff0_12*dmats1[12][4] + coeff0_13*dmats1[13][4] + coeff0_14*dmats1[14][4] + coeff0_15*dmats1[15][4] + coeff0_16*dmats1[16][4] + coeff0_17*dmats1[17][4] + coeff0_18*dmats1[18][4] + coeff0_19*dmats1[19][4];
1518
new_coeff0_5 = coeff0_0*dmats1[0][5] + coeff0_1*dmats1[1][5] + coeff0_2*dmats1[2][5] + coeff0_3*dmats1[3][5] + coeff0_4*dmats1[4][5] + coeff0_5*dmats1[5][5] + coeff0_6*dmats1[6][5] + coeff0_7*dmats1[7][5] + coeff0_8*dmats1[8][5] + coeff0_9*dmats1[9][5] + coeff0_10*dmats1[10][5] + coeff0_11*dmats1[11][5] + coeff0_12*dmats1[12][5] + coeff0_13*dmats1[13][5] + coeff0_14*dmats1[14][5] + coeff0_15*dmats1[15][5] + coeff0_16*dmats1[16][5] + coeff0_17*dmats1[17][5] + coeff0_18*dmats1[18][5] + coeff0_19*dmats1[19][5];
1519
new_coeff0_6 = coeff0_0*dmats1[0][6] + coeff0_1*dmats1[1][6] + coeff0_2*dmats1[2][6] + coeff0_3*dmats1[3][6] + coeff0_4*dmats1[4][6] + coeff0_5*dmats1[5][6] + coeff0_6*dmats1[6][6] + coeff0_7*dmats1[7][6] + coeff0_8*dmats1[8][6] + coeff0_9*dmats1[9][6] + coeff0_10*dmats1[10][6] + coeff0_11*dmats1[11][6] + coeff0_12*dmats1[12][6] + coeff0_13*dmats1[13][6] + coeff0_14*dmats1[14][6] + coeff0_15*dmats1[15][6] + coeff0_16*dmats1[16][6] + coeff0_17*dmats1[17][6] + coeff0_18*dmats1[18][6] + coeff0_19*dmats1[19][6];
1520
new_coeff0_7 = coeff0_0*dmats1[0][7] + coeff0_1*dmats1[1][7] + coeff0_2*dmats1[2][7] + coeff0_3*dmats1[3][7] + coeff0_4*dmats1[4][7] + coeff0_5*dmats1[5][7] + coeff0_6*dmats1[6][7] + coeff0_7*dmats1[7][7] + coeff0_8*dmats1[8][7] + coeff0_9*dmats1[9][7] + coeff0_10*dmats1[10][7] + coeff0_11*dmats1[11][7] + coeff0_12*dmats1[12][7] + coeff0_13*dmats1[13][7] + coeff0_14*dmats1[14][7] + coeff0_15*dmats1[15][7] + coeff0_16*dmats1[16][7] + coeff0_17*dmats1[17][7] + coeff0_18*dmats1[18][7] + coeff0_19*dmats1[19][7];
1521
new_coeff0_8 = coeff0_0*dmats1[0][8] + coeff0_1*dmats1[1][8] + coeff0_2*dmats1[2][8] + coeff0_3*dmats1[3][8] + coeff0_4*dmats1[4][8] + coeff0_5*dmats1[5][8] + coeff0_6*dmats1[6][8] + coeff0_7*dmats1[7][8] + coeff0_8*dmats1[8][8] + coeff0_9*dmats1[9][8] + coeff0_10*dmats1[10][8] + coeff0_11*dmats1[11][8] + coeff0_12*dmats1[12][8] + coeff0_13*dmats1[13][8] + coeff0_14*dmats1[14][8] + coeff0_15*dmats1[15][8] + coeff0_16*dmats1[16][8] + coeff0_17*dmats1[17][8] + coeff0_18*dmats1[18][8] + coeff0_19*dmats1[19][8];
1522
new_coeff0_9 = coeff0_0*dmats1[0][9] + coeff0_1*dmats1[1][9] + coeff0_2*dmats1[2][9] + coeff0_3*dmats1[3][9] + coeff0_4*dmats1[4][9] + coeff0_5*dmats1[5][9] + coeff0_6*dmats1[6][9] + coeff0_7*dmats1[7][9] + coeff0_8*dmats1[8][9] + coeff0_9*dmats1[9][9] + coeff0_10*dmats1[10][9] + coeff0_11*dmats1[11][9] + coeff0_12*dmats1[12][9] + coeff0_13*dmats1[13][9] + coeff0_14*dmats1[14][9] + coeff0_15*dmats1[15][9] + coeff0_16*dmats1[16][9] + coeff0_17*dmats1[17][9] + coeff0_18*dmats1[18][9] + coeff0_19*dmats1[19][9];
1523
new_coeff0_10 = coeff0_0*dmats1[0][10] + coeff0_1*dmats1[1][10] + coeff0_2*dmats1[2][10] + coeff0_3*dmats1[3][10] + coeff0_4*dmats1[4][10] + coeff0_5*dmats1[5][10] + coeff0_6*dmats1[6][10] + coeff0_7*dmats1[7][10] + coeff0_8*dmats1[8][10] + coeff0_9*dmats1[9][10] + coeff0_10*dmats1[10][10] + coeff0_11*dmats1[11][10] + coeff0_12*dmats1[12][10] + coeff0_13*dmats1[13][10] + coeff0_14*dmats1[14][10] + coeff0_15*dmats1[15][10] + coeff0_16*dmats1[16][10] + coeff0_17*dmats1[17][10] + coeff0_18*dmats1[18][10] + coeff0_19*dmats1[19][10];
1524
new_coeff0_11 = coeff0_0*dmats1[0][11] + coeff0_1*dmats1[1][11] + coeff0_2*dmats1[2][11] + coeff0_3*dmats1[3][11] + coeff0_4*dmats1[4][11] + coeff0_5*dmats1[5][11] + coeff0_6*dmats1[6][11] + coeff0_7*dmats1[7][11] + coeff0_8*dmats1[8][11] + coeff0_9*dmats1[9][11] + coeff0_10*dmats1[10][11] + coeff0_11*dmats1[11][11] + coeff0_12*dmats1[12][11] + coeff0_13*dmats1[13][11] + coeff0_14*dmats1[14][11] + coeff0_15*dmats1[15][11] + coeff0_16*dmats1[16][11] + coeff0_17*dmats1[17][11] + coeff0_18*dmats1[18][11] + coeff0_19*dmats1[19][11];
1525
new_coeff0_12 = coeff0_0*dmats1[0][12] + coeff0_1*dmats1[1][12] + coeff0_2*dmats1[2][12] + coeff0_3*dmats1[3][12] + coeff0_4*dmats1[4][12] + coeff0_5*dmats1[5][12] + coeff0_6*dmats1[6][12] + coeff0_7*dmats1[7][12] + coeff0_8*dmats1[8][12] + coeff0_9*dmats1[9][12] + coeff0_10*dmats1[10][12] + coeff0_11*dmats1[11][12] + coeff0_12*dmats1[12][12] + coeff0_13*dmats1[13][12] + coeff0_14*dmats1[14][12] + coeff0_15*dmats1[15][12] + coeff0_16*dmats1[16][12] + coeff0_17*dmats1[17][12] + coeff0_18*dmats1[18][12] + coeff0_19*dmats1[19][12];
1526
new_coeff0_13 = coeff0_0*dmats1[0][13] + coeff0_1*dmats1[1][13] + coeff0_2*dmats1[2][13] + coeff0_3*dmats1[3][13] + coeff0_4*dmats1[4][13] + coeff0_5*dmats1[5][13] + coeff0_6*dmats1[6][13] + coeff0_7*dmats1[7][13] + coeff0_8*dmats1[8][13] + coeff0_9*dmats1[9][13] + coeff0_10*dmats1[10][13] + coeff0_11*dmats1[11][13] + coeff0_12*dmats1[12][13] + coeff0_13*dmats1[13][13] + coeff0_14*dmats1[14][13] + coeff0_15*dmats1[15][13] + coeff0_16*dmats1[16][13] + coeff0_17*dmats1[17][13] + coeff0_18*dmats1[18][13] + coeff0_19*dmats1[19][13];
1527
new_coeff0_14 = coeff0_0*dmats1[0][14] + coeff0_1*dmats1[1][14] + coeff0_2*dmats1[2][14] + coeff0_3*dmats1[3][14] + coeff0_4*dmats1[4][14] + coeff0_5*dmats1[5][14] + coeff0_6*dmats1[6][14] + coeff0_7*dmats1[7][14] + coeff0_8*dmats1[8][14] + coeff0_9*dmats1[9][14] + coeff0_10*dmats1[10][14] + coeff0_11*dmats1[11][14] + coeff0_12*dmats1[12][14] + coeff0_13*dmats1[13][14] + coeff0_14*dmats1[14][14] + coeff0_15*dmats1[15][14] + coeff0_16*dmats1[16][14] + coeff0_17*dmats1[17][14] + coeff0_18*dmats1[18][14] + coeff0_19*dmats1[19][14];
1528
new_coeff0_15 = coeff0_0*dmats1[0][15] + coeff0_1*dmats1[1][15] + coeff0_2*dmats1[2][15] + coeff0_3*dmats1[3][15] + coeff0_4*dmats1[4][15] + coeff0_5*dmats1[5][15] + coeff0_6*dmats1[6][15] + coeff0_7*dmats1[7][15] + coeff0_8*dmats1[8][15] + coeff0_9*dmats1[9][15] + coeff0_10*dmats1[10][15] + coeff0_11*dmats1[11][15] + coeff0_12*dmats1[12][15] + coeff0_13*dmats1[13][15] + coeff0_14*dmats1[14][15] + coeff0_15*dmats1[15][15] + coeff0_16*dmats1[16][15] + coeff0_17*dmats1[17][15] + coeff0_18*dmats1[18][15] + coeff0_19*dmats1[19][15];
1529
new_coeff0_16 = coeff0_0*dmats1[0][16] + coeff0_1*dmats1[1][16] + coeff0_2*dmats1[2][16] + coeff0_3*dmats1[3][16] + coeff0_4*dmats1[4][16] + coeff0_5*dmats1[5][16] + coeff0_6*dmats1[6][16] + coeff0_7*dmats1[7][16] + coeff0_8*dmats1[8][16] + coeff0_9*dmats1[9][16] + coeff0_10*dmats1[10][16] + coeff0_11*dmats1[11][16] + coeff0_12*dmats1[12][16] + coeff0_13*dmats1[13][16] + coeff0_14*dmats1[14][16] + coeff0_15*dmats1[15][16] + coeff0_16*dmats1[16][16] + coeff0_17*dmats1[17][16] + coeff0_18*dmats1[18][16] + coeff0_19*dmats1[19][16];
1530
new_coeff0_17 = coeff0_0*dmats1[0][17] + coeff0_1*dmats1[1][17] + coeff0_2*dmats1[2][17] + coeff0_3*dmats1[3][17] + coeff0_4*dmats1[4][17] + coeff0_5*dmats1[5][17] + coeff0_6*dmats1[6][17] + coeff0_7*dmats1[7][17] + coeff0_8*dmats1[8][17] + coeff0_9*dmats1[9][17] + coeff0_10*dmats1[10][17] + coeff0_11*dmats1[11][17] + coeff0_12*dmats1[12][17] + coeff0_13*dmats1[13][17] + coeff0_14*dmats1[14][17] + coeff0_15*dmats1[15][17] + coeff0_16*dmats1[16][17] + coeff0_17*dmats1[17][17] + coeff0_18*dmats1[18][17] + coeff0_19*dmats1[19][17];
1531
new_coeff0_18 = coeff0_0*dmats1[0][18] + coeff0_1*dmats1[1][18] + coeff0_2*dmats1[2][18] + coeff0_3*dmats1[3][18] + coeff0_4*dmats1[4][18] + coeff0_5*dmats1[5][18] + coeff0_6*dmats1[6][18] + coeff0_7*dmats1[7][18] + coeff0_8*dmats1[8][18] + coeff0_9*dmats1[9][18] + coeff0_10*dmats1[10][18] + coeff0_11*dmats1[11][18] + coeff0_12*dmats1[12][18] + coeff0_13*dmats1[13][18] + coeff0_14*dmats1[14][18] + coeff0_15*dmats1[15][18] + coeff0_16*dmats1[16][18] + coeff0_17*dmats1[17][18] + coeff0_18*dmats1[18][18] + coeff0_19*dmats1[19][18];
1532
new_coeff0_19 = coeff0_0*dmats1[0][19] + coeff0_1*dmats1[1][19] + coeff0_2*dmats1[2][19] + coeff0_3*dmats1[3][19] + coeff0_4*dmats1[4][19] + coeff0_5*dmats1[5][19] + coeff0_6*dmats1[6][19] + coeff0_7*dmats1[7][19] + coeff0_8*dmats1[8][19] + coeff0_9*dmats1[9][19] + coeff0_10*dmats1[10][19] + coeff0_11*dmats1[11][19] + coeff0_12*dmats1[12][19] + coeff0_13*dmats1[13][19] + coeff0_14*dmats1[14][19] + coeff0_15*dmats1[15][19] + coeff0_16*dmats1[16][19] + coeff0_17*dmats1[17][19] + coeff0_18*dmats1[18][19] + coeff0_19*dmats1[19][19];
1533
}
1534
if(combinations[deriv_num][j] == 2)
1535
{
1536
new_coeff0_0 = coeff0_0*dmats2[0][0] + coeff0_1*dmats2[1][0] + coeff0_2*dmats2[2][0] + coeff0_3*dmats2[3][0] + coeff0_4*dmats2[4][0] + coeff0_5*dmats2[5][0] + coeff0_6*dmats2[6][0] + coeff0_7*dmats2[7][0] + coeff0_8*dmats2[8][0] + coeff0_9*dmats2[9][0] + coeff0_10*dmats2[10][0] + coeff0_11*dmats2[11][0] + coeff0_12*dmats2[12][0] + coeff0_13*dmats2[13][0] + coeff0_14*dmats2[14][0] + coeff0_15*dmats2[15][0] + coeff0_16*dmats2[16][0] + coeff0_17*dmats2[17][0] + coeff0_18*dmats2[18][0] + coeff0_19*dmats2[19][0];
1537
new_coeff0_1 = coeff0_0*dmats2[0][1] + coeff0_1*dmats2[1][1] + coeff0_2*dmats2[2][1] + coeff0_3*dmats2[3][1] + coeff0_4*dmats2[4][1] + coeff0_5*dmats2[5][1] + coeff0_6*dmats2[6][1] + coeff0_7*dmats2[7][1] + coeff0_8*dmats2[8][1] + coeff0_9*dmats2[9][1] + coeff0_10*dmats2[10][1] + coeff0_11*dmats2[11][1] + coeff0_12*dmats2[12][1] + coeff0_13*dmats2[13][1] + coeff0_14*dmats2[14][1] + coeff0_15*dmats2[15][1] + coeff0_16*dmats2[16][1] + coeff0_17*dmats2[17][1] + coeff0_18*dmats2[18][1] + coeff0_19*dmats2[19][1];
1538
new_coeff0_2 = coeff0_0*dmats2[0][2] + coeff0_1*dmats2[1][2] + coeff0_2*dmats2[2][2] + coeff0_3*dmats2[3][2] + coeff0_4*dmats2[4][2] + coeff0_5*dmats2[5][2] + coeff0_6*dmats2[6][2] + coeff0_7*dmats2[7][2] + coeff0_8*dmats2[8][2] + coeff0_9*dmats2[9][2] + coeff0_10*dmats2[10][2] + coeff0_11*dmats2[11][2] + coeff0_12*dmats2[12][2] + coeff0_13*dmats2[13][2] + coeff0_14*dmats2[14][2] + coeff0_15*dmats2[15][2] + coeff0_16*dmats2[16][2] + coeff0_17*dmats2[17][2] + coeff0_18*dmats2[18][2] + coeff0_19*dmats2[19][2];
1539
new_coeff0_3 = coeff0_0*dmats2[0][3] + coeff0_1*dmats2[1][3] + coeff0_2*dmats2[2][3] + coeff0_3*dmats2[3][3] + coeff0_4*dmats2[4][3] + coeff0_5*dmats2[5][3] + coeff0_6*dmats2[6][3] + coeff0_7*dmats2[7][3] + coeff0_8*dmats2[8][3] + coeff0_9*dmats2[9][3] + coeff0_10*dmats2[10][3] + coeff0_11*dmats2[11][3] + coeff0_12*dmats2[12][3] + coeff0_13*dmats2[13][3] + coeff0_14*dmats2[14][3] + coeff0_15*dmats2[15][3] + coeff0_16*dmats2[16][3] + coeff0_17*dmats2[17][3] + coeff0_18*dmats2[18][3] + coeff0_19*dmats2[19][3];
1540
new_coeff0_4 = coeff0_0*dmats2[0][4] + coeff0_1*dmats2[1][4] + coeff0_2*dmats2[2][4] + coeff0_3*dmats2[3][4] + coeff0_4*dmats2[4][4] + coeff0_5*dmats2[5][4] + coeff0_6*dmats2[6][4] + coeff0_7*dmats2[7][4] + coeff0_8*dmats2[8][4] + coeff0_9*dmats2[9][4] + coeff0_10*dmats2[10][4] + coeff0_11*dmats2[11][4] + coeff0_12*dmats2[12][4] + coeff0_13*dmats2[13][4] + coeff0_14*dmats2[14][4] + coeff0_15*dmats2[15][4] + coeff0_16*dmats2[16][4] + coeff0_17*dmats2[17][4] + coeff0_18*dmats2[18][4] + coeff0_19*dmats2[19][4];
1541
new_coeff0_5 = coeff0_0*dmats2[0][5] + coeff0_1*dmats2[1][5] + coeff0_2*dmats2[2][5] + coeff0_3*dmats2[3][5] + coeff0_4*dmats2[4][5] + coeff0_5*dmats2[5][5] + coeff0_6*dmats2[6][5] + coeff0_7*dmats2[7][5] + coeff0_8*dmats2[8][5] + coeff0_9*dmats2[9][5] + coeff0_10*dmats2[10][5] + coeff0_11*dmats2[11][5] + coeff0_12*dmats2[12][5] + coeff0_13*dmats2[13][5] + coeff0_14*dmats2[14][5] + coeff0_15*dmats2[15][5] + coeff0_16*dmats2[16][5] + coeff0_17*dmats2[17][5] + coeff0_18*dmats2[18][5] + coeff0_19*dmats2[19][5];
1542
new_coeff0_6 = coeff0_0*dmats2[0][6] + coeff0_1*dmats2[1][6] + coeff0_2*dmats2[2][6] + coeff0_3*dmats2[3][6] + coeff0_4*dmats2[4][6] + coeff0_5*dmats2[5][6] + coeff0_6*dmats2[6][6] + coeff0_7*dmats2[7][6] + coeff0_8*dmats2[8][6] + coeff0_9*dmats2[9][6] + coeff0_10*dmats2[10][6] + coeff0_11*dmats2[11][6] + coeff0_12*dmats2[12][6] + coeff0_13*dmats2[13][6] + coeff0_14*dmats2[14][6] + coeff0_15*dmats2[15][6] + coeff0_16*dmats2[16][6] + coeff0_17*dmats2[17][6] + coeff0_18*dmats2[18][6] + coeff0_19*dmats2[19][6];
1543
new_coeff0_7 = coeff0_0*dmats2[0][7] + coeff0_1*dmats2[1][7] + coeff0_2*dmats2[2][7] + coeff0_3*dmats2[3][7] + coeff0_4*dmats2[4][7] + coeff0_5*dmats2[5][7] + coeff0_6*dmats2[6][7] + coeff0_7*dmats2[7][7] + coeff0_8*dmats2[8][7] + coeff0_9*dmats2[9][7] + coeff0_10*dmats2[10][7] + coeff0_11*dmats2[11][7] + coeff0_12*dmats2[12][7] + coeff0_13*dmats2[13][7] + coeff0_14*dmats2[14][7] + coeff0_15*dmats2[15][7] + coeff0_16*dmats2[16][7] + coeff0_17*dmats2[17][7] + coeff0_18*dmats2[18][7] + coeff0_19*dmats2[19][7];
1544
new_coeff0_8 = coeff0_0*dmats2[0][8] + coeff0_1*dmats2[1][8] + coeff0_2*dmats2[2][8] + coeff0_3*dmats2[3][8] + coeff0_4*dmats2[4][8] + coeff0_5*dmats2[5][8] + coeff0_6*dmats2[6][8] + coeff0_7*dmats2[7][8] + coeff0_8*dmats2[8][8] + coeff0_9*dmats2[9][8] + coeff0_10*dmats2[10][8] + coeff0_11*dmats2[11][8] + coeff0_12*dmats2[12][8] + coeff0_13*dmats2[13][8] + coeff0_14*dmats2[14][8] + coeff0_15*dmats2[15][8] + coeff0_16*dmats2[16][8] + coeff0_17*dmats2[17][8] + coeff0_18*dmats2[18][8] + coeff0_19*dmats2[19][8];
1545
new_coeff0_9 = coeff0_0*dmats2[0][9] + coeff0_1*dmats2[1][9] + coeff0_2*dmats2[2][9] + coeff0_3*dmats2[3][9] + coeff0_4*dmats2[4][9] + coeff0_5*dmats2[5][9] + coeff0_6*dmats2[6][9] + coeff0_7*dmats2[7][9] + coeff0_8*dmats2[8][9] + coeff0_9*dmats2[9][9] + coeff0_10*dmats2[10][9] + coeff0_11*dmats2[11][9] + coeff0_12*dmats2[12][9] + coeff0_13*dmats2[13][9] + coeff0_14*dmats2[14][9] + coeff0_15*dmats2[15][9] + coeff0_16*dmats2[16][9] + coeff0_17*dmats2[17][9] + coeff0_18*dmats2[18][9] + coeff0_19*dmats2[19][9];
1546
new_coeff0_10 = coeff0_0*dmats2[0][10] + coeff0_1*dmats2[1][10] + coeff0_2*dmats2[2][10] + coeff0_3*dmats2[3][10] + coeff0_4*dmats2[4][10] + coeff0_5*dmats2[5][10] + coeff0_6*dmats2[6][10] + coeff0_7*dmats2[7][10] + coeff0_8*dmats2[8][10] + coeff0_9*dmats2[9][10] + coeff0_10*dmats2[10][10] + coeff0_11*dmats2[11][10] + coeff0_12*dmats2[12][10] + coeff0_13*dmats2[13][10] + coeff0_14*dmats2[14][10] + coeff0_15*dmats2[15][10] + coeff0_16*dmats2[16][10] + coeff0_17*dmats2[17][10] + coeff0_18*dmats2[18][10] + coeff0_19*dmats2[19][10];
1547
new_coeff0_11 = coeff0_0*dmats2[0][11] + coeff0_1*dmats2[1][11] + coeff0_2*dmats2[2][11] + coeff0_3*dmats2[3][11] + coeff0_4*dmats2[4][11] + coeff0_5*dmats2[5][11] + coeff0_6*dmats2[6][11] + coeff0_7*dmats2[7][11] + coeff0_8*dmats2[8][11] + coeff0_9*dmats2[9][11] + coeff0_10*dmats2[10][11] + coeff0_11*dmats2[11][11] + coeff0_12*dmats2[12][11] + coeff0_13*dmats2[13][11] + coeff0_14*dmats2[14][11] + coeff0_15*dmats2[15][11] + coeff0_16*dmats2[16][11] + coeff0_17*dmats2[17][11] + coeff0_18*dmats2[18][11] + coeff0_19*dmats2[19][11];
1548
new_coeff0_12 = coeff0_0*dmats2[0][12] + coeff0_1*dmats2[1][12] + coeff0_2*dmats2[2][12] + coeff0_3*dmats2[3][12] + coeff0_4*dmats2[4][12] + coeff0_5*dmats2[5][12] + coeff0_6*dmats2[6][12] + coeff0_7*dmats2[7][12] + coeff0_8*dmats2[8][12] + coeff0_9*dmats2[9][12] + coeff0_10*dmats2[10][12] + coeff0_11*dmats2[11][12] + coeff0_12*dmats2[12][12] + coeff0_13*dmats2[13][12] + coeff0_14*dmats2[14][12] + coeff0_15*dmats2[15][12] + coeff0_16*dmats2[16][12] + coeff0_17*dmats2[17][12] + coeff0_18*dmats2[18][12] + coeff0_19*dmats2[19][12];
1549
new_coeff0_13 = coeff0_0*dmats2[0][13] + coeff0_1*dmats2[1][13] + coeff0_2*dmats2[2][13] + coeff0_3*dmats2[3][13] + coeff0_4*dmats2[4][13] + coeff0_5*dmats2[5][13] + coeff0_6*dmats2[6][13] + coeff0_7*dmats2[7][13] + coeff0_8*dmats2[8][13] + coeff0_9*dmats2[9][13] + coeff0_10*dmats2[10][13] + coeff0_11*dmats2[11][13] + coeff0_12*dmats2[12][13] + coeff0_13*dmats2[13][13] + coeff0_14*dmats2[14][13] + coeff0_15*dmats2[15][13] + coeff0_16*dmats2[16][13] + coeff0_17*dmats2[17][13] + coeff0_18*dmats2[18][13] + coeff0_19*dmats2[19][13];
1550
new_coeff0_14 = coeff0_0*dmats2[0][14] + coeff0_1*dmats2[1][14] + coeff0_2*dmats2[2][14] + coeff0_3*dmats2[3][14] + coeff0_4*dmats2[4][14] + coeff0_5*dmats2[5][14] + coeff0_6*dmats2[6][14] + coeff0_7*dmats2[7][14] + coeff0_8*dmats2[8][14] + coeff0_9*dmats2[9][14] + coeff0_10*dmats2[10][14] + coeff0_11*dmats2[11][14] + coeff0_12*dmats2[12][14] + coeff0_13*dmats2[13][14] + coeff0_14*dmats2[14][14] + coeff0_15*dmats2[15][14] + coeff0_16*dmats2[16][14] + coeff0_17*dmats2[17][14] + coeff0_18*dmats2[18][14] + coeff0_19*dmats2[19][14];
1551
new_coeff0_15 = coeff0_0*dmats2[0][15] + coeff0_1*dmats2[1][15] + coeff0_2*dmats2[2][15] + coeff0_3*dmats2[3][15] + coeff0_4*dmats2[4][15] + coeff0_5*dmats2[5][15] + coeff0_6*dmats2[6][15] + coeff0_7*dmats2[7][15] + coeff0_8*dmats2[8][15] + coeff0_9*dmats2[9][15] + coeff0_10*dmats2[10][15] + coeff0_11*dmats2[11][15] + coeff0_12*dmats2[12][15] + coeff0_13*dmats2[13][15] + coeff0_14*dmats2[14][15] + coeff0_15*dmats2[15][15] + coeff0_16*dmats2[16][15] + coeff0_17*dmats2[17][15] + coeff0_18*dmats2[18][15] + coeff0_19*dmats2[19][15];
1552
new_coeff0_16 = coeff0_0*dmats2[0][16] + coeff0_1*dmats2[1][16] + coeff0_2*dmats2[2][16] + coeff0_3*dmats2[3][16] + coeff0_4*dmats2[4][16] + coeff0_5*dmats2[5][16] + coeff0_6*dmats2[6][16] + coeff0_7*dmats2[7][16] + coeff0_8*dmats2[8][16] + coeff0_9*dmats2[9][16] + coeff0_10*dmats2[10][16] + coeff0_11*dmats2[11][16] + coeff0_12*dmats2[12][16] + coeff0_13*dmats2[13][16] + coeff0_14*dmats2[14][16] + coeff0_15*dmats2[15][16] + coeff0_16*dmats2[16][16] + coeff0_17*dmats2[17][16] + coeff0_18*dmats2[18][16] + coeff0_19*dmats2[19][16];
1553
new_coeff0_17 = coeff0_0*dmats2[0][17] + coeff0_1*dmats2[1][17] + coeff0_2*dmats2[2][17] + coeff0_3*dmats2[3][17] + coeff0_4*dmats2[4][17] + coeff0_5*dmats2[5][17] + coeff0_6*dmats2[6][17] + coeff0_7*dmats2[7][17] + coeff0_8*dmats2[8][17] + coeff0_9*dmats2[9][17] + coeff0_10*dmats2[10][17] + coeff0_11*dmats2[11][17] + coeff0_12*dmats2[12][17] + coeff0_13*dmats2[13][17] + coeff0_14*dmats2[14][17] + coeff0_15*dmats2[15][17] + coeff0_16*dmats2[16][17] + coeff0_17*dmats2[17][17] + coeff0_18*dmats2[18][17] + coeff0_19*dmats2[19][17];
1554
new_coeff0_18 = coeff0_0*dmats2[0][18] + coeff0_1*dmats2[1][18] + coeff0_2*dmats2[2][18] + coeff0_3*dmats2[3][18] + coeff0_4*dmats2[4][18] + coeff0_5*dmats2[5][18] + coeff0_6*dmats2[6][18] + coeff0_7*dmats2[7][18] + coeff0_8*dmats2[8][18] + coeff0_9*dmats2[9][18] + coeff0_10*dmats2[10][18] + coeff0_11*dmats2[11][18] + coeff0_12*dmats2[12][18] + coeff0_13*dmats2[13][18] + coeff0_14*dmats2[14][18] + coeff0_15*dmats2[15][18] + coeff0_16*dmats2[16][18] + coeff0_17*dmats2[17][18] + coeff0_18*dmats2[18][18] + coeff0_19*dmats2[19][18];
1555
new_coeff0_19 = coeff0_0*dmats2[0][19] + coeff0_1*dmats2[1][19] + coeff0_2*dmats2[2][19] + coeff0_3*dmats2[3][19] + coeff0_4*dmats2[4][19] + coeff0_5*dmats2[5][19] + coeff0_6*dmats2[6][19] + coeff0_7*dmats2[7][19] + coeff0_8*dmats2[8][19] + coeff0_9*dmats2[9][19] + coeff0_10*dmats2[10][19] + coeff0_11*dmats2[11][19] + coeff0_12*dmats2[12][19] + coeff0_13*dmats2[13][19] + coeff0_14*dmats2[14][19] + coeff0_15*dmats2[15][19] + coeff0_16*dmats2[16][19] + coeff0_17*dmats2[17][19] + coeff0_18*dmats2[18][19] + coeff0_19*dmats2[19][19];
1556
}
1557
1558
}
1559
// Compute derivatives on reference element as dot product of coefficients and basisvalues
1560
derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2 + new_coeff0_3*basisvalue3 + new_coeff0_4*basisvalue4 + new_coeff0_5*basisvalue5 + new_coeff0_6*basisvalue6 + new_coeff0_7*basisvalue7 + new_coeff0_8*basisvalue8 + new_coeff0_9*basisvalue9 + new_coeff0_10*basisvalue10 + new_coeff0_11*basisvalue11 + new_coeff0_12*basisvalue12 + new_coeff0_13*basisvalue13 + new_coeff0_14*basisvalue14 + new_coeff0_15*basisvalue15 + new_coeff0_16*basisvalue16 + new_coeff0_17*basisvalue17 + new_coeff0_18*basisvalue18 + new_coeff0_19*basisvalue19;
1561
}
1562
1563
// Transform derivatives back to physical element
1564
for (unsigned int row = 0; row < num_derivatives; row++)
1565
{
1566
for (unsigned int col = 0; col < num_derivatives; col++)
1567
{
1568
values[row] += transform[row][col]*derivatives[col];
1569
}
1570
}
1571
// Delete pointer to array of derivatives on FIAT element
1572
delete [] derivatives;
1573
1574
// Delete pointer to array of combinations of derivatives and transform
1575
for (unsigned int row = 0; row < num_derivatives; row++)
1576
{
1577
delete [] combinations[row];
1578
delete [] transform[row];
1579
}
1580
1581
delete [] combinations;
1582
delete [] transform;
1583
}
1584
1585
/// Evaluate order n derivatives of all basis functions at given point in cell
1586
virtual void evaluate_basis_derivatives_all(unsigned int n,
1587
double* values,
1588
const double* coordinates,
1589
const ufc::cell& c) const
1590
{
1591
throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");
1592
}
1593
1594
/// Evaluate linear functional for dof i on the function f
1595
virtual double evaluate_dof(unsigned int i,
1596
const ufc::function& f,
1597
const ufc::cell& c) const
1598
{
1599
// The reference points, direction and weights:
1600
const static double X[20][1][3] = {{{0, 0, 0}}, {{1, 0, 0}}, {{0, 1, 0}}, {{0, 0, 1}}, {{0, 0.666666666666667, 0.333333333333333}}, {{0, 0.333333333333333, 0.666666666666667}}, {{0.666666666666667, 0, 0.333333333333333}}, {{0.333333333333333, 0, 0.666666666666667}}, {{0.666666666666667, 0.333333333333333, 0}}, {{0.333333333333333, 0.666666666666667, 0}}, {{0, 0, 0.333333333333333}}, {{0, 0, 0.666666666666667}}, {{0, 0.333333333333333, 0}}, {{0, 0.666666666666667, 0}}, {{0.333333333333333, 0, 0}}, {{0.666666666666667, 0, 0}}, {{0.333333333333333, 0.333333333333333, 0.333333333333333}}, {{0, 0.333333333333333, 0.333333333333333}}, {{0.333333333333333, 0, 0.333333333333333}}, {{0.333333333333333, 0.333333333333333, 0}}};
1601
const static double W[20][1] = {{1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}};
1602
const static double D[20][1][1] = {{{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}, {{1}}};
1603
1604
const double * const * x = c.coordinates;
1605
double result = 0.0;
1606
// Iterate over the points:
1607
// Evaluate basis functions for affine mapping
1608
const double w0 = 1.0 - X[i][0][0] - X[i][0][1] - X[i][0][2];
1609
const double w1 = X[i][0][0];
1610
const double w2 = X[i][0][1];
1611
const double w3 = X[i][0][2];
1612
1613
// Compute affine mapping y = F(X)
1614
double y[3];
1615
y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0] + w3*x[3][0];
1616
y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1] + w3*x[3][1];
1617
y[2] = w0*x[0][2] + w1*x[1][2] + w2*x[2][2] + w3*x[3][2];
1618
1619
// Evaluate function at physical points
1620
double values[1];
1621
f.evaluate(values, y, c);
1622
1623
// Map function values using appropriate mapping
1624
// Affine map: Do nothing
1625
1626
// Note that we do not map the weights (yet).
1627
1628
// Take directional components
1629
for(int k = 0; k < 1; k++)
1630
result += values[k]*D[i][0][k];
1631
// Multiply by weights
1632
result *= W[i][0];
1633
1634
return result;
1635
}
1636
1637
/// Evaluate linear functionals for all dofs on the function f
1638
virtual void evaluate_dofs(double* values,
1639
const ufc::function& f,
1640
const ufc::cell& c) const
1641
{
1642
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
1643
}
1644
1645
/// Interpolate vertex values from dof values
1646
virtual void interpolate_vertex_values(double* vertex_values,
1647
const double* dof_values,
1648
const ufc::cell& c) const
1649
{
1650
// Evaluate at vertices and use affine mapping
1651
vertex_values[0] = dof_values[0];
1652
vertex_values[1] = dof_values[1];
1653
vertex_values[2] = dof_values[2];
1654
vertex_values[3] = dof_values[3];
1655
}
1656
1657
/// Return the number of sub elements (for a mixed element)
1658
virtual unsigned int num_sub_elements() const
1659
{
1660
return 1;
1661
}
1662
1663
/// Create a new finite element for sub element i (for a mixed element)
1664
virtual ufc::finite_element* create_sub_element(unsigned int i) const
1665
{
1666
return new UFC_AdvectionBilinearForm_finite_element_1();
1667
}
1668
1669
};
1670
1671
/// This class defines the interface for a finite element.
1672
1673
class UFC_AdvectionBilinearForm_finite_element_2_0: public ufc::finite_element
1674
{
1675
public:
1676
1677
/// Constructor
1678
UFC_AdvectionBilinearForm_finite_element_2_0() : ufc::finite_element()
1679
{
1680
// Do nothing
1681
}
1682
1683
/// Destructor
1684
virtual ~UFC_AdvectionBilinearForm_finite_element_2_0()
1685
{
1686
// Do nothing
1687
}
1688
1689
/// Return a string identifying the finite element
1690
virtual const char* signature() const
1691
{
1692
return "Discontinuous Lagrange finite element of degree 0 on a tetrahedron";
1693
}
1694
1695
/// Return the cell shape
1696
virtual ufc::shape cell_shape() const
1697
{
1698
return ufc::tetrahedron;
1699
}
1700
1701
/// Return the dimension of the finite element function space
1702
virtual unsigned int space_dimension() const
1703
{
1704
return 1;
1705
}
1706
1707
/// Return the rank of the value space
1708
virtual unsigned int value_rank() const
1709
{
1710
return 0;
1711
}
1712
1713
/// Return the dimension of the value space for axis i
1714
virtual unsigned int value_dimension(unsigned int i) const
1715
{
1716
return 1;
1717
}
1718
1719
/// Evaluate basis function i at given point in cell
1720
virtual void evaluate_basis(unsigned int i,
1721
double* values,
1722
const double* coordinates,
1723
const ufc::cell& c) const
1724
{
1725
// Extract vertex coordinates
1726
const double * const * element_coordinates = c.coordinates;
1727
1728
// Compute Jacobian of affine map from reference cell
1729
const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
1730
const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
1731
const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];
1732
const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
1733
const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
1734
const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];
1735
const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];
1736
const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];
1737
const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];
1738
1739
// Compute sub determinants
1740
const double d00 = J_11*J_22 - J_12*J_21;
1741
const double d01 = J_12*J_20 - J_10*J_22;
1742
const double d02 = J_10*J_21 - J_11*J_20;
1743
1744
const double d10 = J_02*J_21 - J_01*J_22;
1745
const double d11 = J_00*J_22 - J_02*J_20;
1746
const double d12 = J_01*J_20 - J_00*J_21;
1747
1748
const double d20 = J_01*J_12 - J_02*J_11;
1749
const double d21 = J_02*J_10 - J_00*J_12;
1750
const double d22 = J_00*J_11 - J_01*J_10;
1751
1752
// Compute determinant of Jacobian
1753
double detJ = J_00*d00 + J_10*d10 + J_20*d20;
1754
1755
// Compute inverse of Jacobian
1756
1757
// Compute constants
1758
const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \
1759
+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \
1760
+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);
1761
1762
const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \
1763
+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \
1764
+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);
1765
1766
const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \
1767
+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \
1768
+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);
1769
1770
// Get coordinates and map to the UFC reference element
1771
double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;
1772
double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;
1773
double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;
1774
1775
// Map coordinates to the reference cube
1776
if (std::abs(y + z - 1.0) < 1e-14)
1777
x = 1.0;
1778
else
1779
x = -2.0 * x/(y + z - 1.0) - 1.0;
1780
if (std::abs(z - 1.0) < 1e-14)
1781
y = -1.0;
1782
else
1783
y = 2.0 * y/(1.0 - z) - 1.0;
1784
z = 2.0 * z - 1.0;
1785
1786
// Reset values
1787
*values = 0;
1788
1789
// Map degree of freedom to element degree of freedom
1790
const unsigned int dof = i;
1791
1792
// Generate scalings
1793
const double scalings_y_0 = 1;
1794
const double scalings_z_0 = 1;
1795
1796
// Compute psitilde_a
1797
const double psitilde_a_0 = 1;
1798
1799
// Compute psitilde_bs
1800
const double psitilde_bs_0_0 = 1;
1801
1802
// Compute psitilde_cs
1803
const double psitilde_cs_00_0 = 1;
1804
1805
// Compute basisvalues
1806
const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
1807
1808
// Table(s) of coefficients
1809
const static double coefficients0[1][1] = \
1810
{{1.15470053837925}};
1811
1812
// Extract relevant coefficients
1813
const double coeff0_0 = coefficients0[dof][0];
1814
1815
// Compute value(s)
1816
*values = coeff0_0*basisvalue0;
1817
}
1818
1819
/// Evaluate all basis functions at given point in cell
1820
virtual void evaluate_basis_all(double* values,
1821
const double* coordinates,
1822
const ufc::cell& c) const
1823
{
1824
throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");
1825
}
1826
1827
/// Evaluate order n derivatives of basis function i at given point in cell
1828
virtual void evaluate_basis_derivatives(unsigned int i,
1829
unsigned int n,
1830
double* values,
1831
const double* coordinates,
1832
const ufc::cell& c) const
1833
{
1834
// Extract vertex coordinates
1835
const double * const * element_coordinates = c.coordinates;
1836
1837
// Compute Jacobian of affine map from reference cell
1838
const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
1839
const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
1840
const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];
1841
const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
1842
const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
1843
const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];
1844
const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];
1845
const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];
1846
const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];
1847
1848
// Compute sub determinants
1849
const double d00 = J_11*J_22 - J_12*J_21;
1850
const double d01 = J_12*J_20 - J_10*J_22;
1851
const double d02 = J_10*J_21 - J_11*J_20;
1852
1853
const double d10 = J_02*J_21 - J_01*J_22;
1854
const double d11 = J_00*J_22 - J_02*J_20;
1855
const double d12 = J_01*J_20 - J_00*J_21;
1856
1857
const double d20 = J_01*J_12 - J_02*J_11;
1858
const double d21 = J_02*J_10 - J_00*J_12;
1859
const double d22 = J_00*J_11 - J_01*J_10;
1860
1861
// Compute determinant of Jacobian
1862
double detJ = J_00*d00 + J_10*d10 + J_20*d20;
1863
1864
// Compute inverse of Jacobian
1865
1866
// Compute constants
1867
const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \
1868
+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \
1869
+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);
1870
1871
const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \
1872
+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \
1873
+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);
1874
1875
const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \
1876
+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \
1877
+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);
1878
1879
// Get coordinates and map to the UFC reference element
1880
double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;
1881
double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;
1882
double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;
1883
1884
// Map coordinates to the reference cube
1885
if (std::abs(y + z - 1.0) < 1e-14)
1886
x = 1.0;
1887
else
1888
x = -2.0 * x/(y + z - 1.0) - 1.0;
1889
if (std::abs(z - 1.0) < 1e-14)
1890
y = -1.0;
1891
else
1892
y = 2.0 * y/(1.0 - z) - 1.0;
1893
z = 2.0 * z - 1.0;
1894
1895
// Compute number of derivatives
1896
unsigned int num_derivatives = 1;
1897
1898
for (unsigned int j = 0; j < n; j++)
1899
num_derivatives *= 3;
1900
1901
1902
// Declare pointer to two dimensional array that holds combinations of derivatives and initialise
1903
unsigned int **combinations = new unsigned int *[num_derivatives];
1904
1905
for (unsigned int j = 0; j < num_derivatives; j++)
1906
{
1907
combinations[j] = new unsigned int [n];
1908
for (unsigned int k = 0; k < n; k++)
1909
combinations[j][k] = 0;
1910
}
1911
1912
// Generate combinations of derivatives
1913
for (unsigned int row = 1; row < num_derivatives; row++)
1914
{
1915
for (unsigned int num = 0; num < row; num++)
1916
{
1917
for (unsigned int col = n-1; col+1 > 0; col--)
1918
{
1919
if (combinations[row][col] + 1 > 2)
1920
combinations[row][col] = 0;
1921
else
1922
{
1923
combinations[row][col] += 1;
1924
break;
1925
}
1926
}
1927
}
1928
}
1929
1930
// Compute inverse of Jacobian
1931
const double Jinv[3][3] ={{d00 / detJ, d10 / detJ, d20 / detJ}, {d01 / detJ, d11 / detJ, d21 / detJ}, {d02 / detJ, d12 / detJ, d22 / detJ}};
1932
1933
// Declare transformation matrix
1934
// Declare pointer to two dimensional array and initialise
1935
double **transform = new double *[num_derivatives];
1936
1937
for (unsigned int j = 0; j < num_derivatives; j++)
1938
{
1939
transform[j] = new double [num_derivatives];
1940
for (unsigned int k = 0; k < num_derivatives; k++)
1941
transform[j][k] = 1;
1942
}
1943
1944
// Construct transformation matrix
1945
for (unsigned int row = 0; row < num_derivatives; row++)
1946
{
1947
for (unsigned int col = 0; col < num_derivatives; col++)
1948
{
1949
for (unsigned int k = 0; k < n; k++)
1950
transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
1951
}
1952
}
1953
1954
// Reset values
1955
for (unsigned int j = 0; j < 1*num_derivatives; j++)
1956
values[j] = 0;
1957
1958
// Map degree of freedom to element degree of freedom
1959
const unsigned int dof = i;
1960
1961
// Generate scalings
1962
const double scalings_y_0 = 1;
1963
const double scalings_z_0 = 1;
1964
1965
// Compute psitilde_a
1966
const double psitilde_a_0 = 1;
1967
1968
// Compute psitilde_bs
1969
const double psitilde_bs_0_0 = 1;
1970
1971
// Compute psitilde_cs
1972
const double psitilde_cs_00_0 = 1;
1973
1974
// Compute basisvalues
1975
const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
1976
1977
// Table(s) of coefficients
1978
const static double coefficients0[1][1] = \
1979
{{1.15470053837925}};
1980
1981
// Interesting (new) part
1982
// Tables of derivatives of the polynomial base (transpose)
1983
const static double dmats0[1][1] = \
1984
{{0}};
1985
1986
const static double dmats1[1][1] = \
1987
{{0}};
1988
1989
const static double dmats2[1][1] = \
1990
{{0}};
1991
1992
// Compute reference derivatives
1993
// Declare pointer to array of derivatives on FIAT element
1994
double *derivatives = new double [num_derivatives];
1995
1996
// Declare coefficients
1997
double coeff0_0 = 0;
1998
1999
// Declare new coefficients
2000
double new_coeff0_0 = 0;
2001
2002
// Loop possible derivatives
2003
for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
2004
{
2005
// Get values from coefficients array
2006
new_coeff0_0 = coefficients0[dof][0];
2007
2008
// Loop derivative order
2009
for (unsigned int j = 0; j < n; j++)
2010
{
2011
// Update old coefficients
2012
coeff0_0 = new_coeff0_0;
2013
2014
if(combinations[deriv_num][j] == 0)
2015
{
2016
new_coeff0_0 = coeff0_0*dmats0[0][0];
2017
}
2018
if(combinations[deriv_num][j] == 1)
2019
{
2020
new_coeff0_0 = coeff0_0*dmats1[0][0];
2021
}
2022
if(combinations[deriv_num][j] == 2)
2023
{
2024
new_coeff0_0 = coeff0_0*dmats2[0][0];
2025
}
2026
2027
}
2028
// Compute derivatives on reference element as dot product of coefficients and basisvalues
2029
derivatives[deriv_num] = new_coeff0_0*basisvalue0;
2030
}
2031
2032
// Transform derivatives back to physical element
2033
for (unsigned int row = 0; row < num_derivatives; row++)
2034
{
2035
for (unsigned int col = 0; col < num_derivatives; col++)
2036
{
2037
values[row] += transform[row][col]*derivatives[col];
2038
}
2039
}
2040
// Delete pointer to array of derivatives on FIAT element
2041
delete [] derivatives;
2042
2043
// Delete pointer to array of combinations of derivatives and transform
2044
for (unsigned int row = 0; row < num_derivatives; row++)
2045
{
2046
delete [] combinations[row];
2047
delete [] transform[row];
2048
}
2049
2050
delete [] combinations;
2051
delete [] transform;
2052
}
2053
2054
/// Evaluate order n derivatives of all basis functions at given point in cell
2055
virtual void evaluate_basis_derivatives_all(unsigned int n,
2056
double* values,
2057
const double* coordinates,
2058
const ufc::cell& c) const
2059
{
2060
throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");
2061
}
2062
2063
/// Evaluate linear functional for dof i on the function f
2064
virtual double evaluate_dof(unsigned int i,
2065
const ufc::function& f,
2066
const ufc::cell& c) const
2067
{
2068
// The reference points, direction and weights:
2069
const static double X[1][1][3] = {{{0.25, 0.25, 0.25}}};
2070
const static double W[1][1] = {{1}};
2071
const static double D[1][1][1] = {{{1}}};
2072
2073
const double * const * x = c.coordinates;
2074
double result = 0.0;
2075
// Iterate over the points:
2076
// Evaluate basis functions for affine mapping
2077
const double w0 = 1.0 - X[i][0][0] - X[i][0][1] - X[i][0][2];
2078
const double w1 = X[i][0][0];
2079
const double w2 = X[i][0][1];
2080
const double w3 = X[i][0][2];
2081
2082
// Compute affine mapping y = F(X)
2083
double y[3];
2084
y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0] + w3*x[3][0];
2085
y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1] + w3*x[3][1];
2086
y[2] = w0*x[0][2] + w1*x[1][2] + w2*x[2][2] + w3*x[3][2];
2087
2088
// Evaluate function at physical points
2089
double values[1];
2090
f.evaluate(values, y, c);
2091
2092
// Map function values using appropriate mapping
2093
// Affine map: Do nothing
2094
2095
// Note that we do not map the weights (yet).
2096
2097
// Take directional components
2098
for(int k = 0; k < 1; k++)
2099
result += values[k]*D[i][0][k];
2100
// Multiply by weights
2101
result *= W[i][0];
2102
2103
return result;
2104
}
2105
2106
/// Evaluate linear functionals for all dofs on the function f
2107
virtual void evaluate_dofs(double* values,
2108
const ufc::function& f,
2109
const ufc::cell& c) const
2110
{
2111
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
2112
}
2113
2114
/// Interpolate vertex values from dof values
2115
virtual void interpolate_vertex_values(double* vertex_values,
2116
const double* dof_values,
2117
const ufc::cell& c) const
2118
{
2119
// Evaluate at vertices and use affine mapping
2120
vertex_values[0] = dof_values[0];
2121
vertex_values[1] = dof_values[0];
2122
vertex_values[2] = dof_values[0];
2123
vertex_values[3] = dof_values[0];
2124
}
2125
2126
/// Return the number of sub elements (for a mixed element)
2127
virtual unsigned int num_sub_elements() const
2128
{
2129
return 1;
2130
}
2131
2132
/// Create a new finite element for sub element i (for a mixed element)
2133
virtual ufc::finite_element* create_sub_element(unsigned int i) const
2134
{
2135
return new UFC_AdvectionBilinearForm_finite_element_2_0();
2136
}
2137
2138
};
2139
2140
/// This class defines the interface for a finite element.
2141
2142
class UFC_AdvectionBilinearForm_finite_element_2_1: public ufc::finite_element
2143
{
2144
public:
2145
2146
/// Constructor
2147
UFC_AdvectionBilinearForm_finite_element_2_1() : ufc::finite_element()
2148
{
2149
// Do nothing
2150
}
2151
2152
/// Destructor
2153
virtual ~UFC_AdvectionBilinearForm_finite_element_2_1()
2154
{
2155
// Do nothing
2156
}
2157
2158
/// Return a string identifying the finite element
2159
virtual const char* signature() const
2160
{
2161
return "Discontinuous Lagrange finite element of degree 0 on a tetrahedron";
2162
}
2163
2164
/// Return the cell shape
2165
virtual ufc::shape cell_shape() const
2166
{
2167
return ufc::tetrahedron;
2168
}
2169
2170
/// Return the dimension of the finite element function space
2171
virtual unsigned int space_dimension() const
2172
{
2173
return 1;
2174
}
2175
2176
/// Return the rank of the value space
2177
virtual unsigned int value_rank() const
2178
{
2179
return 0;
2180
}
2181
2182
/// Return the dimension of the value space for axis i
2183
virtual unsigned int value_dimension(unsigned int i) const
2184
{
2185
return 1;
2186
}
2187
2188
/// Evaluate basis function i at given point in cell
2189
virtual void evaluate_basis(unsigned int i,
2190
double* values,
2191
const double* coordinates,
2192
const ufc::cell& c) const
2193
{
2194
// Extract vertex coordinates
2195
const double * const * element_coordinates = c.coordinates;
2196
2197
// Compute Jacobian of affine map from reference cell
2198
const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
2199
const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
2200
const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];
2201
const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
2202
const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
2203
const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];
2204
const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];
2205
const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];
2206
const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];
2207
2208
// Compute sub determinants
2209
const double d00 = J_11*J_22 - J_12*J_21;
2210
const double d01 = J_12*J_20 - J_10*J_22;
2211
const double d02 = J_10*J_21 - J_11*J_20;
2212
2213
const double d10 = J_02*J_21 - J_01*J_22;
2214
const double d11 = J_00*J_22 - J_02*J_20;
2215
const double d12 = J_01*J_20 - J_00*J_21;
2216
2217
const double d20 = J_01*J_12 - J_02*J_11;
2218
const double d21 = J_02*J_10 - J_00*J_12;
2219
const double d22 = J_00*J_11 - J_01*J_10;
2220
2221
// Compute determinant of Jacobian
2222
double detJ = J_00*d00 + J_10*d10 + J_20*d20;
2223
2224
// Compute inverse of Jacobian
2225
2226
// Compute constants
2227
const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \
2228
+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \
2229
+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);
2230
2231
const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \
2232
+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \
2233
+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);
2234
2235
const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \
2236
+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \
2237
+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);
2238
2239
// Get coordinates and map to the UFC reference element
2240
double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;
2241
double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;
2242
double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;
2243
2244
// Map coordinates to the reference cube
2245
if (std::abs(y + z - 1.0) < 1e-14)
2246
x = 1.0;
2247
else
2248
x = -2.0 * x/(y + z - 1.0) - 1.0;
2249
if (std::abs(z - 1.0) < 1e-14)
2250
y = -1.0;
2251
else
2252
y = 2.0 * y/(1.0 - z) - 1.0;
2253
z = 2.0 * z - 1.0;
2254
2255
// Reset values
2256
*values = 0;
2257
2258
// Map degree of freedom to element degree of freedom
2259
const unsigned int dof = i;
2260
2261
// Generate scalings
2262
const double scalings_y_0 = 1;
2263
const double scalings_z_0 = 1;
2264
2265
// Compute psitilde_a
2266
const double psitilde_a_0 = 1;
2267
2268
// Compute psitilde_bs
2269
const double psitilde_bs_0_0 = 1;
2270
2271
// Compute psitilde_cs
2272
const double psitilde_cs_00_0 = 1;
2273
2274
// Compute basisvalues
2275
const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
2276
2277
// Table(s) of coefficients
2278
const static double coefficients0[1][1] = \
2279
{{1.15470053837925}};
2280
2281
// Extract relevant coefficients
2282
const double coeff0_0 = coefficients0[dof][0];
2283
2284
// Compute value(s)
2285
*values = coeff0_0*basisvalue0;
2286
}
2287
2288
/// Evaluate all basis functions at given point in cell
2289
virtual void evaluate_basis_all(double* values,
2290
const double* coordinates,
2291
const ufc::cell& c) const
2292
{
2293
throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");
2294
}
2295
2296
/// Evaluate order n derivatives of basis function i at given point in cell
2297
virtual void evaluate_basis_derivatives(unsigned int i,
2298
unsigned int n,
2299
double* values,
2300
const double* coordinates,
2301
const ufc::cell& c) const
2302
{
2303
// Extract vertex coordinates
2304
const double * const * element_coordinates = c.coordinates;
2305
2306
// Compute Jacobian of affine map from reference cell
2307
const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
2308
const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
2309
const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];
2310
const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
2311
const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
2312
const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];
2313
const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];
2314
const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];
2315
const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];
2316
2317
// Compute sub determinants
2318
const double d00 = J_11*J_22 - J_12*J_21;
2319
const double d01 = J_12*J_20 - J_10*J_22;
2320
const double d02 = J_10*J_21 - J_11*J_20;
2321
2322
const double d10 = J_02*J_21 - J_01*J_22;
2323
const double d11 = J_00*J_22 - J_02*J_20;
2324
const double d12 = J_01*J_20 - J_00*J_21;
2325
2326
const double d20 = J_01*J_12 - J_02*J_11;
2327
const double d21 = J_02*J_10 - J_00*J_12;
2328
const double d22 = J_00*J_11 - J_01*J_10;
2329
2330
// Compute determinant of Jacobian
2331
double detJ = J_00*d00 + J_10*d10 + J_20*d20;
2332
2333
// Compute inverse of Jacobian
2334
2335
// Compute constants
2336
const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \
2337
+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \
2338
+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);
2339
2340
const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \
2341
+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \
2342
+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);
2343
2344
const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \
2345
+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \
2346
+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);
2347
2348
// Get coordinates and map to the UFC reference element
2349
double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;
2350
double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;
2351
double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;
2352
2353
// Map coordinates to the reference cube
2354
if (std::abs(y + z - 1.0) < 1e-14)
2355
x = 1.0;
2356
else
2357
x = -2.0 * x/(y + z - 1.0) - 1.0;
2358
if (std::abs(z - 1.0) < 1e-14)
2359
y = -1.0;
2360
else
2361
y = 2.0 * y/(1.0 - z) - 1.0;
2362
z = 2.0 * z - 1.0;
2363
2364
// Compute number of derivatives
2365
unsigned int num_derivatives = 1;
2366
2367
for (unsigned int j = 0; j < n; j++)
2368
num_derivatives *= 3;
2369
2370
2371
// Declare pointer to two dimensional array that holds combinations of derivatives and initialise
2372
unsigned int **combinations = new unsigned int *[num_derivatives];
2373
2374
for (unsigned int j = 0; j < num_derivatives; j++)
2375
{
2376
combinations[j] = new unsigned int [n];
2377
for (unsigned int k = 0; k < n; k++)
2378
combinations[j][k] = 0;
2379
}
2380
2381
// Generate combinations of derivatives
2382
for (unsigned int row = 1; row < num_derivatives; row++)
2383
{
2384
for (unsigned int num = 0; num < row; num++)
2385
{
2386
for (unsigned int col = n-1; col+1 > 0; col--)
2387
{
2388
if (combinations[row][col] + 1 > 2)
2389
combinations[row][col] = 0;
2390
else
2391
{
2392
combinations[row][col] += 1;
2393
break;
2394
}
2395
}
2396
}
2397
}
2398
2399
// Compute inverse of Jacobian
2400
const double Jinv[3][3] ={{d00 / detJ, d10 / detJ, d20 / detJ}, {d01 / detJ, d11 / detJ, d21 / detJ}, {d02 / detJ, d12 / detJ, d22 / detJ}};
2401
2402
// Declare transformation matrix
2403
// Declare pointer to two dimensional array and initialise
2404
double **transform = new double *[num_derivatives];
2405
2406
for (unsigned int j = 0; j < num_derivatives; j++)
2407
{
2408
transform[j] = new double [num_derivatives];
2409
for (unsigned int k = 0; k < num_derivatives; k++)
2410
transform[j][k] = 1;
2411
}
2412
2413
// Construct transformation matrix
2414
for (unsigned int row = 0; row < num_derivatives; row++)
2415
{
2416
for (unsigned int col = 0; col < num_derivatives; col++)
2417
{
2418
for (unsigned int k = 0; k < n; k++)
2419
transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
2420
}
2421
}
2422
2423
// Reset values
2424
for (unsigned int j = 0; j < 1*num_derivatives; j++)
2425
values[j] = 0;
2426
2427
// Map degree of freedom to element degree of freedom
2428
const unsigned int dof = i;
2429
2430
// Generate scalings
2431
const double scalings_y_0 = 1;
2432
const double scalings_z_0 = 1;
2433
2434
// Compute psitilde_a
2435
const double psitilde_a_0 = 1;
2436
2437
// Compute psitilde_bs
2438
const double psitilde_bs_0_0 = 1;
2439
2440
// Compute psitilde_cs
2441
const double psitilde_cs_00_0 = 1;
2442
2443
// Compute basisvalues
2444
const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
2445
2446
// Table(s) of coefficients
2447
const static double coefficients0[1][1] = \
2448
{{1.15470053837925}};
2449
2450
// Interesting (new) part
2451
// Tables of derivatives of the polynomial base (transpose)
2452
const static double dmats0[1][1] = \
2453
{{0}};
2454
2455
const static double dmats1[1][1] = \
2456
{{0}};
2457
2458
const static double dmats2[1][1] = \
2459
{{0}};
2460
2461
// Compute reference derivatives
2462
// Declare pointer to array of derivatives on FIAT element
2463
double *derivatives = new double [num_derivatives];
2464
2465
// Declare coefficients
2466
double coeff0_0 = 0;
2467
2468
// Declare new coefficients
2469
double new_coeff0_0 = 0;
2470
2471
// Loop possible derivatives
2472
for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
2473
{
2474
// Get values from coefficients array
2475
new_coeff0_0 = coefficients0[dof][0];
2476
2477
// Loop derivative order
2478
for (unsigned int j = 0; j < n; j++)
2479
{
2480
// Update old coefficients
2481
coeff0_0 = new_coeff0_0;
2482
2483
if(combinations[deriv_num][j] == 0)
2484
{
2485
new_coeff0_0 = coeff0_0*dmats0[0][0];
2486
}
2487
if(combinations[deriv_num][j] == 1)
2488
{
2489
new_coeff0_0 = coeff0_0*dmats1[0][0];
2490
}
2491
if(combinations[deriv_num][j] == 2)
2492
{
2493
new_coeff0_0 = coeff0_0*dmats2[0][0];
2494
}
2495
2496
}
2497
// Compute derivatives on reference element as dot product of coefficients and basisvalues
2498
derivatives[deriv_num] = new_coeff0_0*basisvalue0;
2499
}
2500
2501
// Transform derivatives back to physical element
2502
for (unsigned int row = 0; row < num_derivatives; row++)
2503
{
2504
for (unsigned int col = 0; col < num_derivatives; col++)
2505
{
2506
values[row] += transform[row][col]*derivatives[col];
2507
}
2508
}
2509
// Delete pointer to array of derivatives on FIAT element
2510
delete [] derivatives;
2511
2512
// Delete pointer to array of combinations of derivatives and transform
2513
for (unsigned int row = 0; row < num_derivatives; row++)
2514
{
2515
delete [] combinations[row];
2516
delete [] transform[row];
2517
}
2518
2519
delete [] combinations;
2520
delete [] transform;
2521
}
2522
2523
/// Evaluate order n derivatives of all basis functions at given point in cell
2524
virtual void evaluate_basis_derivatives_all(unsigned int n,
2525
double* values,
2526
const double* coordinates,
2527
const ufc::cell& c) const
2528
{
2529
throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");
2530
}
2531
2532
/// Evaluate linear functional for dof i on the function f
2533
virtual double evaluate_dof(unsigned int i,
2534
const ufc::function& f,
2535
const ufc::cell& c) const
2536
{
2537
// The reference points, direction and weights:
2538
const static double X[1][1][3] = {{{0.25, 0.25, 0.25}}};
2539
const static double W[1][1] = {{1}};
2540
const static double D[1][1][1] = {{{1}}};
2541
2542
const double * const * x = c.coordinates;
2543
double result = 0.0;
2544
// Iterate over the points:
2545
// Evaluate basis functions for affine mapping
2546
const double w0 = 1.0 - X[i][0][0] - X[i][0][1] - X[i][0][2];
2547
const double w1 = X[i][0][0];
2548
const double w2 = X[i][0][1];
2549
const double w3 = X[i][0][2];
2550
2551
// Compute affine mapping y = F(X)
2552
double y[3];
2553
y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0] + w3*x[3][0];
2554
y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1] + w3*x[3][1];
2555
y[2] = w0*x[0][2] + w1*x[1][2] + w2*x[2][2] + w3*x[3][2];
2556
2557
// Evaluate function at physical points
2558
double values[1];
2559
f.evaluate(values, y, c);
2560
2561
// Map function values using appropriate mapping
2562
// Affine map: Do nothing
2563
2564
// Note that we do not map the weights (yet).
2565
2566
// Take directional components
2567
for(int k = 0; k < 1; k++)
2568
result += values[k]*D[i][0][k];
2569
// Multiply by weights
2570
result *= W[i][0];
2571
2572
return result;
2573
}
2574
2575
/// Evaluate linear functionals for all dofs on the function f
2576
virtual void evaluate_dofs(double* values,
2577
const ufc::function& f,
2578
const ufc::cell& c) const
2579
{
2580
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
2581
}
2582
2583
/// Interpolate vertex values from dof values
2584
virtual void interpolate_vertex_values(double* vertex_values,
2585
const double* dof_values,
2586
const ufc::cell& c) const
2587
{
2588
// Evaluate at vertices and use affine mapping
2589
vertex_values[0] = dof_values[0];
2590
vertex_values[1] = dof_values[0];
2591
vertex_values[2] = dof_values[0];
2592
vertex_values[3] = dof_values[0];
2593
}
2594
2595
/// Return the number of sub elements (for a mixed element)
2596
virtual unsigned int num_sub_elements() const
2597
{
2598
return 1;
2599
}
2600
2601
/// Create a new finite element for sub element i (for a mixed element)
2602
virtual ufc::finite_element* create_sub_element(unsigned int i) const
2603
{
2604
return new UFC_AdvectionBilinearForm_finite_element_2_1();
2605
}
2606
2607
};
2608
2609
/// This class defines the interface for a finite element.
2610
2611
class UFC_AdvectionBilinearForm_finite_element_2_2: public ufc::finite_element
2612
{
2613
public:
2614
2615
/// Constructor
2616
UFC_AdvectionBilinearForm_finite_element_2_2() : ufc::finite_element()
2617
{
2618
// Do nothing
2619
}
2620
2621
/// Destructor
2622
virtual ~UFC_AdvectionBilinearForm_finite_element_2_2()
2623
{
2624
// Do nothing
2625
}
2626
2627
/// Return a string identifying the finite element
2628
virtual const char* signature() const
2629
{
2630
return "Discontinuous Lagrange finite element of degree 0 on a tetrahedron";
2631
}
2632
2633
/// Return the cell shape
2634
virtual ufc::shape cell_shape() const
2635
{
2636
return ufc::tetrahedron;
2637
}
2638
2639
/// Return the dimension of the finite element function space
2640
virtual unsigned int space_dimension() const
2641
{
2642
return 1;
2643
}
2644
2645
/// Return the rank of the value space
2646
virtual unsigned int value_rank() const
2647
{
2648
return 0;
2649
}
2650
2651
/// Return the dimension of the value space for axis i
2652
virtual unsigned int value_dimension(unsigned int i) const
2653
{
2654
return 1;
2655
}
2656
2657
/// Evaluate basis function i at given point in cell
2658
virtual void evaluate_basis(unsigned int i,
2659
double* values,
2660
const double* coordinates,
2661
const ufc::cell& c) const
2662
{
2663
// Extract vertex coordinates
2664
const double * const * element_coordinates = c.coordinates;
2665
2666
// Compute Jacobian of affine map from reference cell
2667
const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
2668
const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
2669
const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];
2670
const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
2671
const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
2672
const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];
2673
const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];
2674
const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];
2675
const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];
2676
2677
// Compute sub determinants
2678
const double d00 = J_11*J_22 - J_12*J_21;
2679
const double d01 = J_12*J_20 - J_10*J_22;
2680
const double d02 = J_10*J_21 - J_11*J_20;
2681
2682
const double d10 = J_02*J_21 - J_01*J_22;
2683
const double d11 = J_00*J_22 - J_02*J_20;
2684
const double d12 = J_01*J_20 - J_00*J_21;
2685
2686
const double d20 = J_01*J_12 - J_02*J_11;
2687
const double d21 = J_02*J_10 - J_00*J_12;
2688
const double d22 = J_00*J_11 - J_01*J_10;
2689
2690
// Compute determinant of Jacobian
2691
double detJ = J_00*d00 + J_10*d10 + J_20*d20;
2692
2693
// Compute inverse of Jacobian
2694
2695
// Compute constants
2696
const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \
2697
+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \
2698
+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);
2699
2700
const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \
2701
+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \
2702
+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);
2703
2704
const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \
2705
+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \
2706
+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);
2707
2708
// Get coordinates and map to the UFC reference element
2709
double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;
2710
double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;
2711
double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;
2712
2713
// Map coordinates to the reference cube
2714
if (std::abs(y + z - 1.0) < 1e-14)
2715
x = 1.0;
2716
else
2717
x = -2.0 * x/(y + z - 1.0) - 1.0;
2718
if (std::abs(z - 1.0) < 1e-14)
2719
y = -1.0;
2720
else
2721
y = 2.0 * y/(1.0 - z) - 1.0;
2722
z = 2.0 * z - 1.0;
2723
2724
// Reset values
2725
*values = 0;
2726
2727
// Map degree of freedom to element degree of freedom
2728
const unsigned int dof = i;
2729
2730
// Generate scalings
2731
const double scalings_y_0 = 1;
2732
const double scalings_z_0 = 1;
2733
2734
// Compute psitilde_a
2735
const double psitilde_a_0 = 1;
2736
2737
// Compute psitilde_bs
2738
const double psitilde_bs_0_0 = 1;
2739
2740
// Compute psitilde_cs
2741
const double psitilde_cs_00_0 = 1;
2742
2743
// Compute basisvalues
2744
const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
2745
2746
// Table(s) of coefficients
2747
const static double coefficients0[1][1] = \
2748
{{1.15470053837925}};
2749
2750
// Extract relevant coefficients
2751
const double coeff0_0 = coefficients0[dof][0];
2752
2753
// Compute value(s)
2754
*values = coeff0_0*basisvalue0;
2755
}
2756
2757
/// Evaluate all basis functions at given point in cell
2758
virtual void evaluate_basis_all(double* values,
2759
const double* coordinates,
2760
const ufc::cell& c) const
2761
{
2762
throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");
2763
}
2764
2765
/// Evaluate order n derivatives of basis function i at given point in cell
2766
virtual void evaluate_basis_derivatives(unsigned int i,
2767
unsigned int n,
2768
double* values,
2769
const double* coordinates,
2770
const ufc::cell& c) const
2771
{
2772
// Extract vertex coordinates
2773
const double * const * element_coordinates = c.coordinates;
2774
2775
// Compute Jacobian of affine map from reference cell
2776
const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
2777
const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
2778
const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];
2779
const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
2780
const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
2781
const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];
2782
const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];
2783
const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];
2784
const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];
2785
2786
// Compute sub determinants
2787
const double d00 = J_11*J_22 - J_12*J_21;
2788
const double d01 = J_12*J_20 - J_10*J_22;
2789
const double d02 = J_10*J_21 - J_11*J_20;
2790
2791
const double d10 = J_02*J_21 - J_01*J_22;
2792
const double d11 = J_00*J_22 - J_02*J_20;
2793
const double d12 = J_01*J_20 - J_00*J_21;
2794
2795
const double d20 = J_01*J_12 - J_02*J_11;
2796
const double d21 = J_02*J_10 - J_00*J_12;
2797
const double d22 = J_00*J_11 - J_01*J_10;
2798
2799
// Compute determinant of Jacobian
2800
double detJ = J_00*d00 + J_10*d10 + J_20*d20;
2801
2802
// Compute inverse of Jacobian
2803
2804
// Compute constants
2805
const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \
2806
+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \
2807
+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);
2808
2809
const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \
2810
+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \
2811
+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);
2812
2813
const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \
2814
+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \
2815
+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);
2816
2817
// Get coordinates and map to the UFC reference element
2818
double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;
2819
double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;
2820
double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;
2821
2822
// Map coordinates to the reference cube
2823
if (std::abs(y + z - 1.0) < 1e-14)
2824
x = 1.0;
2825
else
2826
x = -2.0 * x/(y + z - 1.0) - 1.0;
2827
if (std::abs(z - 1.0) < 1e-14)
2828
y = -1.0;
2829
else
2830
y = 2.0 * y/(1.0 - z) - 1.0;
2831
z = 2.0 * z - 1.0;
2832
2833
// Compute number of derivatives
2834
unsigned int num_derivatives = 1;
2835
2836
for (unsigned int j = 0; j < n; j++)
2837
num_derivatives *= 3;
2838
2839
2840
// Declare pointer to two dimensional array that holds combinations of derivatives and initialise
2841
unsigned int **combinations = new unsigned int *[num_derivatives];
2842
2843
for (unsigned int j = 0; j < num_derivatives; j++)
2844
{
2845
combinations[j] = new unsigned int [n];
2846
for (unsigned int k = 0; k < n; k++)
2847
combinations[j][k] = 0;
2848
}
2849
2850
// Generate combinations of derivatives
2851
for (unsigned int row = 1; row < num_derivatives; row++)
2852
{
2853
for (unsigned int num = 0; num < row; num++)
2854
{
2855
for (unsigned int col = n-1; col+1 > 0; col--)
2856
{
2857
if (combinations[row][col] + 1 > 2)
2858
combinations[row][col] = 0;
2859
else
2860
{
2861
combinations[row][col] += 1;
2862
break;
2863
}
2864
}
2865
}
2866
}
2867
2868
// Compute inverse of Jacobian
2869
const double Jinv[3][3] ={{d00 / detJ, d10 / detJ, d20 / detJ}, {d01 / detJ, d11 / detJ, d21 / detJ}, {d02 / detJ, d12 / detJ, d22 / detJ}};
2870
2871
// Declare transformation matrix
2872
// Declare pointer to two dimensional array and initialise
2873
double **transform = new double *[num_derivatives];
2874
2875
for (unsigned int j = 0; j < num_derivatives; j++)
2876
{
2877
transform[j] = new double [num_derivatives];
2878
for (unsigned int k = 0; k < num_derivatives; k++)
2879
transform[j][k] = 1;
2880
}
2881
2882
// Construct transformation matrix
2883
for (unsigned int row = 0; row < num_derivatives; row++)
2884
{
2885
for (unsigned int col = 0; col < num_derivatives; col++)
2886
{
2887
for (unsigned int k = 0; k < n; k++)
2888
transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
2889
}
2890
}
2891
2892
// Reset values
2893
for (unsigned int j = 0; j < 1*num_derivatives; j++)
2894
values[j] = 0;
2895
2896
// Map degree of freedom to element degree of freedom
2897
const unsigned int dof = i;
2898
2899
// Generate scalings
2900
const double scalings_y_0 = 1;
2901
const double scalings_z_0 = 1;
2902
2903
// Compute psitilde_a
2904
const double psitilde_a_0 = 1;
2905
2906
// Compute psitilde_bs
2907
const double psitilde_bs_0_0 = 1;
2908
2909
// Compute psitilde_cs
2910
const double psitilde_cs_00_0 = 1;
2911
2912
// Compute basisvalues
2913
const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
2914
2915
// Table(s) of coefficients
2916
const static double coefficients0[1][1] = \
2917
{{1.15470053837925}};
2918
2919
// Interesting (new) part
2920
// Tables of derivatives of the polynomial base (transpose)
2921
const static double dmats0[1][1] = \
2922
{{0}};
2923
2924
const static double dmats1[1][1] = \
2925
{{0}};
2926
2927
const static double dmats2[1][1] = \
2928
{{0}};
2929
2930
// Compute reference derivatives
2931
// Declare pointer to array of derivatives on FIAT element
2932
double *derivatives = new double [num_derivatives];
2933
2934
// Declare coefficients
2935
double coeff0_0 = 0;
2936
2937
// Declare new coefficients
2938
double new_coeff0_0 = 0;
2939
2940
// Loop possible derivatives
2941
for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
2942
{
2943
// Get values from coefficients array
2944
new_coeff0_0 = coefficients0[dof][0];
2945
2946
// Loop derivative order
2947
for (unsigned int j = 0; j < n; j++)
2948
{
2949
// Update old coefficients
2950
coeff0_0 = new_coeff0_0;
2951
2952
if(combinations[deriv_num][j] == 0)
2953
{
2954
new_coeff0_0 = coeff0_0*dmats0[0][0];
2955
}
2956
if(combinations[deriv_num][j] == 1)
2957
{
2958
new_coeff0_0 = coeff0_0*dmats1[0][0];
2959
}
2960
if(combinations[deriv_num][j] == 2)
2961
{
2962
new_coeff0_0 = coeff0_0*dmats2[0][0];
2963
}
2964
2965
}
2966
// Compute derivatives on reference element as dot product of coefficients and basisvalues
2967
derivatives[deriv_num] = new_coeff0_0*basisvalue0;
2968
}
2969
2970
// Transform derivatives back to physical element
2971
for (unsigned int row = 0; row < num_derivatives; row++)
2972
{
2973
for (unsigned int col = 0; col < num_derivatives; col++)
2974
{
2975
values[row] += transform[row][col]*derivatives[col];
2976
}
2977
}
2978
// Delete pointer to array of derivatives on FIAT element
2979
delete [] derivatives;
2980
2981
// Delete pointer to array of combinations of derivatives and transform
2982
for (unsigned int row = 0; row < num_derivatives; row++)
2983
{
2984
delete [] combinations[row];
2985
delete [] transform[row];
2986
}
2987
2988
delete [] combinations;
2989
delete [] transform;
2990
}
2991
2992
/// Evaluate order n derivatives of all basis functions at given point in cell
2993
virtual void evaluate_basis_derivatives_all(unsigned int n,
2994
double* values,
2995
const double* coordinates,
2996
const ufc::cell& c) const
2997
{
2998
throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");
2999
}
3000
3001
/// Evaluate linear functional for dof i on the function f
3002
virtual double evaluate_dof(unsigned int i,
3003
const ufc::function& f,
3004
const ufc::cell& c) const
3005
{
3006
// The reference points, direction and weights:
3007
const static double X[1][1][3] = {{{0.25, 0.25, 0.25}}};
3008
const static double W[1][1] = {{1}};
3009
const static double D[1][1][1] = {{{1}}};
3010
3011
const double * const * x = c.coordinates;
3012
double result = 0.0;
3013
// Iterate over the points:
3014
// Evaluate basis functions for affine mapping
3015
const double w0 = 1.0 - X[i][0][0] - X[i][0][1] - X[i][0][2];
3016
const double w1 = X[i][0][0];
3017
const double w2 = X[i][0][1];
3018
const double w3 = X[i][0][2];
3019
3020
// Compute affine mapping y = F(X)
3021
double y[3];
3022
y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0] + w3*x[3][0];
3023
y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1] + w3*x[3][1];
3024
y[2] = w0*x[0][2] + w1*x[1][2] + w2*x[2][2] + w3*x[3][2];
3025
3026
// Evaluate function at physical points
3027
double values[1];
3028
f.evaluate(values, y, c);
3029
3030
// Map function values using appropriate mapping
3031
// Affine map: Do nothing
3032
3033
// Note that we do not map the weights (yet).
3034
3035
// Take directional components
3036
for(int k = 0; k < 1; k++)
3037
result += values[k]*D[i][0][k];
3038
// Multiply by weights
3039
result *= W[i][0];
3040
3041
return result;
3042
}
3043
3044
/// Evaluate linear functionals for all dofs on the function f
3045
virtual void evaluate_dofs(double* values,
3046
const ufc::function& f,
3047
const ufc::cell& c) const
3048
{
3049
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
3050
}
3051
3052
/// Interpolate vertex values from dof values
3053
virtual void interpolate_vertex_values(double* vertex_values,
3054
const double* dof_values,
3055
const ufc::cell& c) const
3056
{
3057
// Evaluate at vertices and use affine mapping
3058
vertex_values[0] = dof_values[0];
3059
vertex_values[1] = dof_values[0];
3060
vertex_values[2] = dof_values[0];
3061
vertex_values[3] = dof_values[0];
3062
}
3063
3064
/// Return the number of sub elements (for a mixed element)
3065
virtual unsigned int num_sub_elements() const
3066
{
3067
return 1;
3068
}
3069
3070
/// Create a new finite element for sub element i (for a mixed element)
3071
virtual ufc::finite_element* create_sub_element(unsigned int i) const
3072
{
3073
return new UFC_AdvectionBilinearForm_finite_element_2_2();
3074
}
3075
3076
};
3077
3078
/// This class defines the interface for a finite element.
3079
3080
class UFC_AdvectionBilinearForm_finite_element_2: public ufc::finite_element
3081
{
3082
public:
3083
3084
/// Constructor
3085
UFC_AdvectionBilinearForm_finite_element_2() : ufc::finite_element()
3086
{
3087
// Do nothing
3088
}
3089
3090
/// Destructor
3091
virtual ~UFC_AdvectionBilinearForm_finite_element_2()
3092
{
3093
// Do nothing
3094
}
3095
3096
/// Return a string identifying the finite element
3097
virtual const char* signature() const
3098
{
3099
return "Mixed finite element: [Discontinuous Lagrange finite element of degree 0 on a tetrahedron, Discontinuous Lagrange finite element of degree 0 on a tetrahedron, Discontinuous Lagrange finite element of degree 0 on a tetrahedron]";
3100
}
3101
3102
/// Return the cell shape
3103
virtual ufc::shape cell_shape() const
3104
{
3105
return ufc::tetrahedron;
3106
}
3107
3108
/// Return the dimension of the finite element function space
3109
virtual unsigned int space_dimension() const
3110
{
3111
return 3;
3112
}
3113
3114
/// Return the rank of the value space
3115
virtual unsigned int value_rank() const
3116
{
3117
return 1;
3118
}
3119
3120
/// Return the dimension of the value space for axis i
3121
virtual unsigned int value_dimension(unsigned int i) const
3122
{
3123
return 3;
3124
}
3125
3126
/// Evaluate basis function i at given point in cell
3127
virtual void evaluate_basis(unsigned int i,
3128
double* values,
3129
const double* coordinates,
3130
const ufc::cell& c) const
3131
{
3132
// Extract vertex coordinates
3133
const double * const * element_coordinates = c.coordinates;
3134
3135
// Compute Jacobian of affine map from reference cell
3136
const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
3137
const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
3138
const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];
3139
const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
3140
const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
3141
const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];
3142
const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];
3143
const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];
3144
const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];
3145
3146
// Compute sub determinants
3147
const double d00 = J_11*J_22 - J_12*J_21;
3148
const double d01 = J_12*J_20 - J_10*J_22;
3149
const double d02 = J_10*J_21 - J_11*J_20;
3150
3151
const double d10 = J_02*J_21 - J_01*J_22;
3152
const double d11 = J_00*J_22 - J_02*J_20;
3153
const double d12 = J_01*J_20 - J_00*J_21;
3154
3155
const double d20 = J_01*J_12 - J_02*J_11;
3156
const double d21 = J_02*J_10 - J_00*J_12;
3157
const double d22 = J_00*J_11 - J_01*J_10;
3158
3159
// Compute determinant of Jacobian
3160
double detJ = J_00*d00 + J_10*d10 + J_20*d20;
3161
3162
// Compute inverse of Jacobian
3163
3164
// Compute constants
3165
const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \
3166
+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \
3167
+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);
3168
3169
const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \
3170
+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \
3171
+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);
3172
3173
const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \
3174
+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \
3175
+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);
3176
3177
// Get coordinates and map to the UFC reference element
3178
double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;
3179
double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;
3180
double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;
3181
3182
// Map coordinates to the reference cube
3183
if (std::abs(y + z - 1.0) < 1e-14)
3184
x = 1.0;
3185
else
3186
x = -2.0 * x/(y + z - 1.0) - 1.0;
3187
if (std::abs(z - 1.0) < 1e-14)
3188
y = -1.0;
3189
else
3190
y = 2.0 * y/(1.0 - z) - 1.0;
3191
z = 2.0 * z - 1.0;
3192
3193
// Reset values
3194
values[0] = 0;
3195
values[1] = 0;
3196
values[2] = 0;
3197
3198
if (0 <= i && i <= 0)
3199
{
3200
// Map degree of freedom to element degree of freedom
3201
const unsigned int dof = i;
3202
3203
// Generate scalings
3204
const double scalings_y_0 = 1;
3205
const double scalings_z_0 = 1;
3206
3207
// Compute psitilde_a
3208
const double psitilde_a_0 = 1;
3209
3210
// Compute psitilde_bs
3211
const double psitilde_bs_0_0 = 1;
3212
3213
// Compute psitilde_cs
3214
const double psitilde_cs_00_0 = 1;
3215
3216
// Compute basisvalues
3217
const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
3218
3219
// Table(s) of coefficients
3220
const static double coefficients0[1][1] = \
3221
{{1.15470053837925}};
3222
3223
// Extract relevant coefficients
3224
const double coeff0_0 = coefficients0[dof][0];
3225
3226
// Compute value(s)
3227
values[0] = coeff0_0*basisvalue0;
3228
}
3229
3230
if (1 <= i && i <= 1)
3231
{
3232
// Map degree of freedom to element degree of freedom
3233
const unsigned int dof = i - 1;
3234
3235
// Generate scalings
3236
const double scalings_y_0 = 1;
3237
const double scalings_z_0 = 1;
3238
3239
// Compute psitilde_a
3240
const double psitilde_a_0 = 1;
3241
3242
// Compute psitilde_bs
3243
const double psitilde_bs_0_0 = 1;
3244
3245
// Compute psitilde_cs
3246
const double psitilde_cs_00_0 = 1;
3247
3248
// Compute basisvalues
3249
const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
3250
3251
// Table(s) of coefficients
3252
const static double coefficients0[1][1] = \
3253
{{1.15470053837925}};
3254
3255
// Extract relevant coefficients
3256
const double coeff0_0 = coefficients0[dof][0];
3257
3258
// Compute value(s)
3259
values[1] = coeff0_0*basisvalue0;
3260
}
3261
3262
if (2 <= i && i <= 2)
3263
{
3264
// Map degree of freedom to element degree of freedom
3265
const unsigned int dof = i - 2;
3266
3267
// Generate scalings
3268
const double scalings_y_0 = 1;
3269
const double scalings_z_0 = 1;
3270
3271
// Compute psitilde_a
3272
const double psitilde_a_0 = 1;
3273
3274
// Compute psitilde_bs
3275
const double psitilde_bs_0_0 = 1;
3276
3277
// Compute psitilde_cs
3278
const double psitilde_cs_00_0 = 1;
3279
3280
// Compute basisvalues
3281
const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
3282
3283
// Table(s) of coefficients
3284
const static double coefficients0[1][1] = \
3285
{{1.15470053837925}};
3286
3287
// Extract relevant coefficients
3288
const double coeff0_0 = coefficients0[dof][0];
3289
3290
// Compute value(s)
3291
values[2] = coeff0_0*basisvalue0;
3292
}
3293
3294
}
3295
3296
/// Evaluate all basis functions at given point in cell
3297
virtual void evaluate_basis_all(double* values,
3298
const double* coordinates,
3299
const ufc::cell& c) const
3300
{
3301
throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");
3302
}
3303
3304
/// Evaluate order n derivatives of basis function i at given point in cell
3305
virtual void evaluate_basis_derivatives(unsigned int i,
3306
unsigned int n,
3307
double* values,
3308
const double* coordinates,
3309
const ufc::cell& c) const
3310
{
3311
// Extract vertex coordinates
3312
const double * const * element_coordinates = c.coordinates;
3313
3314
// Compute Jacobian of affine map from reference cell
3315
const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
3316
const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
3317
const double J_02 = element_coordinates[3][0] - element_coordinates[0][0];
3318
const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
3319
const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
3320
const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];
3321
const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];
3322
const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];
3323
const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];
3324
3325
// Compute sub determinants
3326
const double d00 = J_11*J_22 - J_12*J_21;
3327
const double d01 = J_12*J_20 - J_10*J_22;
3328
const double d02 = J_10*J_21 - J_11*J_20;
3329
3330
const double d10 = J_02*J_21 - J_01*J_22;
3331
const double d11 = J_00*J_22 - J_02*J_20;
3332
const double d12 = J_01*J_20 - J_00*J_21;
3333
3334
const double d20 = J_01*J_12 - J_02*J_11;
3335
const double d21 = J_02*J_10 - J_00*J_12;
3336
const double d22 = J_00*J_11 - J_01*J_10;
3337
3338
// Compute determinant of Jacobian
3339
double detJ = J_00*d00 + J_10*d10 + J_20*d20;
3340
3341
// Compute inverse of Jacobian
3342
3343
// Compute constants
3344
const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \
3345
+ d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \
3346
+ d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);
3347
3348
const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \
3349
+ d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \
3350
+ d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);
3351
3352
const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \
3353
+ d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \
3354
+ d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);
3355
3356
// Get coordinates and map to the UFC reference element
3357
double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;
3358
double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;
3359
double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;
3360
3361
// Map coordinates to the reference cube
3362
if (std::abs(y + z - 1.0) < 1e-14)
3363
x = 1.0;
3364
else
3365
x = -2.0 * x/(y + z - 1.0) - 1.0;
3366
if (std::abs(z - 1.0) < 1e-14)
3367
y = -1.0;
3368
else
3369
y = 2.0 * y/(1.0 - z) - 1.0;
3370
z = 2.0 * z - 1.0;
3371
3372
// Compute number of derivatives
3373
unsigned int num_derivatives = 1;
3374
3375
for (unsigned int j = 0; j < n; j++)
3376
num_derivatives *= 3;
3377
3378
3379
// Declare pointer to two dimensional array that holds combinations of derivatives and initialise
3380
unsigned int **combinations = new unsigned int *[num_derivatives];
3381
3382
for (unsigned int j = 0; j < num_derivatives; j++)
3383
{
3384
combinations[j] = new unsigned int [n];
3385
for (unsigned int k = 0; k < n; k++)
3386
combinations[j][k] = 0;
3387
}
3388
3389
// Generate combinations of derivatives
3390
for (unsigned int row = 1; row < num_derivatives; row++)
3391
{
3392
for (unsigned int num = 0; num < row; num++)
3393
{
3394
for (unsigned int col = n-1; col+1 > 0; col--)
3395
{
3396
if (combinations[row][col] + 1 > 2)
3397
combinations[row][col] = 0;
3398
else
3399
{
3400
combinations[row][col] += 1;
3401
break;
3402
}
3403
}
3404
}
3405
}
3406
3407
// Compute inverse of Jacobian
3408
const double Jinv[3][3] ={{d00 / detJ, d10 / detJ, d20 / detJ}, {d01 / detJ, d11 / detJ, d21 / detJ}, {d02 / detJ, d12 / detJ, d22 / detJ}};
3409
3410
// Declare transformation matrix
3411
// Declare pointer to two dimensional array and initialise
3412
double **transform = new double *[num_derivatives];
3413
3414
for (unsigned int j = 0; j < num_derivatives; j++)
3415
{
3416
transform[j] = new double [num_derivatives];
3417
for (unsigned int k = 0; k < num_derivatives; k++)
3418
transform[j][k] = 1;
3419
}
3420
3421
// Construct transformation matrix
3422
for (unsigned int row = 0; row < num_derivatives; row++)
3423
{
3424
for (unsigned int col = 0; col < num_derivatives; col++)
3425
{
3426
for (unsigned int k = 0; k < n; k++)
3427
transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
3428
}
3429
}
3430
3431
// Reset values
3432
for (unsigned int j = 0; j < 3*num_derivatives; j++)
3433
values[j] = 0;
3434
3435
if (0 <= i && i <= 0)
3436
{
3437
// Map degree of freedom to element degree of freedom
3438
const unsigned int dof = i;
3439
3440
// Generate scalings
3441
const double scalings_y_0 = 1;
3442
const double scalings_z_0 = 1;
3443
3444
// Compute psitilde_a
3445
const double psitilde_a_0 = 1;
3446
3447
// Compute psitilde_bs
3448
const double psitilde_bs_0_0 = 1;
3449
3450
// Compute psitilde_cs
3451
const double psitilde_cs_00_0 = 1;
3452
3453
// Compute basisvalues
3454
const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
3455
3456
// Table(s) of coefficients
3457
const static double coefficients0[1][1] = \
3458
{{1.15470053837925}};
3459
3460
// Interesting (new) part
3461
// Tables of derivatives of the polynomial base (transpose)
3462
const static double dmats0[1][1] = \
3463
{{0}};
3464
3465
const static double dmats1[1][1] = \
3466
{{0}};
3467
3468
const static double dmats2[1][1] = \
3469
{{0}};
3470
3471
// Compute reference derivatives
3472
// Declare pointer to array of derivatives on FIAT element
3473
double *derivatives = new double [num_derivatives];
3474
3475
// Declare coefficients
3476
double coeff0_0 = 0;
3477
3478
// Declare new coefficients
3479
double new_coeff0_0 = 0;
3480
3481
// Loop possible derivatives
3482
for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
3483
{
3484
// Get values from coefficients array
3485
new_coeff0_0 = coefficients0[dof][0];
3486
3487
// Loop derivative order
3488
for (unsigned int j = 0; j < n; j++)
3489
{
3490
// Update old coefficients
3491
coeff0_0 = new_coeff0_0;
3492
3493
if(combinations[deriv_num][j] == 0)
3494
{
3495
new_coeff0_0 = coeff0_0*dmats0[0][0];
3496
}
3497
if(combinations[deriv_num][j] == 1)
3498
{
3499
new_coeff0_0 = coeff0_0*dmats1[0][0];
3500
}
3501
if(combinations[deriv_num][j] == 2)
3502
{
3503
new_coeff0_0 = coeff0_0*dmats2[0][0];
3504
}
3505
3506
}
3507
// Compute derivatives on reference element as dot product of coefficients and basisvalues
3508
derivatives[deriv_num] = new_coeff0_0*basisvalue0;
3509
}
3510
3511
// Transform derivatives back to physical element
3512
for (unsigned int row = 0; row < num_derivatives; row++)
3513
{
3514
for (unsigned int col = 0; col < num_derivatives; col++)
3515
{
3516
values[row] += transform[row][col]*derivatives[col];
3517
}
3518
}
3519
// Delete pointer to array of derivatives on FIAT element
3520
delete [] derivatives;
3521
3522
// Delete pointer to array of combinations of derivatives and transform
3523
for (unsigned int row = 0; row < num_derivatives; row++)
3524
{
3525
delete [] combinations[row];
3526
delete [] transform[row];
3527
}
3528
3529
delete [] combinations;
3530
delete [] transform;
3531
}
3532
3533
if (1 <= i && i <= 1)
3534
{
3535
// Map degree of freedom to element degree of freedom
3536
const unsigned int dof = i - 1;
3537
3538
// Generate scalings
3539
const double scalings_y_0 = 1;
3540
const double scalings_z_0 = 1;
3541
3542
// Compute psitilde_a
3543
const double psitilde_a_0 = 1;
3544
3545
// Compute psitilde_bs
3546
const double psitilde_bs_0_0 = 1;
3547
3548
// Compute psitilde_cs
3549
const double psitilde_cs_00_0 = 1;
3550
3551
// Compute basisvalues
3552
const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
3553
3554
// Table(s) of coefficients
3555
const static double coefficients0[1][1] = \
3556
{{1.15470053837925}};
3557
3558
// Interesting (new) part
3559
// Tables of derivatives of the polynomial base (transpose)
3560
const static double dmats0[1][1] = \
3561
{{0}};
3562
3563
const static double dmats1[1][1] = \
3564
{{0}};
3565
3566
const static double dmats2[1][1] = \
3567
{{0}};
3568
3569
// Compute reference derivatives
3570
// Declare pointer to array of derivatives on FIAT element
3571
double *derivatives = new double [num_derivatives];
3572
3573
// Declare coefficients
3574
double coeff0_0 = 0;
3575
3576
// Declare new coefficients
3577
double new_coeff0_0 = 0;
3578
3579
// Loop possible derivatives
3580
for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
3581
{
3582
// Get values from coefficients array
3583
new_coeff0_0 = coefficients0[dof][0];
3584
3585
// Loop derivative order
3586
for (unsigned int j = 0; j < n; j++)
3587
{
3588
// Update old coefficients
3589
coeff0_0 = new_coeff0_0;
3590
3591
if(combinations[deriv_num][j] == 0)
3592
{
3593
new_coeff0_0 = coeff0_0*dmats0[0][0];
3594
}
3595
if(combinations[deriv_num][j] == 1)
3596
{
3597
new_coeff0_0 = coeff0_0*dmats1[0][0];
3598
}
3599
if(combinations[deriv_num][j] == 2)
3600
{
3601
new_coeff0_0 = coeff0_0*dmats2[0][0];
3602
}
3603
3604
}
3605
// Compute derivatives on reference element as dot product of coefficients and basisvalues
3606
derivatives[deriv_num] = new_coeff0_0*basisvalue0;
3607
}
3608
3609
// Transform derivatives back to physical element
3610
for (unsigned int row = 0; row < num_derivatives; row++)
3611
{
3612
for (unsigned int col = 0; col < num_derivatives; col++)
3613
{
3614
values[num_derivatives + row] += transform[row][col]*derivatives[col];
3615
}
3616
}
3617
// Delete pointer to array of derivatives on FIAT element
3618
delete [] derivatives;
3619
3620
// Delete pointer to array of combinations of derivatives and transform
3621
for (unsigned int row = 0; row < num_derivatives; row++)
3622
{
3623
delete [] combinations[row];
3624
delete [] transform[row];
3625
}
3626
3627
delete [] combinations;
3628
delete [] transform;
3629
}
3630
3631
if (2 <= i && i <= 2)
3632
{
3633
// Map degree of freedom to element degree of freedom
3634
const unsigned int dof = i - 2;
3635
3636
// Generate scalings
3637
const double scalings_y_0 = 1;
3638
const double scalings_z_0 = 1;
3639
3640
// Compute psitilde_a
3641
const double psitilde_a_0 = 1;
3642
3643
// Compute psitilde_bs
3644
const double psitilde_bs_0_0 = 1;
3645
3646
// Compute psitilde_cs
3647
const double psitilde_cs_00_0 = 1;
3648
3649
// Compute basisvalues
3650
const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
3651
3652
// Table(s) of coefficients
3653
const static double coefficients0[1][1] = \
3654
{{1.15470053837925}};
3655
3656
// Interesting (new) part
3657
// Tables of derivatives of the polynomial base (transpose)
3658
const static double dmats0[1][1] = \
3659
{{0}};
3660
3661
const static double dmats1[1][1] = \
3662
{{0}};
3663
3664
const static double dmats2[1][1] = \
3665
{{0}};
3666
3667
// Compute reference derivatives
3668
// Declare pointer to array of derivatives on FIAT element
3669
double *derivatives = new double [num_derivatives];
3670
3671
// Declare coefficients
3672
double coeff0_0 = 0;
3673
3674
// Declare new coefficients
3675
double new_coeff0_0 = 0;
3676
3677
// Loop possible derivatives
3678
for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
3679
{
3680
// Get values from coefficients array
3681
new_coeff0_0 = coefficients0[dof][0];
3682
3683
// Loop derivative order
3684
for (unsigned int j = 0; j < n; j++)
3685
{
3686
// Update old coefficients
3687
coeff0_0 = new_coeff0_0;
3688
3689
if(combinations[deriv_num][j] == 0)
3690
{
3691
new_coeff0_0 = coeff0_0*dmats0[0][0];
3692
}
3693
if(combinations[deriv_num][j] == 1)
3694
{
3695
new_coeff0_0 = coeff0_0*dmats1[0][0];
3696
}
3697
if(combinations[deriv_num][j] == 2)
3698
{
3699
new_coeff0_0 = coeff0_0*dmats2[0][0];
3700
}
3701
3702
}
3703
// Compute derivatives on reference element as dot product of coefficients and basisvalues
3704
derivatives[deriv_num] = new_coeff0_0*basisvalue0;
3705
}
3706
3707
// Transform derivatives back to physical element
3708
for (unsigned int row = 0; row < num_derivatives; row++)
3709
{
3710
for (unsigned int col = 0; col < num_derivatives; col++)
3711
{
3712
values[2*num_derivatives + row] += transform[row][col]*derivatives[col];
3713
}
3714
}
3715
// Delete pointer to array of derivatives on FIAT element
3716
delete [] derivatives;
3717
3718
// Delete pointer to array of combinations of derivatives and transform
3719
for (unsigned int row = 0; row < num_derivatives; row++)
3720
{
3721
delete [] combinations[row];
3722
delete [] transform[row];
3723
}
3724
3725
delete [] combinations;
3726
delete [] transform;
3727
}
3728
3729
}
3730
3731
/// Evaluate order n derivatives of all basis functions at given point in cell
3732
virtual void evaluate_basis_derivatives_all(unsigned int n,
3733
double* values,
3734
const double* coordinates,
3735
const ufc::cell& c) const
3736
{
3737
throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");
3738
}
3739
3740
/// Evaluate linear functional for dof i on the function f
3741
virtual double evaluate_dof(unsigned int i,
3742
const ufc::function& f,
3743
const ufc::cell& c) const
3744
{
3745
// The reference points, direction and weights:
3746
const static double X[3][1][3] = {{{0.25, 0.25, 0.25}}, {{0.25, 0.25, 0.25}}, {{0.25, 0.25, 0.25}}};
3747
const static double W[3][1] = {{1}, {1}, {1}};
3748
const static double D[3][1][3] = {{{1, 0, 0}}, {{0, 1, 0}}, {{0, 0, 1}}};
3749
3750
const double * const * x = c.coordinates;
3751
double result = 0.0;
3752
// Iterate over the points:
3753
// Evaluate basis functions for affine mapping
3754
const double w0 = 1.0 - X[i][0][0] - X[i][0][1] - X[i][0][2];
3755
const double w1 = X[i][0][0];
3756
const double w2 = X[i][0][1];
3757
const double w3 = X[i][0][2];
3758
3759
// Compute affine mapping y = F(X)
3760
double y[3];
3761
y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0] + w3*x[3][0];
3762
y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1] + w3*x[3][1];
3763
y[2] = w0*x[0][2] + w1*x[1][2] + w2*x[2][2] + w3*x[3][2];
3764
3765
// Evaluate function at physical points
3766
double values[3];
3767
f.evaluate(values, y, c);
3768
3769
// Map function values using appropriate mapping
3770
// Affine map: Do nothing
3771
3772
// Note that we do not map the weights (yet).
3773
3774
// Take directional components
3775
for(int k = 0; k < 3; k++)
3776
result += values[k]*D[i][0][k];
3777
// Multiply by weights
3778
result *= W[i][0];
3779
3780
return result;
3781
}
3782
3783
/// Evaluate linear functionals for all dofs on the function f
3784
virtual void evaluate_dofs(double* values,
3785
const ufc::function& f,
3786
const ufc::cell& c) const
3787
{
3788
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
3789
}
3790
3791
/// Interpolate vertex values from dof values
3792
virtual void interpolate_vertex_values(double* vertex_values,
3793
const double* dof_values,
3794
const ufc::cell& c) const
3795
{
3796
// Evaluate at vertices and use affine mapping
3797
vertex_values[0] = dof_values[0];
3798
vertex_values[3] = dof_values[0];
3799
vertex_values[6] = dof_values[0];
3800
vertex_values[9] = dof_values[0];
3801
// Evaluate at vertices and use affine mapping
3802
vertex_values[1] = dof_values[1];
3803
vertex_values[4] = dof_values[1];
3804
vertex_values[7] = dof_values[1];
3805
vertex_values[10] = dof_values[1];
3806
// Evaluate at vertices and use affine mapping
3807
vertex_values[2] = dof_values[2];
3808
vertex_values[5] = dof_values[2];
3809
vertex_values[8] = dof_values[2];
3810
vertex_values[11] = dof_values[2];
3811
}
3812
3813
/// Return the number of sub elements (for a mixed element)
3814
virtual unsigned int num_sub_elements() const
3815
{
3816
return 3;
3817
}
3818
3819
/// Create a new finite element for sub element i (for a mixed element)
3820
virtual ufc::finite_element* create_sub_element(unsigned int i) const
3821
{
3822
switch ( i )
3823
{
3824
case 0:
3825
return new UFC_AdvectionBilinearForm_finite_element_2_0();
3826
break;
3827
case 1:
3828
return new UFC_AdvectionBilinearForm_finite_element_2_1();
3829
break;
3830
case 2:
3831
return new UFC_AdvectionBilinearForm_finite_element_2_2();
3832
break;
3833
}
3834
return 0;
3835
}
3836
3837
};
3838
3839
/// This class defines the interface for a local-to-global mapping of
3840
/// degrees of freedom (dofs).
3841
3842
class UFC_AdvectionBilinearForm_dof_map_0: public ufc::dof_map
3843
{
3844
private:
3845
3846
unsigned int __global_dimension;
3847
3848
public:
3849
3850
/// Constructor
3851
UFC_AdvectionBilinearForm_dof_map_0() : ufc::dof_map()
3852
{
3853
__global_dimension = 0;
3854
}
3855
3856
/// Destructor
3857
virtual ~UFC_AdvectionBilinearForm_dof_map_0()
3858
{
3859
// Do nothing
3860
}
3861
3862
/// Return a string identifying the dof map
3863
virtual const char* signature() const
3864
{
3865
return "FFC dof map for Lagrange finite element of degree 3 on a tetrahedron";
3866
}
3867
3868
/// Return true iff mesh entities of topological dimension d are needed
3869
virtual bool needs_mesh_entities(unsigned int d) const
3870
{
3871
switch ( d )
3872
{
3873
case 0:
3874
return true;
3875
break;
3876
case 1:
3877
return true;
3878
break;
3879
case 2:
3880
return true;
3881
break;
3882
case 3:
3883
return false;
3884
break;
3885
}
3886
return false;
3887
}
3888
3889
/// Initialize dof map for mesh (return true iff init_cell() is needed)
3890
virtual bool init_mesh(const ufc::mesh& m)
3891
{
3892
__global_dimension = m.num_entities[0] + 2*m.num_entities[1] + m.num_entities[2];
3893
return false;
3894
}
3895
3896
/// Initialize dof map for given cell
3897
virtual void init_cell(const ufc::mesh& m,
3898
const ufc::cell& c)
3899
{
3900
// Do nothing
3901
}
3902
3903
/// Finish initialization of dof map for cells
3904
virtual void init_cell_finalize()
3905
{
3906
// Do nothing
3907
}
3908
3909
/// Return the dimension of the global finite element function space
3910
virtual unsigned int global_dimension() const
3911
{
3912
return __global_dimension;
3913
}
3914
3915
/// Return the dimension of the local finite element function space
3916
virtual unsigned int local_dimension() const
3917
{
3918
return 20;
3919
}
3920
3921
// Return the geometric dimension of the coordinates this dof map provides
3922
virtual unsigned int geometric_dimension() const
3923
{
3924
return 3;
3925
}
3926
3927
/// Return the number of dofs on each cell facet
3928
virtual unsigned int num_facet_dofs() const
3929
{
3930
return 10;
3931
}
3932
3933
/// Return the number of dofs associated with each cell entity of dimension d
3934
virtual unsigned int num_entity_dofs(unsigned int d) const
3935
{
3936
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
3937
}
3938
3939
/// Tabulate the local-to-global mapping of dofs on a cell
3940
virtual void tabulate_dofs(unsigned int* dofs,
3941
const ufc::mesh& m,
3942
const ufc::cell& c) const
3943
{
3944
dofs[0] = c.entity_indices[0][0];
3945
dofs[1] = c.entity_indices[0][1];
3946
dofs[2] = c.entity_indices[0][2];
3947
dofs[3] = c.entity_indices[0][3];
3948
unsigned int offset = m.num_entities[0];
3949
dofs[4] = offset + 2*c.entity_indices[1][0];
3950
dofs[5] = offset + 2*c.entity_indices[1][0] + 1;
3951
dofs[6] = offset + 2*c.entity_indices[1][1];
3952
dofs[7] = offset + 2*c.entity_indices[1][1] + 1;
3953
dofs[8] = offset + 2*c.entity_indices[1][2];
3954
dofs[9] = offset + 2*c.entity_indices[1][2] + 1;
3955
dofs[10] = offset + 2*c.entity_indices[1][3];
3956
dofs[11] = offset + 2*c.entity_indices[1][3] + 1;
3957
dofs[12] = offset + 2*c.entity_indices[1][4];
3958
dofs[13] = offset + 2*c.entity_indices[1][4] + 1;
3959
dofs[14] = offset + 2*c.entity_indices[1][5];
3960
dofs[15] = offset + 2*c.entity_indices[1][5] + 1;
3961
offset = offset + 2*m.num_entities[1];
3962
dofs[16] = offset + c.entity_indices[2][0];
3963
dofs[17] = offset + c.entity_indices[2][1];
3964
dofs[18] = offset + c.entity_indices[2][2];
3965
dofs[19] = offset + c.entity_indices[2][3];
3966
}
3967
3968
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
3969
virtual void tabulate_facet_dofs(unsigned int* dofs,
3970
unsigned int facet) const
3971
{
3972
switch ( facet )
3973
{
3974
case 0:
3975
dofs[0] = 1;
3976
dofs[1] = 2;
3977
dofs[2] = 3;
3978
dofs[3] = 4;
3979
dofs[4] = 5;
3980
dofs[5] = 6;
3981
dofs[6] = 7;
3982
dofs[7] = 8;
3983
dofs[8] = 9;
3984
dofs[9] = 16;
3985
break;
3986
case 1:
3987
dofs[0] = 0;
3988
dofs[1] = 2;
3989
dofs[2] = 3;
3990
dofs[3] = 4;
3991
dofs[4] = 5;
3992
dofs[5] = 10;
3993
dofs[6] = 11;
3994
dofs[7] = 12;
3995
dofs[8] = 13;
3996
dofs[9] = 17;
3997
break;
3998
case 2:
3999
dofs[0] = 0;
4000
dofs[1] = 1;
4001
dofs[2] = 3;
4002
dofs[3] = 6;
4003
dofs[4] = 7;
4004
dofs[5] = 10;
4005
dofs[6] = 11;
4006
dofs[7] = 14;
4007
dofs[8] = 15;
4008
dofs[9] = 18;
4009
break;
4010
case 3:
4011
dofs[0] = 0;
4012
dofs[1] = 1;
4013
dofs[2] = 2;
4014
dofs[3] = 8;
4015
dofs[4] = 9;
4016
dofs[5] = 12;
4017
dofs[6] = 13;
4018
dofs[7] = 14;
4019
dofs[8] = 15;
4020
dofs[9] = 19;
4021
break;
4022
}
4023
}
4024
4025
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
4026
virtual void tabulate_entity_dofs(unsigned int* dofs,
4027
unsigned int d, unsigned int i) const
4028
{
4029
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
4030
}
4031
4032
/// Tabulate the coordinates of all dofs on a cell
4033
virtual void tabulate_coordinates(double** coordinates,
4034
const ufc::cell& c) const
4035
{
4036
const double * const * x = c.coordinates;
4037
coordinates[0][0] = x[0][0];
4038
coordinates[0][1] = x[0][1];
4039
coordinates[0][2] = x[0][2];
4040
coordinates[1][0] = x[1][0];
4041
coordinates[1][1] = x[1][1];
4042
coordinates[1][2] = x[1][2];
4043
coordinates[2][0] = x[2][0];
4044
coordinates[2][1] = x[2][1];
4045
coordinates[2][2] = x[2][2];
4046
coordinates[3][0] = x[3][0];
4047
coordinates[3][1] = x[3][1];
4048
coordinates[3][2] = x[3][2];
4049
coordinates[4][0] = 0.666666666666667*x[2][0] + 0.333333333333333*x[3][0];
4050
coordinates[4][1] = 0.666666666666667*x[2][1] + 0.333333333333333*x[3][1];
4051
coordinates[4][2] = 0.666666666666667*x[2][2] + 0.333333333333333*x[3][2];
4052
coordinates[5][0] = 0.333333333333333*x[2][0] + 0.666666666666667*x[3][0];
4053
coordinates[5][1] = 0.333333333333333*x[2][1] + 0.666666666666667*x[3][1];
4054
coordinates[5][2] = 0.333333333333333*x[2][2] + 0.666666666666667*x[3][2];
4055
coordinates[6][0] = 0.666666666666667*x[1][0] + 0.333333333333333*x[3][0];
4056
coordinates[6][1] = 0.666666666666667*x[1][1] + 0.333333333333333*x[3][1];
4057
coordinates[6][2] = 0.666666666666667*x[1][2] + 0.333333333333333*x[3][2];
4058
coordinates[7][0] = 0.333333333333333*x[1][0] + 0.666666666666667*x[3][0];
4059
coordinates[7][1] = 0.333333333333333*x[1][1] + 0.666666666666667*x[3][1];
4060
coordinates[7][2] = 0.333333333333333*x[1][2] + 0.666666666666667*x[3][2];
4061
coordinates[8][0] = 0.666666666666667*x[1][0] + 0.333333333333333*x[2][0];
4062
coordinates[8][1] = 0.666666666666667*x[1][1] + 0.333333333333333*x[2][1];
4063
coordinates[8][2] = 0.666666666666667*x[1][2] + 0.333333333333333*x[2][2];
4064
coordinates[9][0] = 0.333333333333333*x[1][0] + 0.666666666666667*x[2][0];
4065
coordinates[9][1] = 0.333333333333333*x[1][1] + 0.666666666666667*x[2][1];
4066
coordinates[9][2] = 0.333333333333333*x[1][2] + 0.666666666666667*x[2][2];
4067
coordinates[10][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[3][0];
4068
coordinates[10][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[3][1];
4069
coordinates[10][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[3][2];
4070
coordinates[11][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[3][0];
4071
coordinates[11][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[3][1];
4072
coordinates[11][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[3][2];
4073
coordinates[12][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[2][0];
4074
coordinates[12][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[2][1];
4075
coordinates[12][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[2][2];
4076
coordinates[13][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[2][0];
4077
coordinates[13][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[2][1];
4078
coordinates[13][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[2][2];
4079
coordinates[14][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[1][0];
4080
coordinates[14][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[1][1];
4081
coordinates[14][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[1][2];
4082
coordinates[15][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[1][0];
4083
coordinates[15][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[1][1];
4084
coordinates[15][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[1][2];
4085
coordinates[16][0] = 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0] + 0.333333333333333*x[3][0];
4086
coordinates[16][1] = 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1] + 0.333333333333333*x[3][1];
4087
coordinates[16][2] = 0.333333333333333*x[1][2] + 0.333333333333333*x[2][2] + 0.333333333333333*x[3][2];
4088
coordinates[17][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[2][0] + 0.333333333333333*x[3][0];
4089
coordinates[17][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[2][1] + 0.333333333333333*x[3][1];
4090
coordinates[17][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[2][2] + 0.333333333333333*x[3][2];
4091
coordinates[18][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[3][0];
4092
coordinates[18][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[3][1];
4093
coordinates[18][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[3][2];
4094
coordinates[19][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0];
4095
coordinates[19][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1];
4096
coordinates[19][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[2][2];
4097
}
4098
4099
/// Return the number of sub dof maps (for a mixed element)
4100
virtual unsigned int num_sub_dof_maps() const
4101
{
4102
return 1;
4103
}
4104
4105
/// Create a new dof_map for sub dof map i (for a mixed element)
4106
virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
4107
{
4108
return new UFC_AdvectionBilinearForm_dof_map_0();
4109
}
4110
4111
};
4112
4113
/// This class defines the interface for a local-to-global mapping of
4114
/// degrees of freedom (dofs).
4115
4116
class UFC_AdvectionBilinearForm_dof_map_1: public ufc::dof_map
4117
{
4118
private:
4119
4120
unsigned int __global_dimension;
4121
4122
public:
4123
4124
/// Constructor
4125
UFC_AdvectionBilinearForm_dof_map_1() : ufc::dof_map()
4126
{
4127
__global_dimension = 0;
4128
}
4129
4130
/// Destructor
4131
virtual ~UFC_AdvectionBilinearForm_dof_map_1()
4132
{
4133
// Do nothing
4134
}
4135
4136
/// Return a string identifying the dof map
4137
virtual const char* signature() const
4138
{
4139
return "FFC dof map for Lagrange finite element of degree 3 on a tetrahedron";
4140
}
4141
4142
/// Return true iff mesh entities of topological dimension d are needed
4143
virtual bool needs_mesh_entities(unsigned int d) const
4144
{
4145
switch ( d )
4146
{
4147
case 0:
4148
return true;
4149
break;
4150
case 1:
4151
return true;
4152
break;
4153
case 2:
4154
return true;
4155
break;
4156
case 3:
4157
return false;
4158
break;
4159
}
4160
return false;
4161
}
4162
4163
/// Initialize dof map for mesh (return true iff init_cell() is needed)
4164
virtual bool init_mesh(const ufc::mesh& m)
4165
{
4166
__global_dimension = m.num_entities[0] + 2*m.num_entities[1] + m.num_entities[2];
4167
return false;
4168
}
4169
4170
/// Initialize dof map for given cell
4171
virtual void init_cell(const ufc::mesh& m,
4172
const ufc::cell& c)
4173
{
4174
// Do nothing
4175
}
4176
4177
/// Finish initialization of dof map for cells
4178
virtual void init_cell_finalize()
4179
{
4180
// Do nothing
4181
}
4182
4183
/// Return the dimension of the global finite element function space
4184
virtual unsigned int global_dimension() const
4185
{
4186
return __global_dimension;
4187
}
4188
4189
/// Return the dimension of the local finite element function space
4190
virtual unsigned int local_dimension() const
4191
{
4192
return 20;
4193
}
4194
4195
// Return the geometric dimension of the coordinates this dof map provides
4196
virtual unsigned int geometric_dimension() const
4197
{
4198
return 3;
4199
}
4200
4201
/// Return the number of dofs on each cell facet
4202
virtual unsigned int num_facet_dofs() const
4203
{
4204
return 10;
4205
}
4206
4207
/// Return the number of dofs associated with each cell entity of dimension d
4208
virtual unsigned int num_entity_dofs(unsigned int d) const
4209
{
4210
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
4211
}
4212
4213
/// Tabulate the local-to-global mapping of dofs on a cell
4214
virtual void tabulate_dofs(unsigned int* dofs,
4215
const ufc::mesh& m,
4216
const ufc::cell& c) const
4217
{
4218
dofs[0] = c.entity_indices[0][0];
4219
dofs[1] = c.entity_indices[0][1];
4220
dofs[2] = c.entity_indices[0][2];
4221
dofs[3] = c.entity_indices[0][3];
4222
unsigned int offset = m.num_entities[0];
4223
dofs[4] = offset + 2*c.entity_indices[1][0];
4224
dofs[5] = offset + 2*c.entity_indices[1][0] + 1;
4225
dofs[6] = offset + 2*c.entity_indices[1][1];
4226
dofs[7] = offset + 2*c.entity_indices[1][1] + 1;
4227
dofs[8] = offset + 2*c.entity_indices[1][2];
4228
dofs[9] = offset + 2*c.entity_indices[1][2] + 1;
4229
dofs[10] = offset + 2*c.entity_indices[1][3];
4230
dofs[11] = offset + 2*c.entity_indices[1][3] + 1;
4231
dofs[12] = offset + 2*c.entity_indices[1][4];
4232
dofs[13] = offset + 2*c.entity_indices[1][4] + 1;
4233
dofs[14] = offset + 2*c.entity_indices[1][5];
4234
dofs[15] = offset + 2*c.entity_indices[1][5] + 1;
4235
offset = offset + 2*m.num_entities[1];
4236
dofs[16] = offset + c.entity_indices[2][0];
4237
dofs[17] = offset + c.entity_indices[2][1];
4238
dofs[18] = offset + c.entity_indices[2][2];
4239
dofs[19] = offset + c.entity_indices[2][3];
4240
}
4241
4242
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
4243
virtual void tabulate_facet_dofs(unsigned int* dofs,
4244
unsigned int facet) const
4245
{
4246
switch ( facet )
4247
{
4248
case 0:
4249
dofs[0] = 1;
4250
dofs[1] = 2;
4251
dofs[2] = 3;
4252
dofs[3] = 4;
4253
dofs[4] = 5;
4254
dofs[5] = 6;
4255
dofs[6] = 7;
4256
dofs[7] = 8;
4257
dofs[8] = 9;
4258
dofs[9] = 16;
4259
break;
4260
case 1:
4261
dofs[0] = 0;
4262
dofs[1] = 2;
4263
dofs[2] = 3;
4264
dofs[3] = 4;
4265
dofs[4] = 5;
4266
dofs[5] = 10;
4267
dofs[6] = 11;
4268
dofs[7] = 12;
4269
dofs[8] = 13;
4270
dofs[9] = 17;
4271
break;
4272
case 2:
4273
dofs[0] = 0;
4274
dofs[1] = 1;
4275
dofs[2] = 3;
4276
dofs[3] = 6;
4277
dofs[4] = 7;
4278
dofs[5] = 10;
4279
dofs[6] = 11;
4280
dofs[7] = 14;
4281
dofs[8] = 15;
4282
dofs[9] = 18;
4283
break;
4284
case 3:
4285
dofs[0] = 0;
4286
dofs[1] = 1;
4287
dofs[2] = 2;
4288
dofs[3] = 8;
4289
dofs[4] = 9;
4290
dofs[5] = 12;
4291
dofs[6] = 13;
4292
dofs[7] = 14;
4293
dofs[8] = 15;
4294
dofs[9] = 19;
4295
break;
4296
}
4297
}
4298
4299
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
4300
virtual void tabulate_entity_dofs(unsigned int* dofs,
4301
unsigned int d, unsigned int i) const
4302
{
4303
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
4304
}
4305
4306
/// Tabulate the coordinates of all dofs on a cell
4307
virtual void tabulate_coordinates(double** coordinates,
4308
const ufc::cell& c) const
4309
{
4310
const double * const * x = c.coordinates;
4311
coordinates[0][0] = x[0][0];
4312
coordinates[0][1] = x[0][1];
4313
coordinates[0][2] = x[0][2];
4314
coordinates[1][0] = x[1][0];
4315
coordinates[1][1] = x[1][1];
4316
coordinates[1][2] = x[1][2];
4317
coordinates[2][0] = x[2][0];
4318
coordinates[2][1] = x[2][1];
4319
coordinates[2][2] = x[2][2];
4320
coordinates[3][0] = x[3][0];
4321
coordinates[3][1] = x[3][1];
4322
coordinates[3][2] = x[3][2];
4323
coordinates[4][0] = 0.666666666666667*x[2][0] + 0.333333333333333*x[3][0];
4324
coordinates[4][1] = 0.666666666666667*x[2][1] + 0.333333333333333*x[3][1];
4325
coordinates[4][2] = 0.666666666666667*x[2][2] + 0.333333333333333*x[3][2];
4326
coordinates[5][0] = 0.333333333333333*x[2][0] + 0.666666666666667*x[3][0];
4327
coordinates[5][1] = 0.333333333333333*x[2][1] + 0.666666666666667*x[3][1];
4328
coordinates[5][2] = 0.333333333333333*x[2][2] + 0.666666666666667*x[3][2];
4329
coordinates[6][0] = 0.666666666666667*x[1][0] + 0.333333333333333*x[3][0];
4330
coordinates[6][1] = 0.666666666666667*x[1][1] + 0.333333333333333*x[3][1];
4331
coordinates[6][2] = 0.666666666666667*x[1][2] + 0.333333333333333*x[3][2];
4332
coordinates[7][0] = 0.333333333333333*x[1][0] + 0.666666666666667*x[3][0];
4333
coordinates[7][1] = 0.333333333333333*x[1][1] + 0.666666666666667*x[3][1];
4334
coordinates[7][2] = 0.333333333333333*x[1][2] + 0.666666666666667*x[3][2];
4335
coordinates[8][0] = 0.666666666666667*x[1][0] + 0.333333333333333*x[2][0];
4336
coordinates[8][1] = 0.666666666666667*x[1][1] + 0.333333333333333*x[2][1];
4337
coordinates[8][2] = 0.666666666666667*x[1][2] + 0.333333333333333*x[2][2];
4338
coordinates[9][0] = 0.333333333333333*x[1][0] + 0.666666666666667*x[2][0];
4339
coordinates[9][1] = 0.333333333333333*x[1][1] + 0.666666666666667*x[2][1];
4340
coordinates[9][2] = 0.333333333333333*x[1][2] + 0.666666666666667*x[2][2];
4341
coordinates[10][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[3][0];
4342
coordinates[10][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[3][1];
4343
coordinates[10][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[3][2];
4344
coordinates[11][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[3][0];
4345
coordinates[11][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[3][1];
4346
coordinates[11][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[3][2];
4347
coordinates[12][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[2][0];
4348
coordinates[12][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[2][1];
4349
coordinates[12][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[2][2];
4350
coordinates[13][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[2][0];
4351
coordinates[13][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[2][1];
4352
coordinates[13][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[2][2];
4353
coordinates[14][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[1][0];
4354
coordinates[14][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[1][1];
4355
coordinates[14][2] = 0.666666666666667*x[0][2] + 0.333333333333333*x[1][2];
4356
coordinates[15][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[1][0];
4357
coordinates[15][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[1][1];
4358
coordinates[15][2] = 0.333333333333333*x[0][2] + 0.666666666666667*x[1][2];
4359
coordinates[16][0] = 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0] + 0.333333333333333*x[3][0];
4360
coordinates[16][1] = 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1] + 0.333333333333333*x[3][1];
4361
coordinates[16][2] = 0.333333333333333*x[1][2] + 0.333333333333333*x[2][2] + 0.333333333333333*x[3][2];
4362
coordinates[17][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[2][0] + 0.333333333333333*x[3][0];
4363
coordinates[17][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[2][1] + 0.333333333333333*x[3][1];
4364
coordinates[17][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[2][2] + 0.333333333333333*x[3][2];
4365
coordinates[18][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[3][0];
4366
coordinates[18][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[3][1];
4367
coordinates[18][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[3][2];
4368
coordinates[19][0] = 0.333333333333333*x[0][0] + 0.333333333333333*x[1][0] + 0.333333333333333*x[2][0];
4369
coordinates[19][1] = 0.333333333333333*x[0][1] + 0.333333333333333*x[1][1] + 0.333333333333333*x[2][1];
4370
coordinates[19][2] = 0.333333333333333*x[0][2] + 0.333333333333333*x[1][2] + 0.333333333333333*x[2][2];
4371
}
4372
4373
/// Return the number of sub dof maps (for a mixed element)
4374
virtual unsigned int num_sub_dof_maps() const
4375
{
4376
return 1;
4377
}
4378
4379
/// Create a new dof_map for sub dof map i (for a mixed element)
4380
virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
4381
{
4382
return new UFC_AdvectionBilinearForm_dof_map_1();
4383
}
4384
4385
};
4386
4387
/// This class defines the interface for a local-to-global mapping of
4388
/// degrees of freedom (dofs).
4389
4390
class UFC_AdvectionBilinearForm_dof_map_2_0: public ufc::dof_map
4391
{
4392
private:
4393
4394
unsigned int __global_dimension;
4395
4396
public:
4397
4398
/// Constructor
4399
UFC_AdvectionBilinearForm_dof_map_2_0() : ufc::dof_map()
4400
{
4401
__global_dimension = 0;
4402
}
4403
4404
/// Destructor
4405
virtual ~UFC_AdvectionBilinearForm_dof_map_2_0()
4406
{
4407
// Do nothing
4408
}
4409
4410
/// Return a string identifying the dof map
4411
virtual const char* signature() const
4412
{
4413
return "FFC dof map for Discontinuous Lagrange finite element of degree 0 on a tetrahedron";
4414
}
4415
4416
/// Return true iff mesh entities of topological dimension d are needed
4417
virtual bool needs_mesh_entities(unsigned int d) const
4418
{
4419
switch ( d )
4420
{
4421
case 0:
4422
return false;
4423
break;
4424
case 1:
4425
return false;
4426
break;
4427
case 2:
4428
return false;
4429
break;
4430
case 3:
4431
return true;
4432
break;
4433
}
4434
return false;
4435
}
4436
4437
/// Initialize dof map for mesh (return true iff init_cell() is needed)
4438
virtual bool init_mesh(const ufc::mesh& m)
4439
{
4440
__global_dimension = m.num_entities[3];
4441
return false;
4442
}
4443
4444
/// Initialize dof map for given cell
4445
virtual void init_cell(const ufc::mesh& m,
4446
const ufc::cell& c)
4447
{
4448
// Do nothing
4449
}
4450
4451
/// Finish initialization of dof map for cells
4452
virtual void init_cell_finalize()
4453
{
4454
// Do nothing
4455
}
4456
4457
/// Return the dimension of the global finite element function space
4458
virtual unsigned int global_dimension() const
4459
{
4460
return __global_dimension;
4461
}
4462
4463
/// Return the dimension of the local finite element function space
4464
virtual unsigned int local_dimension() const
4465
{
4466
return 1;
4467
}
4468
4469
// Return the geometric dimension of the coordinates this dof map provides
4470
virtual unsigned int geometric_dimension() const
4471
{
4472
return 3;
4473
}
4474
4475
/// Return the number of dofs on each cell facet
4476
virtual unsigned int num_facet_dofs() const
4477
{
4478
return 0;
4479
}
4480
4481
/// Return the number of dofs associated with each cell entity of dimension d
4482
virtual unsigned int num_entity_dofs(unsigned int d) const
4483
{
4484
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
4485
}
4486
4487
/// Tabulate the local-to-global mapping of dofs on a cell
4488
virtual void tabulate_dofs(unsigned int* dofs,
4489
const ufc::mesh& m,
4490
const ufc::cell& c) const
4491
{
4492
dofs[0] = c.entity_indices[3][0];
4493
}
4494
4495
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
4496
virtual void tabulate_facet_dofs(unsigned int* dofs,
4497
unsigned int facet) const
4498
{
4499
switch ( facet )
4500
{
4501
case 0:
4502
4503
break;
4504
case 1:
4505
4506
break;
4507
case 2:
4508
4509
break;
4510
case 3:
4511
4512
break;
4513
}
4514
}
4515
4516
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
4517
virtual void tabulate_entity_dofs(unsigned int* dofs,
4518
unsigned int d, unsigned int i) const
4519
{
4520
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
4521
}
4522
4523
/// Tabulate the coordinates of all dofs on a cell
4524
virtual void tabulate_coordinates(double** coordinates,
4525
const ufc::cell& c) const
4526
{
4527
const double * const * x = c.coordinates;
4528
coordinates[0][0] = 0.25*x[0][0] + 0.25*x[1][0] + 0.25*x[2][0] + 0.25*x[3][0];
4529
coordinates[0][1] = 0.25*x[0][1] + 0.25*x[1][1] + 0.25*x[2][1] + 0.25*x[3][1];
4530
coordinates[0][2] = 0.25*x[0][2] + 0.25*x[1][2] + 0.25*x[2][2] + 0.25*x[3][2];
4531
}
4532
4533
/// Return the number of sub dof maps (for a mixed element)
4534
virtual unsigned int num_sub_dof_maps() const
4535
{
4536
return 1;
4537
}
4538
4539
/// Create a new dof_map for sub dof map i (for a mixed element)
4540
virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
4541
{
4542
return new UFC_AdvectionBilinearForm_dof_map_2_0();
4543
}
4544
4545
};
4546
4547
/// This class defines the interface for a local-to-global mapping of
4548
/// degrees of freedom (dofs).
4549
4550
class UFC_AdvectionBilinearForm_dof_map_2_1: public ufc::dof_map
4551
{
4552
private:
4553
4554
unsigned int __global_dimension;
4555
4556
public:
4557
4558
/// Constructor
4559
UFC_AdvectionBilinearForm_dof_map_2_1() : ufc::dof_map()
4560
{
4561
__global_dimension = 0;
4562
}
4563
4564
/// Destructor
4565
virtual ~UFC_AdvectionBilinearForm_dof_map_2_1()
4566
{
4567
// Do nothing
4568
}
4569
4570
/// Return a string identifying the dof map
4571
virtual const char* signature() const
4572
{
4573
return "FFC dof map for Discontinuous Lagrange finite element of degree 0 on a tetrahedron";
4574
}
4575
4576
/// Return true iff mesh entities of topological dimension d are needed
4577
virtual bool needs_mesh_entities(unsigned int d) const
4578
{
4579
switch ( d )
4580
{
4581
case 0:
4582
return false;
4583
break;
4584
case 1:
4585
return false;
4586
break;
4587
case 2:
4588
return false;
4589
break;
4590
case 3:
4591
return true;
4592
break;
4593
}
4594
return false;
4595
}
4596
4597
/// Initialize dof map for mesh (return true iff init_cell() is needed)
4598
virtual bool init_mesh(const ufc::mesh& m)
4599
{
4600
__global_dimension = m.num_entities[3];
4601
return false;
4602
}
4603
4604
/// Initialize dof map for given cell
4605
virtual void init_cell(const ufc::mesh& m,
4606
const ufc::cell& c)
4607
{
4608
// Do nothing
4609
}
4610
4611
/// Finish initialization of dof map for cells
4612
virtual void init_cell_finalize()
4613
{
4614
// Do nothing
4615
}
4616
4617
/// Return the dimension of the global finite element function space
4618
virtual unsigned int global_dimension() const
4619
{
4620
return __global_dimension;
4621
}
4622
4623
/// Return the dimension of the local finite element function space
4624
virtual unsigned int local_dimension() const
4625
{
4626
return 1;
4627
}
4628
4629
// Return the geometric dimension of the coordinates this dof map provides
4630
virtual unsigned int geometric_dimension() const
4631
{
4632
return 3;
4633
}
4634
4635
/// Return the number of dofs on each cell facet
4636
virtual unsigned int num_facet_dofs() const
4637
{
4638
return 0;
4639
}
4640
4641
/// Return the number of dofs associated with each cell entity of dimension d
4642
virtual unsigned int num_entity_dofs(unsigned int d) const
4643
{
4644
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
4645
}
4646
4647
/// Tabulate the local-to-global mapping of dofs on a cell
4648
virtual void tabulate_dofs(unsigned int* dofs,
4649
const ufc::mesh& m,
4650
const ufc::cell& c) const
4651
{
4652
dofs[0] = c.entity_indices[3][0];
4653
}
4654
4655
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
4656
virtual void tabulate_facet_dofs(unsigned int* dofs,
4657
unsigned int facet) const
4658
{
4659
switch ( facet )
4660
{
4661
case 0:
4662
4663
break;
4664
case 1:
4665
4666
break;
4667
case 2:
4668
4669
break;
4670
case 3:
4671
4672
break;
4673
}
4674
}
4675
4676
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
4677
virtual void tabulate_entity_dofs(unsigned int* dofs,
4678
unsigned int d, unsigned int i) const
4679
{
4680
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
4681
}
4682
4683
/// Tabulate the coordinates of all dofs on a cell
4684
virtual void tabulate_coordinates(double** coordinates,
4685
const ufc::cell& c) const
4686
{
4687
const double * const * x = c.coordinates;
4688
coordinates[0][0] = 0.25*x[0][0] + 0.25*x[1][0] + 0.25*x[2][0] + 0.25*x[3][0];
4689
coordinates[0][1] = 0.25*x[0][1] + 0.25*x[1][1] + 0.25*x[2][1] + 0.25*x[3][1];
4690
coordinates[0][2] = 0.25*x[0][2] + 0.25*x[1][2] + 0.25*x[2][2] + 0.25*x[3][2];
4691
}
4692
4693
/// Return the number of sub dof maps (for a mixed element)
4694
virtual unsigned int num_sub_dof_maps() const
4695
{
4696
return 1;
4697
}
4698
4699
/// Create a new dof_map for sub dof map i (for a mixed element)
4700
virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
4701
{
4702
return new UFC_AdvectionBilinearForm_dof_map_2_1();
4703
}
4704
4705
};
4706
4707
/// This class defines the interface for a local-to-global mapping of
4708
/// degrees of freedom (dofs).
4709
4710
class UFC_AdvectionBilinearForm_dof_map_2_2: public ufc::dof_map
4711
{
4712
private:
4713
4714
unsigned int __global_dimension;
4715
4716
public:
4717
4718
/// Constructor
4719
UFC_AdvectionBilinearForm_dof_map_2_2() : ufc::dof_map()
4720
{
4721
__global_dimension = 0;
4722
}
4723
4724
/// Destructor
4725
virtual ~UFC_AdvectionBilinearForm_dof_map_2_2()
4726
{
4727
// Do nothing
4728
}
4729
4730
/// Return a string identifying the dof map
4731
virtual const char* signature() const
4732
{
4733
return "FFC dof map for Discontinuous Lagrange finite element of degree 0 on a tetrahedron";
4734
}
4735
4736
/// Return true iff mesh entities of topological dimension d are needed
4737
virtual bool needs_mesh_entities(unsigned int d) const
4738
{
4739
switch ( d )
4740
{
4741
case 0:
4742
return false;
4743
break;
4744
case 1:
4745
return false;
4746
break;
4747
case 2:
4748
return false;
4749
break;
4750
case 3:
4751
return true;
4752
break;
4753
}
4754
return false;
4755
}
4756
4757
/// Initialize dof map for mesh (return true iff init_cell() is needed)
4758
virtual bool init_mesh(const ufc::mesh& m)
4759
{
4760
__global_dimension = m.num_entities[3];
4761
return false;
4762
}
4763
4764
/// Initialize dof map for given cell
4765
virtual void init_cell(const ufc::mesh& m,
4766
const ufc::cell& c)
4767
{
4768
// Do nothing
4769
}
4770
4771
/// Finish initialization of dof map for cells
4772
virtual void init_cell_finalize()
4773
{
4774
// Do nothing
4775
}
4776
4777
/// Return the dimension of the global finite element function space
4778
virtual unsigned int global_dimension() const
4779
{
4780
return __global_dimension;
4781
}
4782
4783
/// Return the dimension of the local finite element function space
4784
virtual unsigned int local_dimension() const
4785
{
4786
return 1;
4787
}
4788
4789
// Return the geometric dimension of the coordinates this dof map provides
4790
virtual unsigned int geometric_dimension() const
4791
{
4792
return 3;
4793
}
4794
4795
/// Return the number of dofs on each cell facet
4796
virtual unsigned int num_facet_dofs() const
4797
{
4798
return 0;
4799
}
4800
4801
/// Return the number of dofs associated with each cell entity of dimension d
4802
virtual unsigned int num_entity_dofs(unsigned int d) const
4803
{
4804
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
4805
}
4806
4807
/// Tabulate the local-to-global mapping of dofs on a cell
4808
virtual void tabulate_dofs(unsigned int* dofs,
4809
const ufc::mesh& m,
4810
const ufc::cell& c) const
4811
{
4812
dofs[0] = c.entity_indices[3][0];
4813
}
4814
4815
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
4816
virtual void tabulate_facet_dofs(unsigned int* dofs,
4817
unsigned int facet) const
4818
{
4819
switch ( facet )
4820
{
4821
case 0:
4822
4823
break;
4824
case 1:
4825
4826
break;
4827
case 2:
4828
4829
break;
4830
case 3:
4831
4832
break;
4833
}
4834
}
4835
4836
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
4837
virtual void tabulate_entity_dofs(unsigned int* dofs,
4838
unsigned int d, unsigned int i) const
4839
{
4840
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
4841
}
4842
4843
/// Tabulate the coordinates of all dofs on a cell
4844
virtual void tabulate_coordinates(double** coordinates,
4845
const ufc::cell& c) const
4846
{
4847
const double * const * x = c.coordinates;
4848
coordinates[0][0] = 0.25*x[0][0] + 0.25*x[1][0] + 0.25*x[2][0] + 0.25*x[3][0];
4849
coordinates[0][1] = 0.25*x[0][1] + 0.25*x[1][1] + 0.25*x[2][1] + 0.25*x[3][1];
4850
coordinates[0][2] = 0.25*x[0][2] + 0.25*x[1][2] + 0.25*x[2][2] + 0.25*x[3][2];
4851
}
4852
4853
/// Return the number of sub dof maps (for a mixed element)
4854
virtual unsigned int num_sub_dof_maps() const
4855
{
4856
return 1;
4857
}
4858
4859
/// Create a new dof_map for sub dof map i (for a mixed element)
4860
virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
4861
{
4862
return new UFC_AdvectionBilinearForm_dof_map_2_2();
4863
}
4864
4865
};
4866
4867
/// This class defines the interface for a local-to-global mapping of
4868
/// degrees of freedom (dofs).
4869
4870
class UFC_AdvectionBilinearForm_dof_map_2: public ufc::dof_map
4871
{
4872
private:
4873
4874
unsigned int __global_dimension;
4875
4876
public:
4877
4878
/// Constructor
4879
UFC_AdvectionBilinearForm_dof_map_2() : ufc::dof_map()
4880
{
4881
__global_dimension = 0;
4882
}
4883
4884
/// Destructor
4885
virtual ~UFC_AdvectionBilinearForm_dof_map_2()
4886
{
4887
// Do nothing
4888
}
4889
4890
/// Return a string identifying the dof map
4891
virtual const char* signature() const
4892
{
4893
return "FFC dof map for Mixed finite element: [Discontinuous Lagrange finite element of degree 0 on a tetrahedron, Discontinuous Lagrange finite element of degree 0 on a tetrahedron, Discontinuous Lagrange finite element of degree 0 on a tetrahedron]";
4894
}
4895
4896
/// Return true iff mesh entities of topological dimension d are needed
4897
virtual bool needs_mesh_entities(unsigned int d) const
4898
{
4899
switch ( d )
4900
{
4901
case 0:
4902
return false;
4903
break;
4904
case 1:
4905
return false;
4906
break;
4907
case 2:
4908
return false;
4909
break;
4910
case 3:
4911
return true;
4912
break;
4913
}
4914
return false;
4915
}
4916
4917
/// Initialize dof map for mesh (return true iff init_cell() is needed)
4918
virtual bool init_mesh(const ufc::mesh& m)
4919
{
4920
__global_dimension = 3*m.num_entities[3];
4921
return false;
4922
}
4923
4924
/// Initialize dof map for given cell
4925
virtual void init_cell(const ufc::mesh& m,
4926
const ufc::cell& c)
4927
{
4928
// Do nothing
4929
}
4930
4931
/// Finish initialization of dof map for cells
4932
virtual void init_cell_finalize()
4933
{
4934
// Do nothing
4935
}
4936
4937
/// Return the dimension of the global finite element function space
4938
virtual unsigned int global_dimension() const
4939
{
4940
return __global_dimension;
4941
}
4942
4943
/// Return the dimension of the local finite element function space
4944
virtual unsigned int local_dimension() const
4945
{
4946
return 3;
4947
}
4948
4949
// Return the geometric dimension of the coordinates this dof map provides
4950
virtual unsigned int geometric_dimension() const
4951
{
4952
return 3;
4953
}
4954
4955
/// Return the number of dofs on each cell facet
4956
virtual unsigned int num_facet_dofs() const
4957
{
4958
return 0;
4959
}
4960
4961
/// Return the number of dofs associated with each cell entity of dimension d
4962
virtual unsigned int num_entity_dofs(unsigned int d) const
4963
{
4964
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
4965
}
4966
4967
/// Tabulate the local-to-global mapping of dofs on a cell
4968
virtual void tabulate_dofs(unsigned int* dofs,
4969
const ufc::mesh& m,
4970
const ufc::cell& c) const
4971
{
4972
dofs[0] = c.entity_indices[3][0];
4973
unsigned int offset = m.num_entities[3];
4974
dofs[1] = offset + c.entity_indices[3][0];
4975
offset = offset + m.num_entities[3];
4976
dofs[2] = offset + c.entity_indices[3][0];
4977
}
4978
4979
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
4980
virtual void tabulate_facet_dofs(unsigned int* dofs,
4981
unsigned int facet) const
4982
{
4983
switch ( facet )
4984
{
4985
case 0:
4986
4987
break;
4988
case 1:
4989
4990
break;
4991
case 2:
4992
4993
break;
4994
case 3:
4995
4996
break;
4997
}
4998
}
4999
5000
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
5001
virtual void tabulate_entity_dofs(unsigned int* dofs,
5002
unsigned int d, unsigned int i) const
5003
{
5004
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
5005
}
5006
5007
/// Tabulate the coordinates of all dofs on a cell
5008
virtual void tabulate_coordinates(double** coordinates,
5009
const ufc::cell& c) const
5010
{
5011
const double * const * x = c.coordinates;
5012
coordinates[0][0] = 0.25*x[0][0] + 0.25*x[1][0] + 0.25*x[2][0] + 0.25*x[3][0];
5013
coordinates[0][1] = 0.25*x[0][1] + 0.25*x[1][1] + 0.25*x[2][1] + 0.25*x[3][1];
5014
coordinates[0][2] = 0.25*x[0][2] + 0.25*x[1][2] + 0.25*x[2][2] + 0.25*x[3][2];
5015
coordinates[1][0] = 0.25*x[0][0] + 0.25*x[1][0] + 0.25*x[2][0] + 0.25*x[3][0];
5016
coordinates[1][1] = 0.25*x[0][1] + 0.25*x[1][1] + 0.25*x[2][1] + 0.25*x[3][1];
5017
coordinates[1][2] = 0.25*x[0][2] + 0.25*x[1][2] + 0.25*x[2][2] + 0.25*x[3][2];
5018
coordinates[2][0] = 0.25*x[0][0] + 0.25*x[1][0] + 0.25*x[2][0] + 0.25*x[3][0];
5019
coordinates[2][1] = 0.25*x[0][1] + 0.25*x[1][1] + 0.25*x[2][1] + 0.25*x[3][1];
5020
coordinates[2][2] = 0.25*x[0][2] + 0.25*x[1][2] + 0.25*x[2][2] + 0.25*x[3][2];
5021
}
5022
5023
/// Return the number of sub dof maps (for a mixed element)
5024
virtual unsigned int num_sub_dof_maps() const
5025
{
5026
return 3;
5027
}
5028
5029
/// Create a new dof_map for sub dof map i (for a mixed element)
5030
virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
5031
{
5032
switch ( i )
5033
{
5034
case 0:
5035
return new UFC_AdvectionBilinearForm_dof_map_2_0();
5036
break;
5037
case 1:
5038
return new UFC_AdvectionBilinearForm_dof_map_2_1();
5039
break;
5040
case 2:
5041
return new UFC_AdvectionBilinearForm_dof_map_2_2();
5042
break;
5043
}
5044
return 0;
5045
}
5046
5047
};
5048
5049
/// This class defines the interface for the tabulation of the cell
5050
/// tensor corresponding to the local contribution to a form from
5051
/// the integral over a cell.
5052
5053
class UFC_AdvectionBilinearForm_cell_integral_0: public ufc::cell_integral
5054
{
5055
public:
5056
5057
/// Constructor
5058
UFC_AdvectionBilinearForm_cell_integral_0() : ufc::cell_integral()
5059
{
5060
// Do nothing
5061
}
5062
5063
/// Destructor
5064
virtual ~UFC_AdvectionBilinearForm_cell_integral_0()
5065
{
5066
// Do nothing
5067
}
5068
5069
/// Tabulate the tensor for the contribution from a local cell
5070
virtual void tabulate_tensor(double* A,
5071
const double * const * w,
5072
const ufc::cell& c) const
5073
{
5074
// Extract vertex coordinates
5075
const double * const * x = c.coordinates;
5076
5077
// Compute Jacobian of affine map from reference cell
5078
const double J_00 = x[1][0] - x[0][0];
5079
const double J_01 = x[2][0] - x[0][0];
5080
const double J_02 = x[3][0] - x[0][0];
5081
const double J_10 = x[1][1] - x[0][1];
5082
const double J_11 = x[2][1] - x[0][1];
5083
const double J_12 = x[3][1] - x[0][1];
5084
const double J_20 = x[1][2] - x[0][2];
5085
const double J_21 = x[2][2] - x[0][2];
5086
const double J_22 = x[3][2] - x[0][2];
5087
5088
// Compute sub determinants
5089
const double d_00 = J_11*J_22 - J_12*J_21;
5090
const double d_01 = J_12*J_20 - J_10*J_22;
5091
const double d_02 = J_10*J_21 - J_11*J_20;
5092
5093
const double d_10 = J_02*J_21 - J_01*J_22;
5094
const double d_11 = J_00*J_22 - J_02*J_20;
5095
const double d_12 = J_01*J_20 - J_00*J_21;
5096
5097
const double d_20 = J_01*J_12 - J_02*J_11;
5098
const double d_21 = J_02*J_10 - J_00*J_12;
5099
const double d_22 = J_00*J_11 - J_01*J_10;
5100
5101
// Compute determinant of Jacobian
5102
double detJ = J_00*d_00 + J_10*d_10 + J_20*d_20;
5103
5104
// Compute inverse of Jacobian
5105
const double Jinv_00 = d_00 / detJ;
5106
const double Jinv_01 = d_10 / detJ;
5107
const double Jinv_02 = d_20 / detJ;
5108
const double Jinv_10 = d_01 / detJ;
5109
const double Jinv_11 = d_11 / detJ;
5110
const double Jinv_12 = d_21 / detJ;
5111
const double Jinv_20 = d_02 / detJ;
5112
const double Jinv_21 = d_12 / detJ;
5113
const double Jinv_22 = d_22 / detJ;
5114
5115
// Set scale factor
5116
const double det = std::abs(detJ);
5117
5118
// Compute coefficients
5119
const double c0_0_0_0 = w[0][0];
5120
const double c0_0_0_1 = w[0][1];
5121
const double c0_0_0_2 = w[0][2];
5122
5123
// Compute geometry tensors
5124
const double G0_0_0_0 = det*c0_0_0_0*Jinv_00;
5125
const double G0_0_0_1 = det*c0_0_0_0*Jinv_10;
5126
const double G0_0_0_2 = det*c0_0_0_0*Jinv_20;
5127
const double G0_1_1_0 = det*c0_0_0_1*Jinv_01;
5128
const double G0_1_1_1 = det*c0_0_0_1*Jinv_11;
5129
const double G0_1_1_2 = det*c0_0_0_1*Jinv_21;
5130
const double G0_2_2_0 = det*c0_0_0_2*Jinv_02;
5131
const double G0_2_2_1 = det*c0_0_0_2*Jinv_12;
5132
const double G0_2_2_2 = det*c0_0_0_2*Jinv_22;
5133
5134
// Compute element tensor
5135
A[0] = -0.00282738095238095*G0_0_0_0 - 0.00282738095238095*G0_0_0_1 - 0.00282738095238095*G0_0_0_2 - 0.00282738095238095*G0_1_1_0 - 0.00282738095238095*G0_1_1_1 - 0.00282738095238095*G0_1_1_2 - 0.00282738095238095*G0_2_2_0 - 0.00282738095238095*G0_2_2_1 - 0.00282738095238095*G0_2_2_2;
5136
A[1] = 0.000818452380952383*G0_0_0_0 + 0.000818452380952383*G0_1_1_0 + 0.000818452380952383*G0_2_2_0;
5137
A[2] = 0.000818452380952382*G0_0_0_1 + 0.000818452380952382*G0_1_1_1 + 0.000818452380952382*G0_2_2_1;
5138
A[3] = 0.000818452380952379*G0_0_0_2 + 0.000818452380952379*G0_1_1_2 + 0.000818452380952379*G0_2_2_2;
5139
A[4] = 0.00200892857142857*G0_0_0_1 + 0.00200892857142857*G0_0_0_2 + 0.00200892857142857*G0_1_1_1 + 0.00200892857142857*G0_1_1_2 + 0.00200892857142857*G0_2_2_1 + 0.00200892857142857*G0_2_2_2;
5140
A[5] = 0.00200892857142857*G0_0_0_1 + 0.00200892857142857*G0_0_0_2 + 0.00200892857142857*G0_1_1_1 + 0.00200892857142857*G0_1_1_2 + 0.00200892857142857*G0_2_2_1 + 0.00200892857142857*G0_2_2_2;
5141
A[6] = 0.00200892857142858*G0_0_0_0 + 0.00200892857142858*G0_0_0_2 + 0.00200892857142858*G0_1_1_0 + 0.00200892857142858*G0_1_1_2 + 0.00200892857142858*G0_2_2_0 + 0.00200892857142858*G0_2_2_2;
5142
A[7] = 0.00200892857142857*G0_0_0_0 + 0.00200892857142857*G0_0_0_2 + 0.00200892857142857*G0_1_1_0 + 0.00200892857142857*G0_1_1_2 + 0.00200892857142857*G0_2_2_0 + 0.00200892857142857*G0_2_2_2;
5143
A[8] = 0.00200892857142858*G0_0_0_0 + 0.00200892857142858*G0_0_0_1 + 0.00200892857142858*G0_1_1_0 + 0.00200892857142858*G0_1_1_1 + 0.00200892857142858*G0_2_2_0 + 0.00200892857142858*G0_2_2_1;
5144
A[9] = 0.00200892857142857*G0_0_0_0 + 0.00200892857142857*G0_0_0_1 + 0.00200892857142857*G0_1_1_0 + 0.00200892857142857*G0_1_1_1 + 0.00200892857142857*G0_2_2_0 + 0.00200892857142857*G0_2_2_1;
5145
A[10] = 0.00267857142857142*G0_0_0_0 + 0.00267857142857142*G0_0_0_1 + 0.00401785714285713*G0_0_0_2 + 0.00267857142857142*G0_1_1_0 + 0.00267857142857142*G0_1_1_1 + 0.00401785714285713*G0_1_1_2 + 0.00267857142857142*G0_2_2_0 + 0.00267857142857142*G0_2_2_1 + 0.00401785714285713*G0_2_2_2;
5146
A[11] = -0.00200892857142857*G0_0_0_0 - 0.00200892857142857*G0_0_0_1 - 0.00200892857142856*G0_0_0_2 - 0.00200892857142857*G0_1_1_0 - 0.00200892857142857*G0_1_1_1 - 0.00200892857142856*G0_1_1_2 - 0.00200892857142857*G0_2_2_0 - 0.00200892857142857*G0_2_2_1 - 0.00200892857142856*G0_2_2_2;
5147
A[12] = 0.00267857142857143*G0_0_0_0 + 0.00401785714285714*G0_0_0_1 + 0.00267857142857143*G0_0_0_2 + 0.00267857142857143*G0_1_1_0 + 0.00401785714285714*G0_1_1_1 + 0.00267857142857143*G0_1_1_2 + 0.00267857142857143*G0_2_2_0 + 0.00401785714285714*G0_2_2_1 + 0.00267857142857143*G0_2_2_2;
5148
A[13] = -0.00200892857142857*G0_0_0_0 - 0.00200892857142857*G0_0_0_1 - 0.00200892857142857*G0_0_0_2 - 0.00200892857142857*G0_1_1_0 - 0.00200892857142857*G0_1_1_1 - 0.00200892857142857*G0_1_1_2 - 0.00200892857142857*G0_2_2_0 - 0.00200892857142857*G0_2_2_1 - 0.00200892857142857*G0_2_2_2;
5149
A[14] = 0.00401785714285714*G0_0_0_0 + 0.00267857142857143*G0_0_0_1 + 0.00267857142857143*G0_0_0_2 + 0.00401785714285714*G0_1_1_0 + 0.00267857142857143*G0_1_1_1 + 0.00267857142857143*G0_1_1_2 + 0.00401785714285714*G0_2_2_0 + 0.00267857142857143*G0_2_2_1 + 0.00267857142857143*G0_2_2_2;
5150
A[15] = -0.00200892857142857*G0_0_0_0 - 0.00200892857142858*G0_0_0_1 - 0.00200892857142858*G0_0_0_2 - 0.00200892857142857*G0_1_1_0 - 0.00200892857142858*G0_1_1_1 - 0.00200892857142858*G0_1_1_2 - 0.00200892857142857*G0_2_2_0 - 0.00200892857142858*G0_2_2_1 - 0.00200892857142858*G0_2_2_2;
5151
A[16] = 0.00736607142857143*G0_0_0_0 + 0.00736607142857144*G0_0_0_1 + 0.00736607142857144*G0_0_0_2 + 0.00736607142857143*G0_1_1_0 + 0.00736607142857144*G0_1_1_1 + 0.00736607142857144*G0_1_1_2 + 0.00736607142857143*G0_2_2_0 + 0.00736607142857144*G0_2_2_1 + 0.00736607142857144*G0_2_2_2;
5152
A[17] = -0.00736607142857144*G0_0_0_0 - 0.0046875*G0_0_0_1 - 0.0046875*G0_0_0_2 - 0.00736607142857144*G0_1_1_0 - 0.0046875*G0_1_1_1 - 0.0046875*G0_1_1_2 - 0.00736607142857144*G0_2_2_0 - 0.0046875*G0_2_2_1 - 0.0046875*G0_2_2_2;
5153
A[18] = -0.0046875*G0_0_0_0 - 0.00736607142857144*G0_0_0_1 - 0.0046875*G0_0_0_2 - 0.0046875*G0_1_1_0 - 0.00736607142857144*G0_1_1_1 - 0.0046875*G0_1_1_2 - 0.0046875*G0_2_2_0 - 0.00736607142857144*G0_2_2_1 - 0.0046875*G0_2_2_2;
5154
A[19] = -0.0046875*G0_0_0_0 - 0.00468749999999999*G0_0_0_1 - 0.00736607142857144*G0_0_0_2 - 0.0046875*G0_1_1_0 - 0.00468749999999999*G0_1_1_1 - 0.00736607142857144*G0_1_1_2 - 0.0046875*G0_2_2_0 - 0.00468749999999999*G0_2_2_1 - 0.00736607142857144*G0_2_2_2;
5155
A[20] = -0.00081845238095238*G0_0_0_0 - 0.000818452380952381*G0_0_0_1 - 0.00081845238095238*G0_0_0_2 - 0.00081845238095238*G0_1_1_0 - 0.000818452380952381*G0_1_1_1 - 0.00081845238095238*G0_1_1_2 - 0.00081845238095238*G0_2_2_0 - 0.000818452380952381*G0_2_2_1 - 0.00081845238095238*G0_2_2_2;
5156
A[21] = 0.00282738095238095*G0_0_0_0 + 0.00282738095238095*G0_1_1_0 + 0.00282738095238095*G0_2_2_0;
5157
A[22] = 0.000818452380952381*G0_0_0_1 + 0.000818452380952381*G0_1_1_1 + 0.000818452380952381*G0_2_2_1;
5158
A[23] = 0.00081845238095238*G0_0_0_2 + 0.00081845238095238*G0_1_1_2 + 0.00081845238095238*G0_2_2_2;
5159
A[24] = 0.00200892857142856*G0_0_0_1 + 0.00200892857142856*G0_0_0_2 + 0.00200892857142856*G0_1_1_1 + 0.00200892857142856*G0_1_1_2 + 0.00200892857142856*G0_2_2_1 + 0.00200892857142856*G0_2_2_2;
5160
A[25] = 0.00200892857142857*G0_0_0_1 + 0.00200892857142857*G0_0_0_2 + 0.00200892857142857*G0_1_1_1 + 0.00200892857142857*G0_1_1_2 + 0.00200892857142857*G0_2_2_1 + 0.00200892857142857*G0_2_2_2;
5161
A[26] = -0.00267857142857142*G0_0_0_0 + 0.00133928571428571*G0_0_0_2 - 0.00267857142857142*G0_1_1_0 + 0.00133928571428571*G0_1_1_2 - 0.00267857142857142*G0_2_2_0 + 0.00133928571428571*G0_2_2_2;
5162
A[27] = 0.00200892857142857*G0_0_0_0 + 0.00200892857142857*G0_1_1_0 + 0.00200892857142857*G0_2_2_0;
5163
A[28] = -0.00267857142857143*G0_0_0_0 + 0.00133928571428571*G0_0_0_1 - 0.00267857142857143*G0_1_1_0 + 0.00133928571428571*G0_1_1_1 - 0.00267857142857143*G0_2_2_0 + 0.00133928571428571*G0_2_2_1;
5164
A[29] = 0.00200892857142857*G0_0_0_0 + 0.00200892857142857*G0_1_1_0 + 0.00200892857142857*G0_2_2_0;
5165
A[30] = -0.00200892857142857*G0_0_0_0 - 0.00200892857142857*G0_0_0_1 - 0.00200892857142857*G0_1_1_0 - 0.00200892857142857*G0_1_1_1 - 0.00200892857142857*G0_2_2_0 - 0.00200892857142857*G0_2_2_1;
5166
A[31] = -0.00200892857142857*G0_0_0_0 - 0.00200892857142857*G0_0_0_1 - 0.00200892857142857*G0_1_1_0 - 0.00200892857142857*G0_1_1_1 - 0.00200892857142857*G0_2_2_0 - 0.00200892857142857*G0_2_2_1;
5167
A[32] = -0.00200892857142857*G0_0_0_0 - 0.00200892857142857*G0_0_0_2 - 0.00200892857142857*G0_1_1_0 - 0.00200892857142857*G0_1_1_2 - 0.00200892857142857*G0_2_2_0 - 0.00200892857142857*G0_2_2_2;
5168
A[33] = -0.00200892857142856*G0_0_0_0 - 0.00200892857142856*G0_0_0_2 - 0.00200892857142856*G0_1_1_0 - 0.00200892857142856*G0_1_1_2 - 0.00200892857142856*G0_2_2_0 - 0.00200892857142856*G0_2_2_2;
5169
A[34] = 0.00200892857142857*G0_0_0_0 + 0.00200892857142857*G0_1_1_0 + 0.00200892857142857*G0_2_2_0;
5170
A[35] = -0.00401785714285714*G0_0_0_0 - 0.00133928571428571*G0_0_0_1 - 0.00133928571428571*G0_0_0_2 - 0.00401785714285714*G0_1_1_0 - 0.00133928571428571*G0_1_1_1 - 0.00133928571428571*G0_1_1_2 - 0.00401785714285714*G0_2_2_0 - 0.00133928571428571*G0_2_2_1 - 0.00133928571428571*G0_2_2_2;
5171
A[36] = 0.00736607142857142*G0_0_0_0 + 0.00267857142857143*G0_0_0_1 + 0.00267857142857142*G0_0_0_2 + 0.00736607142857142*G0_1_1_0 + 0.00267857142857143*G0_1_1_1 + 0.00267857142857142*G0_1_1_2 + 0.00736607142857142*G0_2_2_0 + 0.00267857142857143*G0_2_2_1 + 0.00267857142857142*G0_2_2_2;
5172
A[37] = -0.00736607142857142*G0_0_0_0 - 0.00736607142857142*G0_1_1_0 - 0.00736607142857142*G0_2_2_0;
5173
A[38] = 0.0046875*G0_0_0_0 - 0.00267857142857143*G0_0_0_1 + 0.0046875*G0_1_1_0 - 0.00267857142857143*G0_1_1_1 + 0.0046875*G0_2_2_0 - 0.00267857142857143*G0_2_2_1;
5174
A[39] = 0.0046875*G0_0_0_0 - 0.00267857142857142*G0_0_0_2 + 0.0046875*G0_1_1_0 - 0.00267857142857142*G0_1_1_2 + 0.0046875*G0_2_2_0 - 0.00267857142857142*G0_2_2_2;
5175
A[40] = -0.000818452380952381*G0_0_0_0 - 0.000818452380952381*G0_0_0_1 - 0.00081845238095238*G0_0_0_2 - 0.000818452380952381*G0_1_1_0 - 0.000818452380952381*G0_1_1_1 - 0.00081845238095238*G0_1_1_2 - 0.000818452380952381*G0_2_2_0 - 0.000818452380952381*G0_2_2_1 - 0.00081845238095238*G0_2_2_2;
5176
A[41] = 0.000818452380952381*G0_0_0_0 + 0.000818452380952381*G0_1_1_0 + 0.000818452380952381*G0_2_2_0;
5177
A[42] = 0.00282738095238095*G0_0_0_1 + 0.00282738095238095*G0_1_1_1 + 0.00282738095238095*G0_2_2_1;
5178
A[43] = 0.000818452380952381*G0_0_0_2 + 0.000818452380952381*G0_1_1_2 + 0.000818452380952381*G0_2_2_2;
5179
A[44] = -0.00267857142857143*G0_0_0_1 + 0.00133928571428571*G0_0_0_2 - 0.00267857142857143*G0_1_1_1 + 0.00133928571428571*G0_1_1_2 - 0.00267857142857143*G0_2_2_1 + 0.00133928571428571*G0_2_2_2;
5180
A[45] = 0.00200892857142857*G0_0_0_1 + 0.00200892857142857*G0_1_1_1 + 0.00200892857142857*G0_2_2_1;
5181
A[46] = 0.00200892857142857*G0_0_0_0 + 0.00200892857142857*G0_0_0_2 + 0.00200892857142857*G0_1_1_0 + 0.00200892857142857*G0_1_1_2 + 0.00200892857142857*G0_2_2_0 + 0.00200892857142857*G0_2_2_2;
5182
A[47] = 0.00200892857142857*G0_0_0_0 + 0.00200892857142856*G0_0_0_2 + 0.00200892857142857*G0_1_1_0 + 0.00200892857142856*G0_1_1_2 + 0.00200892857142857*G0_2_2_0 + 0.00200892857142856*G0_2_2_2;
5183
A[48] = 0.00200892857142857*G0_0_0_1 + 0.00200892857142857*G0_1_1_1 + 0.00200892857142857*G0_2_2_1;
5184
A[49] = 0.00133928571428571*G0_0_0_0 - 0.00267857142857143*G0_0_0_1 + 0.00133928571428571*G0_1_1_0 - 0.00267857142857143*G0_1_1_1 + 0.00133928571428571*G0_2_2_0 - 0.00267857142857143*G0_2_2_1;
5185
A[50] = -0.00200892857142857*G0_0_0_0 - 0.00200892857142857*G0_0_0_1 - 0.00200892857142857*G0_1_1_0 - 0.00200892857142857*G0_1_1_1 - 0.00200892857142857*G0_2_2_0 - 0.00200892857142857*G0_2_2_1;
5186
A[51] = -0.00200892857142857*G0_0_0_0 - 0.00200892857142857*G0_0_0_1 - 0.00200892857142857*G0_1_1_0 - 0.00200892857142857*G0_1_1_1 - 0.00200892857142857*G0_2_2_0 - 0.00200892857142857*G0_2_2_1;
5187
A[52] = 0.00200892857142857*G0_0_0_1 + 0.00200892857142857*G0_1_1_1 + 0.00200892857142857*G0_2_2_1;
5188
A[53] = -0.00133928571428571*G0_0_0_0 - 0.00401785714285714*G0_0_0_1 - 0.0013392857142857*G0_0_0_2 - 0.00133928571428571*G0_1_1_0 - 0.00401785714285714*G0_1_1_1 - 0.0013392857142857*G0_1_1_2 - 0.00133928571428571*G0_2_2_0 - 0.00401785714285714*G0_2_2_1 - 0.0013392857142857*G0_2_2_2;
5189
A[54] = -0.00200892857142857*G0_0_0_1 - 0.00200892857142857*G0_0_0_2 - 0.00200892857142857*G0_1_1_1 - 0.00200892857142857*G0_1_1_2 - 0.00200892857142857*G0_2_2_1 - 0.00200892857142857*G0_2_2_2;
5190
A[55] = -0.00200892857142857*G0_0_0_1 - 0.00200892857142857*G0_0_0_2 - 0.00200892857142857*G0_1_1_1 - 0.00200892857142857*G0_1_1_2 - 0.00200892857142857*G0_2_2_1 - 0.00200892857142857*G0_2_2_2;
5191
A[56] = 0.0026785714285714*G0_0_0_0 + 0.0073660714285714*G0_0_0_1 + 0.0026785714285714*G0_0_0_2 + 0.0026785714285714*G0_1_1_0 + 0.0073660714285714*G0_1_1_1 + 0.0026785714285714*G0_1_1_2 + 0.0026785714285714*G0_2_2_0 + 0.0073660714285714*G0_2_2_1 + 0.0026785714285714*G0_2_2_2;
5192
A[57] = -0.0026785714285714*G0_0_0_0 + 0.0046875*G0_0_0_1 - 0.0026785714285714*G0_1_1_0 + 0.0046875*G0_1_1_1 - 0.0026785714285714*G0_2_2_0 + 0.0046875*G0_2_2_1;
5193
A[58] = -0.0073660714285714*G0_0_0_1 - 0.0073660714285714*G0_1_1_1 - 0.0073660714285714*G0_2_2_1;
5194
A[59] = 0.0046875*G0_0_0_1 - 0.00267857142857141*G0_0_0_2 + 0.0046875*G0_1_1_1 - 0.00267857142857141*G0_1_1_2 + 0.0046875*G0_2_2_1 - 0.00267857142857141*G0_2_2_2;
5195
A[60] = -0.00081845238095238*G0_0_0_0 - 0.00081845238095238*G0_0_0_1 - 0.000818452380952378*G0_0_0_2 - 0.00081845238095238*G0_1_1_0 - 0.00081845238095238*G0_1_1_1 - 0.000818452380952378*G0_1_1_2 - 0.00081845238095238*G0_2_2_0 - 0.00081845238095238*G0_2_2_1 - 0.000818452380952378*G0_2_2_2;
5196
A[61] = 0.00081845238095238*G0_0_0_0 + 0.00081845238095238*G0_1_1_0 + 0.00081845238095238*G0_2_2_0;
5197
A[62] = 0.000818452380952379*G0_0_0_1 + 0.000818452380952379*G0_1_1_1 + 0.000818452380952379*G0_2_2_1;
5198
A[63] = 0.00282738095238095*G0_0_0_2 + 0.00282738095238095*G0_1_1_2 + 0.00282738095238095*G0_2_2_2;
5199
A[64] = 0.00200892857142857*G0_0_0_2 + 0.00200892857142857*G0_1_1_2 + 0.00200892857142857*G0_2_2_2;
5200
A[65] = 0.00133928571428571*G0_0_0_1 - 0.00267857142857143*G0_0_0_2 + 0.00133928571428571*G0_1_1_1 - 0.00267857142857143*G0_1_1_2 + 0.00133928571428571*G0_2_2_1 - 0.00267857142857143*G0_2_2_2;
5201
A[66] = 0.00200892857142857*G0_0_0_2 + 0.00200892857142857*G0_1_1_2 + 0.00200892857142857*G0_2_2_2;
5202
A[67] = 0.00133928571428571*G0_0_0_0 - 0.00267857142857143*G0_0_0_2 + 0.00133928571428571*G0_1_1_0 - 0.00267857142857143*G0_1_1_2 + 0.00133928571428571*G0_2_2_0 - 0.00267857142857143*G0_2_2_2;
5203
A[68] = 0.00200892857142857*G0_0_0_0 + 0.00200892857142857*G0_0_0_1 + 0.00200892857142857*G0_1_1_0 + 0.00200892857142857*G0_1_1_1 + 0.00200892857142857*G0_2_2_0 + 0.00200892857142857*G0_2_2_1;
5204
A[69] = 0.00200892857142857*G0_0_0_0 + 0.00200892857142857*G0_0_0_1 + 0.00200892857142857*G0_1_1_0 + 0.00200892857142857*G0_1_1_1 + 0.00200892857142857*G0_2_2_0 + 0.00200892857142857*G0_2_2_1;
5205
A[70] = 0.00200892857142857*G0_0_0_2 + 0.00200892857142857*G0_1_1_2 + 0.00200892857142857*G0_2_2_2;
5206
A[71] = -0.00133928571428571*G0_0_0_0 - 0.00133928571428571*G0_0_0_1 - 0.00401785714285714*G0_0_0_2 - 0.00133928571428571*G0_1_1_0 - 0.00133928571428571*G0_1_1_1 - 0.00401785714285714*G0_1_1_2 - 0.00133928571428571*G0_2_2_0 - 0.00133928571428571*G0_2_2_1 - 0.00401785714285714*G0_2_2_2;
5207
A[72] = -0.00200892857142857*G0_0_0_0 - 0.00200892857142857*G0_0_0_2 - 0.00200892857142857*G0_1_1_0 - 0.00200892857142857*G0_1_1_2 - 0.00200892857142857*G0_2_2_0 - 0.00200892857142857*G0_2_2_2;
5208
A[73] = -0.00200892857142857*G0_0_0_0 - 0.00200892857142856*G0_0_0_2 - 0.00200892857142857*G0_1_1_0 - 0.00200892857142856*G0_1_1_2 - 0.00200892857142857*G0_2_2_0 - 0.00200892857142856*G0_2_2_2;
5209
A[74] = -0.00200892857142857*G0_0_0_1 - 0.00200892857142857*G0_0_0_2 - 0.00200892857142857*G0_1_1_1 - 0.00200892857142857*G0_1_1_2 - 0.00200892857142857*G0_2_2_1 - 0.00200892857142857*G0_2_2_2;
5210
A[75] = -0.00200892857142857*G0_0_0_1 - 0.00200892857142857*G0_0_0_2 - 0.00200892857142857*G0_1_1_1 - 0.00200892857142857*G0_1_1_2 - 0.00200892857142857*G0_2_2_1 - 0.00200892857142857*G0_2_2_2;
5211
A[76] = 0.00267857142857141*G0_0_0_0 + 0.00267857142857141*G0_0_0_1 + 0.00736607142857141*G0_0_0_2 + 0.00267857142857141*G0_1_1_0 + 0.00267857142857141*G0_1_1_1 + 0.00736607142857141*G0_1_1_2 + 0.00267857142857141*G0_2_2_0 + 0.00267857142857141*G0_2_2_1 + 0.00736607142857141*G0_2_2_2;
5212
A[77] = -0.00267857142857141*G0_0_0_0 + 0.0046875*G0_0_0_2 - 0.00267857142857141*G0_1_1_0 + 0.0046875*G0_1_1_2 - 0.00267857142857141*G0_2_2_0 + 0.0046875*G0_2_2_2;
5213
A[78] = -0.00267857142857141*G0_0_0_1 + 0.00468749999999999*G0_0_0_2 - 0.00267857142857141*G0_1_1_1 + 0.00468749999999999*G0_1_1_2 - 0.00267857142857141*G0_2_2_1 + 0.00468749999999999*G0_2_2_2;
5214
A[79] = -0.00736607142857141*G0_0_0_2 - 0.00736607142857141*G0_1_1_2 - 0.00736607142857141*G0_2_2_2;
5215
A[80] = -0.00200892857142857*G0_0_0_0 - 0.00200892857142857*G0_0_0_1 - 0.00200892857142857*G0_0_0_2 - 0.00200892857142857*G0_1_1_0 - 0.00200892857142857*G0_1_1_1 - 0.00200892857142857*G0_1_1_2 - 0.00200892857142857*G0_2_2_0 - 0.00200892857142857*G0_2_2_1 - 0.00200892857142857*G0_2_2_2;
5216
A[81] = 0.00200892857142857*G0_0_0_0 + 0.00200892857142857*G0_1_1_0 + 0.00200892857142857*G0_2_2_0;
5217
A[82] = 0.00401785714285714*G0_0_0_1 + 0.00401785714285714*G0_1_1_1 + 0.00401785714285714*G0_2_2_1;
5218
A[83] = -0.00200892857142857*G0_0_0_2 - 0.00200892857142857*G0_1_1_2 - 0.00200892857142857*G0_2_2_2;
5219
A[84] = 0.0200892857142857*G0_0_0_1 + 0.0200892857142857*G0_0_0_2 + 0.0200892857142857*G0_1_1_1 + 0.0200892857142857*G0_1_1_2 + 0.0200892857142857*G0_2_2_1 + 0.0200892857142857*G0_2_2_2;
5220
A[85] = -0.0100446428571428*G0_0_0_1 - 0.00401785714285713*G0_0_0_2 - 0.0100446428571428*G0_1_1_1 - 0.00401785714285713*G0_1_1_2 - 0.0100446428571428*G0_2_2_1 - 0.00401785714285713*G0_2_2_2;
5221
A[86] = -0.00401785714285715*G0_0_0_0 - 0.00200892857142857*G0_0_0_2 - 0.00401785714285715*G0_1_1_0 - 0.00200892857142857*G0_1_1_2 - 0.00401785714285715*G0_2_2_0 - 0.00200892857142857*G0_2_2_2;
5222
A[87] = -0.0100446428571428*G0_0_0_0 - 0.00803571428571428*G0_0_0_2 - 0.0100446428571428*G0_1_1_0 - 0.00803571428571428*G0_1_1_2 - 0.0100446428571428*G0_2_2_0 - 0.00803571428571428*G0_2_2_2;
5223
A[88] = -0.0100446428571428*G0_0_0_0 - 0.00200892857142856*G0_0_0_1 - 0.0100446428571428*G0_1_1_0 - 0.00200892857142856*G0_1_1_1 - 0.0100446428571428*G0_2_2_0 - 0.00200892857142856*G0_2_2_1;
5224
A[89] = 0.0200892857142857*G0_0_0_0 + 0.0100446428571429*G0_0_0_1 + 0.0200892857142857*G0_1_1_0 + 0.0100446428571429*G0_1_1_1 + 0.0200892857142857*G0_2_2_0 + 0.0100446428571429*G0_2_2_1;
5225
A[90] = 0.00401785714285715*G0_0_0_0 + 0.00401785714285714*G0_0_0_1 + 0.00200892857142856*G0_0_0_2 + 0.00401785714285715*G0_1_1_0 + 0.00401785714285714*G0_1_1_1 + 0.00200892857142856*G0_1_1_2 + 0.00401785714285715*G0_2_2_0 + 0.00401785714285714*G0_2_2_1 + 0.00200892857142856*G0_2_2_2;
5226
A[91] = 0.0100446428571429*G0_0_0_0 + 0.0100446428571428*G0_0_0_1 + 0.00200892857142857*G0_0_0_2 + 0.0100446428571429*G0_1_1_0 + 0.0100446428571428*G0_1_1_1 + 0.00200892857142857*G0_1_1_2 + 0.0100446428571429*G0_2_2_0 + 0.0100446428571428*G0_2_2_1 + 0.00200892857142857*G0_2_2_2;
5227
A[92] = 0.0100446428571429*G0_0_0_0 + 0.00803571428571428*G0_0_0_1 + 0.0100446428571429*G0_0_0_2 + 0.0100446428571429*G0_1_1_0 + 0.00803571428571428*G0_1_1_1 + 0.0100446428571429*G0_1_1_2 + 0.0100446428571429*G0_2_2_0 + 0.00803571428571428*G0_2_2_1 + 0.0100446428571429*G0_2_2_2;
5228
A[93] = -0.0200892857142857*G0_0_0_0 - 0.0100446428571428*G0_0_0_1 - 0.0200892857142857*G0_0_0_2 - 0.0200892857142857*G0_1_1_0 - 0.0100446428571428*G0_1_1_1 - 0.0200892857142857*G0_1_1_2 - 0.0200892857142857*G0_2_2_0 - 0.0100446428571428*G0_2_2_1 - 0.0200892857142857*G0_2_2_2;
5229
A[94] = 0.00200892857142857*G0_0_0_1 + 0.00200892857142858*G0_0_0_2 + 0.00200892857142857*G0_1_1_1 + 0.00200892857142858*G0_1_1_2 + 0.00200892857142857*G0_2_2_1 + 0.00200892857142858*G0_2_2_2;
5230
A[95] = 0.00200892857142856*G0_0_0_1 + 0.00200892857142857*G0_0_0_2 + 0.00200892857142856*G0_1_1_1 + 0.00200892857142857*G0_1_1_2 + 0.00200892857142856*G0_2_2_1 + 0.00200892857142857*G0_2_2_2;
5231
A[96] = 0.0120535714285714*G0_0_0_0 - 0.0120535714285714*G0_0_0_1 + 0.00602678571428572*G0_0_0_2 + 0.0120535714285714*G0_1_1_0 - 0.0120535714285714*G0_1_1_1 + 0.00602678571428572*G0_1_1_2 + 0.0120535714285714*G0_2_2_0 - 0.0120535714285714*G0_2_2_1 + 0.00602678571428572*G0_2_2_2;
5232
A[97] = -0.0120535714285714*G0_0_0_0 - 0.0241071428571429*G0_0_0_1 - 0.00602678571428571*G0_0_0_2 - 0.0120535714285714*G0_1_1_0 - 0.0241071428571429*G0_1_1_1 - 0.00602678571428571*G0_1_1_2 - 0.0120535714285714*G0_2_2_0 - 0.0241071428571429*G0_2_2_1 - 0.00602678571428571*G0_2_2_2;
5233
A[98] = 0.0120535714285714*G0_0_0_1 + 0.0060267857142857*G0_0_0_2 + 0.0120535714285714*G0_1_1_1 + 0.0060267857142857*G0_1_1_2 + 0.0120535714285714*G0_2_2_1 + 0.0060267857142857*G0_2_2_2;
5234
A[99] = -0.0120535714285714*G0_0_0_1 - 0.00602678571428572*G0_0_0_2 - 0.0120535714285714*G0_1_1_1 - 0.00602678571428572*G0_1_1_2 - 0.0120535714285714*G0_2_2_1 - 0.00602678571428572*G0_2_2_2;
5235
A[100] = -0.00200892857142857*G0_0_0_0 - 0.00200892857142857*G0_0_0_1 - 0.00200892857142857*G0_0_0_2 - 0.00200892857142857*G0_1_1_0 - 0.00200892857142857*G0_1_1_1 - 0.00200892857142857*G0_1_1_2 - 0.00200892857142857*G0_2_2_0 - 0.00200892857142857*G0_2_2_1 - 0.00200892857142857*G0_2_2_2;
5236
A[101] = 0.00200892857142857*G0_0_0_0 + 0.00200892857142857*G0_1_1_0 + 0.00200892857142857*G0_2_2_0;
5237
A[102] = -0.00200892857142856*G0_0_0_1 - 0.00200892857142856*G0_1_1_1 - 0.00200892857142856*G0_2_2_1;
5238
A[103] = 0.00401785714285714*G0_0_0_2 + 0.00401785714285714*G0_1_1_2 + 0.00401785714285714*G0_2_2_2;
5239
A[104] = -0.00401785714285716*G0_0_0_1 - 0.0100446428571428*G0_0_0_2 - 0.00401785714285716*G0_1_1_1 - 0.0100446428571428*G0_1_1_2 - 0.00401785714285716*G0_2_2_1 - 0.0100446428571428*G0_2_2_2;
5240
A[105] = 0.0200892857142857*G0_0_0_1 + 0.0200892857142857*G0_0_0_2 + 0.0200892857142857*G0_1_1_1 + 0.0200892857142857*G0_1_1_2 + 0.0200892857142857*G0_2_2_1 + 0.0200892857142857*G0_2_2_2;
5241
A[106] = -0.0100446428571428*G0_0_0_0 - 0.00200892857142856*G0_0_0_2 - 0.0100446428571428*G0_1_1_0 - 0.00200892857142856*G0_1_1_2 - 0.0100446428571428*G0_2_2_0 - 0.00200892857142856*G0_2_2_2;
5242
A[107] = 0.0200892857142857*G0_0_0_0 + 0.0100446428571428*G0_0_0_2 + 0.0200892857142857*G0_1_1_0 + 0.0100446428571428*G0_1_1_2 + 0.0200892857142857*G0_2_2_0 + 0.0100446428571428*G0_2_2_2;
5243
A[108] = -0.00401785714285714*G0_0_0_0 - 0.00200892857142857*G0_0_0_1 - 0.00401785714285714*G0_1_1_0 - 0.00200892857142857*G0_1_1_1 - 0.00401785714285714*G0_2_2_0 - 0.00200892857142857*G0_2_2_1;
5244
A[109] = -0.0100446428571428*G0_0_0_0 - 0.00803571428571427*G0_0_0_1 - 0.0100446428571428*G0_1_1_0 - 0.00803571428571427*G0_1_1_1 - 0.0100446428571428*G0_2_2_0 - 0.00803571428571427*G0_2_2_1;
5245
A[110] = 0.0100446428571429*G0_0_0_0 + 0.0100446428571429*G0_0_0_1 + 0.00803571428571429*G0_0_0_2 + 0.0100446428571429*G0_1_1_0 + 0.0100446428571429*G0_1_1_1 + 0.00803571428571429*G0_1_1_2 + 0.0100446428571429*G0_2_2_0 + 0.0100446428571429*G0_2_2_1 + 0.00803571428571429*G0_2_2_2;
5246
A[111] = -0.0200892857142857*G0_0_0_0 - 0.0200892857142857*G0_0_0_1 - 0.0100446428571429*G0_0_0_2 - 0.0200892857142857*G0_1_1_0 - 0.0200892857142857*G0_1_1_1 - 0.0100446428571429*G0_1_1_2 - 0.0200892857142857*G0_2_2_0 - 0.0200892857142857*G0_2_2_1 - 0.0100446428571429*G0_2_2_2;
5247
A[112] = 0.00401785714285714*G0_0_0_0 + 0.00200892857142856*G0_0_0_1 + 0.00401785714285714*G0_0_0_2 + 0.00401785714285714*G0_1_1_0 + 0.00200892857142856*G0_1_1_1 + 0.00401785714285714*G0_1_1_2 + 0.00401785714285714*G0_2_2_0 + 0.00200892857142856*G0_2_2_1 + 0.00401785714285714*G0_2_2_2;
5248
A[113] = 0.0100446428571428*G0_0_0_0 + 0.00200892857142858*G0_0_0_1 + 0.0100446428571428*G0_0_0_2 + 0.0100446428571428*G0_1_1_0 + 0.00200892857142858*G0_1_1_1 + 0.0100446428571428*G0_1_1_2 + 0.0100446428571428*G0_2_2_0 + 0.00200892857142858*G0_2_2_1 + 0.0100446428571428*G0_2_2_2;
5249
A[114] = 0.00200892857142858*G0_0_0_1 + 0.00200892857142857*G0_0_0_2 + 0.00200892857142858*G0_1_1_1 + 0.00200892857142857*G0_1_1_2 + 0.00200892857142858*G0_2_2_1 + 0.00200892857142857*G0_2_2_2;
5250
A[115] = 0.00200892857142856*G0_0_0_1 + 0.00200892857142856*G0_0_0_2 + 0.00200892857142856*G0_1_1_1 + 0.00200892857142856*G0_1_1_2 + 0.00200892857142856*G0_2_2_1 + 0.00200892857142856*G0_2_2_2;
5251
A[116] = 0.0120535714285714*G0_0_0_0 + 0.00602678571428569*G0_0_0_1 - 0.0120535714285714*G0_0_0_2 + 0.0120535714285714*G0_1_1_0 + 0.00602678571428569*G0_1_1_1 - 0.0120535714285714*G0_1_1_2 + 0.0120535714285714*G0_2_2_0 + 0.00602678571428569*G0_2_2_1 - 0.0120535714285714*G0_2_2_2;
5252
A[117] = -0.0120535714285714*G0_0_0_0 - 0.00602678571428571*G0_0_0_1 - 0.0241071428571428*G0_0_0_2 - 0.0120535714285714*G0_1_1_0 - 0.00602678571428571*G0_1_1_1 - 0.0241071428571428*G0_1_1_2 - 0.0120535714285714*G0_2_2_0 - 0.00602678571428571*G0_2_2_1 - 0.0241071428571428*G0_2_2_2;
5253
A[118] = -0.0060267857142857*G0_0_0_1 - 0.0120535714285714*G0_0_0_2 - 0.0060267857142857*G0_1_1_1 - 0.0120535714285714*G0_1_1_2 - 0.0060267857142857*G0_2_2_1 - 0.0120535714285714*G0_2_2_2;
5254
A[119] = 0.00602678571428571*G0_0_0_1 + 0.0120535714285714*G0_0_0_2 + 0.00602678571428571*G0_1_1_1 + 0.0120535714285714*G0_1_1_2 + 0.00602678571428571*G0_2_2_1 + 0.0120535714285714*G0_2_2_2;
5255
A[120] = -0.00200892857142858*G0_0_0_0 - 0.00200892857142857*G0_0_0_1 - 0.00200892857142858*G0_0_0_2 - 0.00200892857142858*G0_1_1_0 - 0.00200892857142857*G0_1_1_1 - 0.00200892857142858*G0_1_1_2 - 0.00200892857142858*G0_2_2_0 - 0.00200892857142857*G0_2_2_1 - 0.00200892857142858*G0_2_2_2;
5256
A[121] = 0.00401785714285714*G0_0_0_0 + 0.00401785714285714*G0_1_1_0 + 0.00401785714285714*G0_2_2_0;
5257
A[122] = 0.00200892857142856*G0_0_0_1 + 0.00200892857142856*G0_1_1_1 + 0.00200892857142856*G0_2_2_1;
5258
A[123] = -0.00200892857142857*G0_0_0_2 - 0.00200892857142857*G0_1_1_2 - 0.00200892857142857*G0_2_2_2;
5259
A[124] = -0.00401785714285713*G0_0_0_1 - 0.00200892857142857*G0_0_0_2 - 0.00401785714285713*G0_1_1_1 - 0.00200892857142857*G0_1_1_2 - 0.00401785714285713*G0_2_2_1 - 0.00200892857142857*G0_2_2_2;
5260
A[125] = -0.0100446428571428*G0_0_0_1 - 0.00803571428571427*G0_0_0_2 - 0.0100446428571428*G0_1_1_1 - 0.00803571428571427*G0_1_1_2 - 0.0100446428571428*G0_2_2_1 - 0.00803571428571427*G0_2_2_2;
5261
A[126] = 0.0200892857142857*G0_0_0_0 + 0.0200892857142857*G0_0_0_2 + 0.0200892857142857*G0_1_1_0 + 0.0200892857142857*G0_1_1_2 + 0.0200892857142857*G0_2_2_0 + 0.0200892857142857*G0_2_2_2;
5262
A[127] = -0.0100446428571429*G0_0_0_0 - 0.00401785714285713*G0_0_0_2 - 0.0100446428571429*G0_1_1_0 - 0.00401785714285713*G0_1_1_2 - 0.0100446428571429*G0_2_2_0 - 0.00401785714285713*G0_2_2_2;
5263
A[128] = 0.0100446428571429*G0_0_0_0 + 0.0200892857142857*G0_0_0_1 + 0.0100446428571429*G0_1_1_0 + 0.0200892857142857*G0_1_1_1 + 0.0100446428571429*G0_2_2_0 + 0.0200892857142857*G0_2_2_1;
5264
A[129] = -0.00200892857142858*G0_0_0_0 - 0.0100446428571428*G0_0_0_1 - 0.00200892857142858*G0_1_1_0 - 0.0100446428571428*G0_1_1_1 - 0.00200892857142858*G0_2_2_0 - 0.0100446428571428*G0_2_2_1;
5265
A[130] = 0.00401785714285715*G0_0_0_0 + 0.00401785714285715*G0_0_0_1 + 0.00200892857142858*G0_0_0_2 + 0.00401785714285715*G0_1_1_0 + 0.00401785714285715*G0_1_1_1 + 0.00200892857142858*G0_1_1_2 + 0.00401785714285715*G0_2_2_0 + 0.00401785714285715*G0_2_2_1 + 0.00200892857142858*G0_2_2_2;
5266
A[131] = 0.0100446428571429*G0_0_0_0 + 0.0100446428571428*G0_0_0_1 + 0.00200892857142857*G0_0_0_2 + 0.0100446428571429*G0_1_1_0 + 0.0100446428571428*G0_1_1_1 + 0.00200892857142857*G0_1_1_2 + 0.0100446428571429*G0_2_2_0 + 0.0100446428571428*G0_2_2_1 + 0.00200892857142857*G0_2_2_2;
5267
A[132] = 0.00200892857142857*G0_0_0_0 + 0.00200892857142858*G0_0_0_2 + 0.00200892857142857*G0_1_1_0 + 0.00200892857142858*G0_1_1_2 + 0.00200892857142857*G0_2_2_0 + 0.00200892857142858*G0_2_2_2;
5268
A[133] = 0.00200892857142858*G0_0_0_0 + 0.00200892857142858*G0_0_0_2 + 0.00200892857142858*G0_1_1_0 + 0.00200892857142858*G0_1_1_2 + 0.00200892857142858*G0_2_2_0 + 0.00200892857142858*G0_2_2_2;
5269
A[134] = 0.00803571428571429*G0_0_0_0 + 0.0100446428571429*G0_0_0_1 + 0.0100446428571429*G0_0_0_2 + 0.00803571428571429*G0_1_1_0 + 0.0100446428571429*G0_1_1_1 + 0.0100446428571429*G0_1_1_2 + 0.00803571428571429*G0_2_2_0 + 0.0100446428571429*G0_2_2_1 + 0.0100446428571429*G0_2_2_2;
5270
A[135] = -0.0100446428571429*G0_0_0_0 - 0.0200892857142857*G0_0_0_1 - 0.0200892857142857*G0_0_0_2 - 0.0100446428571429*G0_1_1_0 - 0.0200892857142857*G0_1_1_1 - 0.0200892857142857*G0_1_1_2 - 0.0100446428571429*G0_2_2_0 - 0.0200892857142857*G0_2_2_1 - 0.0200892857142857*G0_2_2_2;
5271
A[136] = -0.0120535714285714*G0_0_0_0 + 0.0120535714285714*G0_0_0_1 + 0.00602678571428572*G0_0_0_2 - 0.0120535714285714*G0_1_1_0 + 0.0120535714285714*G0_1_1_1 + 0.00602678571428572*G0_1_1_2 - 0.0120535714285714*G0_2_2_0 + 0.0120535714285714*G0_2_2_1 + 0.00602678571428572*G0_2_2_2;
5272
A[137] = 0.0120535714285714*G0_0_0_0 + 0.00602678571428569*G0_0_0_2 + 0.0120535714285714*G0_1_1_0 + 0.00602678571428569*G0_1_1_2 + 0.0120535714285714*G0_2_2_0 + 0.00602678571428569*G0_2_2_2;
5273
A[138] = -0.0241071428571429*G0_0_0_0 - 0.0120535714285714*G0_0_0_1 - 0.00602678571428575*G0_0_0_2 - 0.0241071428571429*G0_1_1_0 - 0.0120535714285714*G0_1_1_1 - 0.00602678571428575*G0_1_1_2 - 0.0241071428571429*G0_2_2_0 - 0.0120535714285714*G0_2_2_1 - 0.00602678571428575*G0_2_2_2;
5274
A[139] = -0.0120535714285714*G0_0_0_0 - 0.00602678571428572*G0_0_0_2 - 0.0120535714285714*G0_1_1_0 - 0.00602678571428572*G0_1_1_2 - 0.0120535714285714*G0_2_2_0 - 0.00602678571428572*G0_2_2_2;
5275
A[140] = -0.00200892857142857*G0_0_0_0 - 0.00200892857142857*G0_0_0_1 - 0.00200892857142858*G0_0_0_2 - 0.00200892857142857*G0_1_1_0 - 0.00200892857142857*G0_1_1_1 - 0.00200892857142858*G0_1_1_2 - 0.00200892857142857*G0_2_2_0 - 0.00200892857142857*G0_2_2_1 - 0.00200892857142858*G0_2_2_2;
5276
A[141] = -0.00200892857142857*G0_0_0_0 - 0.00200892857142857*G0_1_1_0 - 0.00200892857142857*G0_2_2_0;
5277
A[142] = 0.00200892857142857*G0_0_0_1 + 0.00200892857142857*G0_1_1_1 + 0.00200892857142857*G0_2_2_1;
5278
A[143] = 0.00401785714285714*G0_0_0_2 + 0.00401785714285714*G0_1_1_2 + 0.00401785714285714*G0_2_2_2;
5279
A[144] = -0.0100446428571429*G0_0_0_1 - 0.00200892857142857*G0_0_0_2 - 0.0100446428571429*G0_1_1_1 - 0.00200892857142857*G0_1_1_2 - 0.0100446428571429*G0_2_2_1 - 0.00200892857142857*G0_2_2_2;
5280
A[145] = 0.0200892857142857*G0_0_0_1 + 0.0100446428571428*G0_0_0_2 + 0.0200892857142857*G0_1_1_1 + 0.0100446428571428*G0_1_1_2 + 0.0200892857142857*G0_2_2_1 + 0.0100446428571428*G0_2_2_2;
5281
A[146] = -0.00401785714285714*G0_0_0_0 - 0.0100446428571428*G0_0_0_2 - 0.00401785714285714*G0_1_1_0 - 0.0100446428571428*G0_1_1_2 - 0.00401785714285714*G0_2_2_0 - 0.0100446428571428*G0_2_2_2;
5282
A[147] = 0.0200892857142857*G0_0_0_0 + 0.0200892857142857*G0_0_0_2 + 0.0200892857142857*G0_1_1_0 + 0.0200892857142857*G0_1_1_2 + 0.0200892857142857*G0_2_2_0 + 0.0200892857142857*G0_2_2_2;
5283
A[148] = -0.0080357142857143*G0_0_0_0 - 0.0100446428571429*G0_0_0_1 - 0.0080357142857143*G0_1_1_0 - 0.0100446428571429*G0_1_1_1 - 0.0080357142857143*G0_2_2_0 - 0.0100446428571429*G0_2_2_1;
5284
A[149] = -0.00200892857142856*G0_0_0_0 - 0.00401785714285714*G0_0_0_1 - 0.00200892857142856*G0_1_1_0 - 0.00401785714285714*G0_1_1_1 - 0.00200892857142856*G0_2_2_0 - 0.00401785714285714*G0_2_2_1;
5285
A[150] = 0.0100446428571429*G0_0_0_0 + 0.0100446428571429*G0_0_0_1 + 0.00803571428571429*G0_0_0_2 + 0.0100446428571429*G0_1_1_0 + 0.0100446428571429*G0_1_1_1 + 0.00803571428571429*G0_1_1_2 + 0.0100446428571429*G0_2_2_0 + 0.0100446428571429*G0_2_2_1 + 0.00803571428571429*G0_2_2_2;
5286
A[151] = -0.0200892857142857*G0_0_0_0 - 0.0200892857142857*G0_0_0_1 - 0.0100446428571429*G0_0_0_2 - 0.0200892857142857*G0_1_1_0 - 0.0200892857142857*G0_1_1_1 - 0.0100446428571429*G0_1_1_2 - 0.0200892857142857*G0_2_2_0 - 0.0200892857142857*G0_2_2_1 - 0.0100446428571429*G0_2_2_2;
5287
A[152] = 0.00200892857142857*G0_0_0_0 + 0.00200892857142857*G0_0_0_2 + 0.00200892857142857*G0_1_1_0 + 0.00200892857142857*G0_1_1_2 + 0.00200892857142857*G0_2_2_0 + 0.00200892857142857*G0_2_2_2;
5288
A[153] = 0.00200892857142856*G0_0_0_0 + 0.00200892857142856*G0_0_0_2 + 0.00200892857142856*G0_1_1_0 + 0.00200892857142856*G0_1_1_2 + 0.00200892857142856*G0_2_2_0 + 0.00200892857142856*G0_2_2_2;
5289
A[154] = 0.00200892857142858*G0_0_0_0 + 0.00401785714285713*G0_0_0_1 + 0.00401785714285714*G0_0_0_2 + 0.00200892857142858*G0_1_1_0 + 0.00401785714285713*G0_1_1_1 + 0.00401785714285714*G0_1_1_2 + 0.00200892857142858*G0_2_2_0 + 0.00401785714285713*G0_2_2_1 + 0.00401785714285714*G0_2_2_2;
5290
A[155] = 0.00200892857142856*G0_0_0_0 + 0.0100446428571429*G0_0_0_1 + 0.0100446428571429*G0_0_0_2 + 0.00200892857142856*G0_1_1_0 + 0.0100446428571429*G0_1_1_1 + 0.0100446428571429*G0_1_1_2 + 0.00200892857142856*G0_2_2_0 + 0.0100446428571429*G0_2_2_1 + 0.0100446428571429*G0_2_2_2;
5291
A[156] = 0.0060267857142857*G0_0_0_0 + 0.0120535714285714*G0_0_0_1 - 0.0120535714285714*G0_0_0_2 + 0.0060267857142857*G0_1_1_0 + 0.0120535714285714*G0_1_1_1 - 0.0120535714285714*G0_1_1_2 + 0.0060267857142857*G0_2_2_0 + 0.0120535714285714*G0_2_2_1 - 0.0120535714285714*G0_2_2_2;
5292
A[157] = -0.00602678571428571*G0_0_0_0 - 0.0120535714285714*G0_0_0_2 - 0.00602678571428571*G0_1_1_0 - 0.0120535714285714*G0_1_1_2 - 0.00602678571428571*G0_2_2_0 - 0.0120535714285714*G0_2_2_2;
5293
A[158] = -0.0060267857142857*G0_0_0_0 - 0.0120535714285714*G0_0_0_1 - 0.0241071428571428*G0_0_0_2 - 0.0060267857142857*G0_1_1_0 - 0.0120535714285714*G0_1_1_1 - 0.0241071428571428*G0_1_1_2 - 0.0060267857142857*G0_2_2_0 - 0.0120535714285714*G0_2_2_1 - 0.0241071428571428*G0_2_2_2;
5294
A[159] = 0.00602678571428572*G0_0_0_0 + 0.0120535714285714*G0_0_0_2 + 0.00602678571428572*G0_1_1_0 + 0.0120535714285714*G0_1_1_2 + 0.00602678571428572*G0_2_2_0 + 0.0120535714285714*G0_2_2_2;
5295
A[160] = -0.00200892857142858*G0_0_0_0 - 0.00200892857142858*G0_0_0_1 - 0.00200892857142858*G0_0_0_2 - 0.00200892857142858*G0_1_1_0 - 0.00200892857142858*G0_1_1_1 - 0.00200892857142858*G0_1_1_2 - 0.00200892857142858*G0_2_2_0 - 0.00200892857142858*G0_2_2_1 - 0.00200892857142858*G0_2_2_2;
5296
A[161] = 0.00401785714285715*G0_0_0_0 + 0.00401785714285715*G0_1_1_0 + 0.00401785714285715*G0_2_2_0;
5297
A[162] = -0.00200892857142857*G0_0_0_1 - 0.00200892857142857*G0_1_1_1 - 0.00200892857142857*G0_2_2_1;
5298
A[163] = 0.00200892857142858*G0_0_0_2 + 0.00200892857142858*G0_1_1_2 + 0.00200892857142858*G0_2_2_2;
5299
A[164] = -0.00803571428571428*G0_0_0_1 - 0.0100446428571429*G0_0_0_2 - 0.00803571428571428*G0_1_1_1 - 0.0100446428571429*G0_1_1_2 - 0.00803571428571428*G0_2_2_1 - 0.0100446428571429*G0_2_2_2;
5300
A[165] = -0.00200892857142857*G0_0_0_1 - 0.00401785714285714*G0_0_0_2 - 0.00200892857142857*G0_1_1_1 - 0.00401785714285714*G0_1_1_2 - 0.00200892857142857*G0_2_2_1 - 0.00401785714285714*G0_2_2_2;
5301
A[166] = 0.0100446428571429*G0_0_0_0 + 0.0200892857142857*G0_0_0_2 + 0.0100446428571429*G0_1_1_0 + 0.0200892857142857*G0_1_1_2 + 0.0100446428571429*G0_2_2_0 + 0.0200892857142857*G0_2_2_2;
5302
A[167] = -0.00200892857142857*G0_0_0_0 - 0.0100446428571428*G0_0_0_2 - 0.00200892857142857*G0_1_1_0 - 0.0100446428571428*G0_1_1_2 - 0.00200892857142857*G0_2_2_0 - 0.0100446428571428*G0_2_2_2;
5303
A[168] = 0.0200892857142857*G0_0_0_0 + 0.0200892857142857*G0_0_0_1 + 0.0200892857142857*G0_1_1_0 + 0.0200892857142857*G0_1_1_1 + 0.0200892857142857*G0_2_2_0 + 0.0200892857142857*G0_2_2_1;
5304
A[169] = -0.0100446428571429*G0_0_0_0 - 0.00401785714285714*G0_0_0_1 - 0.0100446428571429*G0_1_1_0 - 0.00401785714285714*G0_1_1_1 - 0.0100446428571429*G0_2_2_0 - 0.00401785714285714*G0_2_2_1;
5305
A[170] = 0.00200892857142857*G0_0_0_0 + 0.00200892857142857*G0_0_0_1 + 0.00200892857142857*G0_1_1_0 + 0.00200892857142857*G0_1_1_1 + 0.00200892857142857*G0_2_2_0 + 0.00200892857142857*G0_2_2_1;
5306
A[171] = 0.00200892857142857*G0_0_0_0 + 0.00200892857142857*G0_0_0_1 + 0.00200892857142857*G0_1_1_0 + 0.00200892857142857*G0_1_1_1 + 0.00200892857142857*G0_2_2_0 + 0.00200892857142857*G0_2_2_1;
5307
A[172] = 0.00401785714285713*G0_0_0_0 + 0.00200892857142858*G0_0_0_1 + 0.00401785714285713*G0_0_0_2 + 0.00401785714285713*G0_1_1_0 + 0.00200892857142858*G0_1_1_1 + 0.00401785714285713*G0_1_1_2 + 0.00401785714285713*G0_2_2_0 + 0.00200892857142858*G0_2_2_1 + 0.00401785714285713*G0_2_2_2;
5308
A[173] = 0.0100446428571429*G0_0_0_0 + 0.00200892857142858*G0_0_0_1 + 0.0100446428571429*G0_0_0_2 + 0.0100446428571429*G0_1_1_0 + 0.00200892857142858*G0_1_1_1 + 0.0100446428571429*G0_1_1_2 + 0.0100446428571429*G0_2_2_0 + 0.00200892857142858*G0_2_2_1 + 0.0100446428571429*G0_2_2_2;
5309
A[174] = 0.0080357142857143*G0_0_0_0 + 0.0100446428571429*G0_0_0_1 + 0.0100446428571429*G0_0_0_2 + 0.0080357142857143*G0_1_1_0 + 0.0100446428571429*G0_1_1_1 + 0.0100446428571429*G0_1_1_2 + 0.0080357142857143*G0_2_2_0 + 0.0100446428571429*G0_2_2_1 + 0.0100446428571429*G0_2_2_2;
5310
A[175] = -0.0100446428571429*G0_0_0_0 - 0.0200892857142857*G0_0_0_1 - 0.0200892857142857*G0_0_0_2 - 0.0100446428571429*G0_1_1_0 - 0.0200892857142857*G0_1_1_1 - 0.0200892857142857*G0_1_1_2 - 0.0100446428571429*G0_2_2_0 - 0.0200892857142857*G0_2_2_1 - 0.0200892857142857*G0_2_2_2;
5311
A[176] = -0.0120535714285714*G0_0_0_0 + 0.00602678571428574*G0_0_0_1 + 0.0120535714285714*G0_0_0_2 - 0.0120535714285714*G0_1_1_0 + 0.00602678571428574*G0_1_1_1 + 0.0120535714285714*G0_1_1_2 - 0.0120535714285714*G0_2_2_0 + 0.00602678571428574*G0_2_2_1 + 0.0120535714285714*G0_2_2_2;
5312
A[177] = 0.0120535714285714*G0_0_0_0 + 0.00602678571428572*G0_0_0_1 + 0.0120535714285714*G0_1_1_0 + 0.00602678571428572*G0_1_1_1 + 0.0120535714285714*G0_2_2_0 + 0.00602678571428572*G0_2_2_1;
5313
A[178] = -0.0120535714285714*G0_0_0_0 - 0.00602678571428574*G0_0_0_1 - 0.0120535714285714*G0_1_1_0 - 0.00602678571428574*G0_1_1_1 - 0.0120535714285714*G0_2_2_0 - 0.00602678571428574*G0_2_2_1;
5314
A[179] = -0.0241071428571429*G0_0_0_0 - 0.00602678571428574*G0_0_0_1 - 0.0120535714285714*G0_0_0_2 - 0.0241071428571429*G0_1_1_0 - 0.00602678571428574*G0_1_1_1 - 0.0120535714285714*G0_1_1_2 - 0.0241071428571429*G0_2_2_0 - 0.00602678571428574*G0_2_2_1 - 0.0120535714285714*G0_2_2_2;
5315
A[180] = -0.00200892857142857*G0_0_0_0 - 0.00200892857142857*G0_0_0_1 - 0.00200892857142857*G0_0_0_2 - 0.00200892857142857*G0_1_1_0 - 0.00200892857142857*G0_1_1_1 - 0.00200892857142857*G0_1_1_2 - 0.00200892857142857*G0_2_2_0 - 0.00200892857142857*G0_2_2_1 - 0.00200892857142857*G0_2_2_2;
5316
A[181] = -0.00200892857142857*G0_0_0_0 - 0.00200892857142857*G0_1_1_0 - 0.00200892857142857*G0_2_2_0;
5317
A[182] = 0.00401785714285714*G0_0_0_1 + 0.00401785714285714*G0_1_1_1 + 0.00401785714285714*G0_2_2_1;
5318
A[183] = 0.00200892857142857*G0_0_0_2 + 0.00200892857142857*G0_1_1_2 + 0.00200892857142857*G0_2_2_2;
5319
A[184] = 0.0100446428571429*G0_0_0_1 + 0.0200892857142857*G0_0_0_2 + 0.0100446428571429*G0_1_1_1 + 0.0200892857142857*G0_1_1_2 + 0.0100446428571429*G0_2_2_1 + 0.0200892857142857*G0_2_2_2;
5320
A[185] = -0.00200892857142857*G0_0_0_1 - 0.0100446428571428*G0_0_0_2 - 0.00200892857142857*G0_1_1_1 - 0.0100446428571428*G0_1_1_2 - 0.00200892857142857*G0_2_2_1 - 0.0100446428571428*G0_2_2_2;
5321
A[186] = -0.00803571428571429*G0_0_0_0 - 0.0100446428571428*G0_0_0_2 - 0.00803571428571429*G0_1_1_0 - 0.0100446428571428*G0_1_1_2 - 0.00803571428571429*G0_2_2_0 - 0.0100446428571428*G0_2_2_2;
5322
A[187] = -0.00200892857142857*G0_0_0_0 - 0.00401785714285714*G0_0_0_2 - 0.00200892857142857*G0_1_1_0 - 0.00401785714285714*G0_1_1_2 - 0.00200892857142857*G0_2_2_0 - 0.00401785714285714*G0_2_2_2;
5323
A[188] = -0.00401785714285715*G0_0_0_0 - 0.0100446428571428*G0_0_0_1 - 0.00401785714285715*G0_1_1_0 - 0.0100446428571428*G0_1_1_1 - 0.00401785714285715*G0_2_2_0 - 0.0100446428571428*G0_2_2_1;
5324
A[189] = 0.0200892857142857*G0_0_0_0 + 0.0200892857142857*G0_0_0_1 + 0.0200892857142857*G0_1_1_0 + 0.0200892857142857*G0_1_1_1 + 0.0200892857142857*G0_2_2_0 + 0.0200892857142857*G0_2_2_1;
5325
A[190] = 0.00200892857142858*G0_0_0_0 + 0.00200892857142857*G0_0_0_1 + 0.00200892857142858*G0_1_1_0 + 0.00200892857142857*G0_1_1_1 + 0.00200892857142858*G0_2_2_0 + 0.00200892857142857*G0_2_2_1;
5326
A[191] = 0.00200892857142857*G0_0_0_0 + 0.00200892857142857*G0_0_0_1 + 0.00200892857142857*G0_1_1_0 + 0.00200892857142857*G0_1_1_1 + 0.00200892857142857*G0_2_2_0 + 0.00200892857142857*G0_2_2_1;
5327
A[192] = 0.0100446428571429*G0_0_0_0 + 0.00803571428571429*G0_0_0_1 + 0.0100446428571429*G0_0_0_2 + 0.0100446428571429*G0_1_1_0 + 0.00803571428571429*G0_1_1_1 + 0.0100446428571429*G0_1_1_2 + 0.0100446428571429*G0_2_2_0 + 0.00803571428571429*G0_2_2_1 + 0.0100446428571429*G0_2_2_2;
5328
A[193] = -0.0200892857142857*G0_0_0_0 - 0.0100446428571429*G0_0_0_1 - 0.0200892857142857*G0_0_0_2 - 0.0200892857142857*G0_1_1_0 - 0.0100446428571429*G0_1_1_1 - 0.0200892857142857*G0_1_1_2 - 0.0200892857142857*G0_2_2_0 - 0.0100446428571429*G0_2_2_1 - 0.0200892857142857*G0_2_2_2;
5329
A[194] = 0.00200892857142857*G0_0_0_0 + 0.00401785714285713*G0_0_0_1 + 0.00401785714285714*G0_0_0_2 + 0.00200892857142857*G0_1_1_0 + 0.00401785714285713*G0_1_1_1 + 0.00401785714285714*G0_1_1_2 + 0.00200892857142857*G0_2_2_0 + 0.00401785714285713*G0_2_2_1 + 0.00401785714285714*G0_2_2_2;
5330
A[195] = 0.00200892857142856*G0_0_0_0 + 0.0100446428571428*G0_0_0_1 + 0.0100446428571429*G0_0_0_2 + 0.00200892857142856*G0_1_1_0 + 0.0100446428571428*G0_1_1_1 + 0.0100446428571429*G0_1_1_2 + 0.00200892857142856*G0_2_2_0 + 0.0100446428571428*G0_2_2_1 + 0.0100446428571429*G0_2_2_2;
5331
A[196] = 0.00602678571428574*G0_0_0_0 - 0.0120535714285714*G0_0_0_1 + 0.0120535714285714*G0_0_0_2 + 0.00602678571428574*G0_1_1_0 - 0.0120535714285714*G0_1_1_1 + 0.0120535714285714*G0_1_1_2 + 0.00602678571428574*G0_2_2_0 - 0.0120535714285714*G0_2_2_1 + 0.0120535714285714*G0_2_2_2;
5332
A[197] = -0.00602678571428573*G0_0_0_0 - 0.0120535714285714*G0_0_0_1 - 0.00602678571428573*G0_1_1_0 - 0.0120535714285714*G0_1_1_1 - 0.00602678571428573*G0_2_2_0 - 0.0120535714285714*G0_2_2_1;
5333
A[198] = 0.00602678571428571*G0_0_0_0 + 0.0120535714285714*G0_0_0_1 + 0.00602678571428571*G0_1_1_0 + 0.0120535714285714*G0_1_1_1 + 0.00602678571428571*G0_2_2_0 + 0.0120535714285714*G0_2_2_1;
5334
A[199] = -0.00602678571428571*G0_0_0_0 - 0.0241071428571428*G0_0_0_1 - 0.0120535714285714*G0_0_0_2 - 0.00602678571428571*G0_1_1_0 - 0.0241071428571428*G0_1_1_1 - 0.0120535714285714*G0_1_1_2 - 0.00602678571428571*G0_2_2_0 - 0.0241071428571428*G0_2_2_1 - 0.0120535714285714*G0_2_2_2;
5335
A[200] = -0.00401785714285713*G0_0_0_0 - 0.00401785714285714*G0_0_0_1 - 0.00401785714285713*G0_0_0_2 - 0.00401785714285713*G0_1_1_0 - 0.00401785714285714*G0_1_1_1 - 0.00401785714285713*G0_1_1_2 - 0.00401785714285713*G0_2_2_0 - 0.00401785714285714*G0_2_2_1 - 0.00401785714285713*G0_2_2_2;
5336
A[201] = 0.00200892857142856*G0_0_0_0 + 0.00200892857142856*G0_1_1_0 + 0.00200892857142856*G0_2_2_0;
5337
A[202] = 0.00200892857142856*G0_0_0_1 + 0.00200892857142856*G0_1_1_1 + 0.00200892857142856*G0_2_2_1;
5338
A[203] = -0.00200892857142857*G0_0_0_2 - 0.00200892857142857*G0_1_1_2 - 0.00200892857142857*G0_2_2_2;
5339
A[204] = -0.00401785714285713*G0_0_0_1 - 0.00200892857142857*G0_0_0_2 - 0.00401785714285713*G0_1_1_1 - 0.00200892857142857*G0_1_1_2 - 0.00401785714285713*G0_2_2_1 - 0.00200892857142857*G0_2_2_2;
5340
A[205] = -0.0100446428571429*G0_0_0_1 - 0.00803571428571428*G0_0_0_2 - 0.0100446428571429*G0_1_1_1 - 0.00803571428571428*G0_1_1_2 - 0.0100446428571429*G0_2_2_1 - 0.00803571428571428*G0_2_2_2;
5341
A[206] = -0.00401785714285714*G0_0_0_0 - 0.00200892857142859*G0_0_0_2 - 0.00401785714285714*G0_1_1_0 - 0.00200892857142859*G0_1_1_2 - 0.00401785714285714*G0_2_2_0 - 0.00200892857142859*G0_2_2_2;
5342
A[207] = -0.0100446428571429*G0_0_0_0 - 0.00803571428571428*G0_0_0_2 - 0.0100446428571429*G0_1_1_0 - 0.00803571428571428*G0_1_1_2 - 0.0100446428571429*G0_2_2_0 - 0.00803571428571428*G0_2_2_2;
5343
A[208] = -0.00200892857142857*G0_0_0_0 - 0.00200892857142858*G0_0_0_1 - 0.00200892857142857*G0_1_1_0 - 0.00200892857142858*G0_1_1_1 - 0.00200892857142857*G0_2_2_0 - 0.00200892857142858*G0_2_2_1;
5344
A[209] = -0.00200892857142858*G0_0_0_0 - 0.00200892857142857*G0_0_0_1 - 0.00200892857142858*G0_1_1_0 - 0.00200892857142857*G0_1_1_1 - 0.00200892857142858*G0_2_2_0 - 0.00200892857142857*G0_2_2_1;
5345
A[210] = -0.0200892857142857*G0_0_0_0 - 0.0200892857142857*G0_0_0_1 - 0.0200892857142857*G0_1_1_0 - 0.0200892857142857*G0_1_1_1 - 0.0200892857142857*G0_2_2_0 - 0.0200892857142857*G0_2_2_1;
5346
A[211] = 0.0100446428571429*G0_0_0_0 + 0.0100446428571428*G0_0_0_1 + 0.0060267857142857*G0_0_0_2 + 0.0100446428571429*G0_1_1_0 + 0.0100446428571428*G0_1_1_1 + 0.0060267857142857*G0_1_1_2 + 0.0100446428571429*G0_2_2_0 + 0.0100446428571428*G0_2_2_1 + 0.0060267857142857*G0_2_2_2;
5347
A[212] = -0.0100446428571428*G0_0_0_0 + 0.0100446428571428*G0_0_0_1 - 0.0100446428571428*G0_0_0_2 - 0.0100446428571428*G0_1_1_0 + 0.0100446428571428*G0_1_1_1 - 0.0100446428571428*G0_1_1_2 - 0.0100446428571428*G0_2_2_0 + 0.0100446428571428*G0_2_2_1 - 0.0100446428571428*G0_2_2_2;
5348
A[213] = 0.00200892857142857*G0_0_0_0 - 0.00803571428571427*G0_0_0_1 + 0.00200892857142858*G0_0_0_2 + 0.00200892857142857*G0_1_1_0 - 0.00803571428571427*G0_1_1_1 + 0.00200892857142858*G0_1_1_2 + 0.00200892857142857*G0_2_2_0 - 0.00803571428571427*G0_2_2_1 + 0.00200892857142858*G0_2_2_2;
5349
A[214] = 0.0100446428571428*G0_0_0_0 - 0.0100446428571428*G0_0_0_1 - 0.0100446428571428*G0_0_0_2 + 0.0100446428571428*G0_1_1_0 - 0.0100446428571428*G0_1_1_1 - 0.0100446428571428*G0_1_1_2 + 0.0100446428571428*G0_2_2_0 - 0.0100446428571428*G0_2_2_1 - 0.0100446428571428*G0_2_2_2;
5350
A[215] = -0.00803571428571426*G0_0_0_0 + 0.00200892857142859*G0_0_0_1 + 0.00200892857142859*G0_0_0_2 - 0.00803571428571426*G0_1_1_0 + 0.00200892857142859*G0_1_1_1 + 0.00200892857142859*G0_1_1_2 - 0.00803571428571426*G0_2_2_0 + 0.00200892857142859*G0_2_2_1 + 0.00200892857142859*G0_2_2_2;
5351
A[216] = -0.0120535714285714*G0_0_0_0 - 0.0120535714285714*G0_0_0_1 - 0.00602678571428574*G0_0_0_2 - 0.0120535714285714*G0_1_1_0 - 0.0120535714285714*G0_1_1_1 - 0.00602678571428574*G0_1_1_2 - 0.0120535714285714*G0_2_2_0 - 0.0120535714285714*G0_2_2_1 - 0.00602678571428574*G0_2_2_2;
5352
A[217] = 0.0120535714285715*G0_0_0_0 + 0.0241071428571428*G0_0_0_1 + 0.0180803571428571*G0_0_0_2 + 0.0120535714285715*G0_1_1_0 + 0.0241071428571428*G0_1_1_1 + 0.0180803571428571*G0_1_1_2 + 0.0120535714285715*G0_2_2_0 + 0.0241071428571428*G0_2_2_1 + 0.0180803571428571*G0_2_2_2;
5353
A[218] = 0.0241071428571428*G0_0_0_0 + 0.0120535714285715*G0_0_0_1 + 0.0180803571428571*G0_0_0_2 + 0.0241071428571428*G0_1_1_0 + 0.0120535714285715*G0_1_1_1 + 0.0180803571428571*G0_1_1_2 + 0.0241071428571428*G0_2_2_0 + 0.0120535714285715*G0_2_2_1 + 0.0180803571428571*G0_2_2_2;
5354
A[219] = 0.0120535714285714*G0_0_0_0 + 0.0120535714285714*G0_0_0_1 + 0.00602678571428575*G0_0_0_2 + 0.0120535714285714*G0_1_1_0 + 0.0120535714285714*G0_1_1_1 + 0.00602678571428575*G0_1_1_2 + 0.0120535714285714*G0_2_2_0 + 0.0120535714285714*G0_2_2_1 + 0.00602678571428575*G0_2_2_2;
5355
A[220] = 0.00200892857142857*G0_0_0_0 + 0.00200892857142856*G0_0_0_1 + 0.00200892857142856*G0_0_0_2 + 0.00200892857142857*G0_1_1_0 + 0.00200892857142856*G0_1_1_1 + 0.00200892857142856*G0_1_1_2 + 0.00200892857142857*G0_2_2_0 + 0.00200892857142856*G0_2_2_1 + 0.00200892857142856*G0_2_2_2;
5356
A[221] = 0.00200892857142857*G0_0_0_0 + 0.00200892857142857*G0_1_1_0 + 0.00200892857142857*G0_2_2_0;
5357
A[222] = 0.00200892857142857*G0_0_0_1 + 0.00200892857142857*G0_1_1_1 + 0.00200892857142857*G0_2_2_1;
5358
A[223] = 0.00401785714285714*G0_0_0_2 + 0.00401785714285714*G0_1_1_2 + 0.00401785714285714*G0_2_2_2;
5359
A[224] = -0.0100446428571429*G0_0_0_1 - 0.00200892857142857*G0_0_0_2 - 0.0100446428571429*G0_1_1_1 - 0.00200892857142857*G0_1_1_2 - 0.0100446428571429*G0_2_2_1 - 0.00200892857142857*G0_2_2_2;
5360
A[225] = 0.0200892857142857*G0_0_0_1 + 0.0100446428571428*G0_0_0_2 + 0.0200892857142857*G0_1_1_1 + 0.0100446428571428*G0_1_1_2 + 0.0200892857142857*G0_2_2_1 + 0.0100446428571428*G0_2_2_2;
5361
A[226] = -0.0100446428571428*G0_0_0_0 - 0.00200892857142855*G0_0_0_2 - 0.0100446428571428*G0_1_1_0 - 0.00200892857142855*G0_1_1_2 - 0.0100446428571428*G0_2_2_0 - 0.00200892857142855*G0_2_2_2;
5362
A[227] = 0.0200892857142857*G0_0_0_0 + 0.0100446428571428*G0_0_0_2 + 0.0200892857142857*G0_1_1_0 + 0.0100446428571428*G0_1_1_2 + 0.0200892857142857*G0_2_2_0 + 0.0100446428571428*G0_2_2_2;
5363
A[228] = -0.00200892857142857*G0_0_0_0 - 0.00200892857142856*G0_0_0_1 - 0.00200892857142857*G0_1_1_0 - 0.00200892857142856*G0_1_1_1 - 0.00200892857142857*G0_2_2_0 - 0.00200892857142856*G0_2_2_1;
5364
A[229] = -0.00200892857142856*G0_0_0_0 - 0.00200892857142857*G0_0_0_1 - 0.00200892857142856*G0_1_1_0 - 0.00200892857142857*G0_1_1_1 - 0.00200892857142856*G0_2_2_0 - 0.00200892857142857*G0_2_2_1;
5365
A[230] = 0.00401785714285715*G0_0_0_0 + 0.00401785714285715*G0_0_0_1 - 0.00602678571428568*G0_0_0_2 + 0.00401785714285715*G0_1_1_0 + 0.00401785714285715*G0_1_1_1 - 0.00602678571428568*G0_1_1_2 + 0.00401785714285715*G0_2_2_0 + 0.00401785714285715*G0_2_2_1 - 0.00602678571428568*G0_2_2_2;
5366
A[231] = -0.0200892857142857*G0_0_0_0 - 0.0200892857142857*G0_0_0_1 - 0.0200892857142857*G0_1_1_0 - 0.0200892857142857*G0_1_1_1 - 0.0200892857142857*G0_2_2_0 - 0.0200892857142857*G0_2_2_1;
5367
A[232] = 0.00803571428571429*G0_0_0_0 - 0.00200892857142857*G0_0_0_1 + 0.00803571428571428*G0_0_0_2 + 0.00803571428571429*G0_1_1_0 - 0.00200892857142857*G0_1_1_1 + 0.00803571428571428*G0_1_1_2 + 0.00803571428571429*G0_2_2_0 - 0.00200892857142857*G0_2_2_1 + 0.00803571428571428*G0_2_2_2;
5368
A[233] = 0.00200892857142856*G0_0_0_0 - 0.00200892857142857*G0_0_0_1 + 0.00200892857142856*G0_0_0_2 + 0.00200892857142856*G0_1_1_0 - 0.00200892857142857*G0_1_1_1 + 0.00200892857142856*G0_1_1_2 + 0.00200892857142856*G0_2_2_0 - 0.00200892857142857*G0_2_2_1 + 0.00200892857142856*G0_2_2_2;
5369
A[234] = -0.00200892857142855*G0_0_0_0 + 0.00803571428571428*G0_0_0_1 + 0.00803571428571428*G0_0_0_2 - 0.00200892857142855*G0_1_1_0 + 0.00803571428571428*G0_1_1_1 + 0.00803571428571428*G0_1_1_2 - 0.00200892857142855*G0_2_2_0 + 0.00803571428571428*G0_2_2_1 + 0.00803571428571428*G0_2_2_2;
5370
A[235] = -0.00200892857142858*G0_0_0_0 + 0.00200892857142855*G0_0_0_1 + 0.00200892857142855*G0_0_0_2 - 0.00200892857142858*G0_1_1_0 + 0.00200892857142855*G0_1_1_1 + 0.00200892857142855*G0_1_1_2 - 0.00200892857142858*G0_2_2_0 + 0.00200892857142855*G0_2_2_1 + 0.00200892857142855*G0_2_2_2;
5371
A[236] = 0.0060267857142857*G0_0_0_0 + 0.0060267857142857*G0_0_0_1 - 0.0060267857142857*G0_0_0_2 + 0.0060267857142857*G0_1_1_0 + 0.0060267857142857*G0_1_1_1 - 0.0060267857142857*G0_1_1_2 + 0.0060267857142857*G0_2_2_0 + 0.0060267857142857*G0_2_2_1 - 0.0060267857142857*G0_2_2_2;
5372
A[237] = -0.00602678571428571*G0_0_0_0 + 0.00602678571428569*G0_0_0_1 - 0.0180803571428571*G0_0_0_2 - 0.00602678571428571*G0_1_1_0 + 0.00602678571428569*G0_1_1_1 - 0.0180803571428571*G0_1_1_2 - 0.00602678571428571*G0_2_2_0 + 0.00602678571428569*G0_2_2_1 - 0.0180803571428571*G0_2_2_2;
5373
A[238] = 0.0060267857142857*G0_0_0_0 - 0.00602678571428571*G0_0_0_1 - 0.0180803571428571*G0_0_0_2 + 0.0060267857142857*G0_1_1_0 - 0.00602678571428571*G0_1_1_1 - 0.0180803571428571*G0_1_1_2 + 0.0060267857142857*G0_2_2_0 - 0.00602678571428571*G0_2_2_1 - 0.0180803571428571*G0_2_2_2;
5374
A[239] = -0.00602678571428572*G0_0_0_0 - 0.0060267857142857*G0_0_0_1 + 0.0060267857142857*G0_0_0_2 - 0.00602678571428572*G0_1_1_0 - 0.0060267857142857*G0_1_1_1 + 0.0060267857142857*G0_1_1_2 - 0.00602678571428572*G0_2_2_0 - 0.0060267857142857*G0_2_2_1 + 0.0060267857142857*G0_2_2_2;
5375
A[240] = -0.00401785714285713*G0_0_0_0 - 0.00401785714285713*G0_0_0_1 - 0.00401785714285713*G0_0_0_2 - 0.00401785714285713*G0_1_1_0 - 0.00401785714285713*G0_1_1_1 - 0.00401785714285713*G0_1_1_2 - 0.00401785714285713*G0_2_2_0 - 0.00401785714285713*G0_2_2_1 - 0.00401785714285713*G0_2_2_2;
5376
A[241] = 0.00200892857142857*G0_0_0_0 + 0.00200892857142857*G0_1_1_0 + 0.00200892857142857*G0_2_2_0;
5377
A[242] = -0.00200892857142857*G0_0_0_1 - 0.00200892857142857*G0_1_1_1 - 0.00200892857142857*G0_2_2_1;
5378
A[243] = 0.00200892857142857*G0_0_0_2 + 0.00200892857142857*G0_1_1_2 + 0.00200892857142857*G0_2_2_2;
5379
A[244] = -0.00803571428571428*G0_0_0_1 - 0.0100446428571428*G0_0_0_2 - 0.00803571428571428*G0_1_1_1 - 0.0100446428571428*G0_1_1_2 - 0.00803571428571428*G0_2_2_1 - 0.0100446428571428*G0_2_2_2;
5380
A[245] = -0.00200892857142858*G0_0_0_1 - 0.00401785714285716*G0_0_0_2 - 0.00200892857142858*G0_1_1_1 - 0.00401785714285716*G0_1_1_2 - 0.00200892857142858*G0_2_2_1 - 0.00401785714285716*G0_2_2_2;
5381
A[246] = -0.00200892857142858*G0_0_0_0 - 0.00200892857142859*G0_0_0_2 - 0.00200892857142858*G0_1_1_0 - 0.00200892857142859*G0_1_1_2 - 0.00200892857142858*G0_2_2_0 - 0.00200892857142859*G0_2_2_2;
5382
A[247] = -0.00200892857142858*G0_0_0_0 - 0.00200892857142858*G0_0_0_2 - 0.00200892857142858*G0_1_1_0 - 0.00200892857142858*G0_1_1_2 - 0.00200892857142858*G0_2_2_0 - 0.00200892857142858*G0_2_2_2;
5383
A[248] = -0.00401785714285713*G0_0_0_0 - 0.00200892857142858*G0_0_0_1 - 0.00401785714285713*G0_1_1_0 - 0.00200892857142858*G0_1_1_1 - 0.00401785714285713*G0_2_2_0 - 0.00200892857142858*G0_2_2_1;
5384
A[249] = -0.0100446428571428*G0_0_0_0 - 0.00803571428571426*G0_0_0_1 - 0.0100446428571428*G0_1_1_0 - 0.00803571428571426*G0_1_1_1 - 0.0100446428571428*G0_2_2_0 - 0.00803571428571426*G0_2_2_1;
5385
A[250] = -0.0100446428571429*G0_0_0_0 - 0.0100446428571429*G0_0_0_1 + 0.0100446428571428*G0_0_0_2 - 0.0100446428571429*G0_1_1_0 - 0.0100446428571429*G0_1_1_1 + 0.0100446428571428*G0_1_1_2 - 0.0100446428571429*G0_2_2_0 - 0.0100446428571429*G0_2_2_1 + 0.0100446428571428*G0_2_2_2;
5386
A[251] = 0.00200892857142858*G0_0_0_0 + 0.00200892857142858*G0_0_0_1 - 0.00803571428571427*G0_0_0_2 + 0.00200892857142858*G0_1_1_0 + 0.00200892857142858*G0_1_1_1 - 0.00803571428571427*G0_1_1_2 + 0.00200892857142858*G0_2_2_0 + 0.00200892857142858*G0_2_2_1 - 0.00803571428571427*G0_2_2_2;
5387
A[252] = -0.0200892857142857*G0_0_0_0 - 0.0200892857142857*G0_0_0_2 - 0.0200892857142857*G0_1_1_0 - 0.0200892857142857*G0_1_1_2 - 0.0200892857142857*G0_2_2_0 - 0.0200892857142857*G0_2_2_2;
5388
A[253] = 0.0100446428571428*G0_0_0_0 + 0.0060267857142857*G0_0_0_1 + 0.0100446428571428*G0_0_0_2 + 0.0100446428571428*G0_1_1_0 + 0.0060267857142857*G0_1_1_1 + 0.0100446428571428*G0_1_1_2 + 0.0100446428571428*G0_2_2_0 + 0.0060267857142857*G0_2_2_1 + 0.0100446428571428*G0_2_2_2;
5389
A[254] = 0.0100446428571428*G0_0_0_0 - 0.0100446428571429*G0_0_0_1 - 0.0100446428571429*G0_0_0_2 + 0.0100446428571428*G0_1_1_0 - 0.0100446428571429*G0_1_1_1 - 0.0100446428571429*G0_1_1_2 + 0.0100446428571428*G0_2_2_0 - 0.0100446428571429*G0_2_2_1 - 0.0100446428571429*G0_2_2_2;
5390
A[255] = -0.00803571428571427*G0_0_0_0 + 0.00200892857142859*G0_0_0_1 + 0.00200892857142859*G0_0_0_2 - 0.00803571428571427*G0_1_1_0 + 0.00200892857142859*G0_1_1_1 + 0.00200892857142859*G0_1_1_2 - 0.00803571428571427*G0_2_2_0 + 0.00200892857142859*G0_2_2_1 + 0.00200892857142859*G0_2_2_2;
5391
A[256] = -0.0120535714285714*G0_0_0_0 - 0.00602678571428573*G0_0_0_1 - 0.0120535714285714*G0_0_0_2 - 0.0120535714285714*G0_1_1_0 - 0.00602678571428573*G0_1_1_1 - 0.0120535714285714*G0_1_1_2 - 0.0120535714285714*G0_2_2_0 - 0.00602678571428573*G0_2_2_1 - 0.0120535714285714*G0_2_2_2;
5392
A[257] = 0.0120535714285715*G0_0_0_0 + 0.0180803571428571*G0_0_0_1 + 0.0241071428571429*G0_0_0_2 + 0.0120535714285715*G0_1_1_0 + 0.0180803571428571*G0_1_1_1 + 0.0241071428571429*G0_1_1_2 + 0.0120535714285715*G0_2_2_0 + 0.0180803571428571*G0_2_2_1 + 0.0241071428571429*G0_2_2_2;
5393
A[258] = 0.0120535714285714*G0_0_0_0 + 0.00602678571428574*G0_0_0_1 + 0.0120535714285714*G0_0_0_2 + 0.0120535714285714*G0_1_1_0 + 0.00602678571428574*G0_1_1_1 + 0.0120535714285714*G0_1_1_2 + 0.0120535714285714*G0_2_2_0 + 0.00602678571428574*G0_2_2_1 + 0.0120535714285714*G0_2_2_2;
5394
A[259] = 0.0241071428571428*G0_0_0_0 + 0.0180803571428571*G0_0_0_1 + 0.0120535714285714*G0_0_0_2 + 0.0241071428571428*G0_1_1_0 + 0.0180803571428571*G0_1_1_1 + 0.0120535714285714*G0_1_1_2 + 0.0241071428571428*G0_2_2_0 + 0.0180803571428571*G0_2_2_1 + 0.0120535714285714*G0_2_2_2;
5395
A[260] = 0.00200892857142856*G0_0_0_0 + 0.00200892857142856*G0_0_0_1 + 0.00200892857142856*G0_0_0_2 + 0.00200892857142856*G0_1_1_0 + 0.00200892857142856*G0_1_1_1 + 0.00200892857142856*G0_1_1_2 + 0.00200892857142856*G0_2_2_0 + 0.00200892857142856*G0_2_2_1 + 0.00200892857142856*G0_2_2_2;
5396
A[261] = 0.00200892857142857*G0_0_0_0 + 0.00200892857142857*G0_1_1_0 + 0.00200892857142857*G0_2_2_0;
5397
A[262] = 0.00401785714285714*G0_0_0_1 + 0.00401785714285714*G0_1_1_1 + 0.00401785714285714*G0_2_2_1;
5398
A[263] = 0.00200892857142857*G0_0_0_2 + 0.00200892857142857*G0_1_1_2 + 0.00200892857142857*G0_2_2_2;
5399
A[264] = 0.0100446428571429*G0_0_0_1 + 0.0200892857142857*G0_0_0_2 + 0.0100446428571429*G0_1_1_1 + 0.0200892857142857*G0_1_1_2 + 0.0100446428571429*G0_2_2_1 + 0.0200892857142857*G0_2_2_2;
5400
A[265] = -0.00200892857142856*G0_0_0_1 - 0.0100446428571428*G0_0_0_2 - 0.00200892857142856*G0_1_1_1 - 0.0100446428571428*G0_1_1_2 - 0.00200892857142856*G0_2_2_1 - 0.0100446428571428*G0_2_2_2;
5401
A[266] = -0.00200892857142857*G0_0_0_0 - 0.00200892857142856*G0_0_0_2 - 0.00200892857142857*G0_1_1_0 - 0.00200892857142856*G0_1_1_2 - 0.00200892857142857*G0_2_2_0 - 0.00200892857142856*G0_2_2_2;
5402
A[267] = -0.00200892857142856*G0_0_0_0 - 0.00200892857142856*G0_0_0_2 - 0.00200892857142856*G0_1_1_0 - 0.00200892857142856*G0_1_1_2 - 0.00200892857142856*G0_2_2_0 - 0.00200892857142856*G0_2_2_2;
5403
A[268] = -0.0100446428571429*G0_0_0_0 - 0.00200892857142857*G0_0_0_1 - 0.0100446428571429*G0_1_1_0 - 0.00200892857142857*G0_1_1_1 - 0.0100446428571429*G0_2_2_0 - 0.00200892857142857*G0_2_2_1;
5404
A[269] = 0.0200892857142857*G0_0_0_0 + 0.0100446428571428*G0_0_0_1 + 0.0200892857142857*G0_1_1_0 + 0.0100446428571428*G0_1_1_1 + 0.0200892857142857*G0_2_2_0 + 0.0100446428571428*G0_2_2_1;
5405
A[270] = 0.00803571428571429*G0_0_0_0 + 0.00803571428571428*G0_0_0_1 - 0.00200892857142856*G0_0_0_2 + 0.00803571428571429*G0_1_1_0 + 0.00803571428571428*G0_1_1_1 - 0.00200892857142856*G0_1_1_2 + 0.00803571428571429*G0_2_2_0 + 0.00803571428571428*G0_2_2_1 - 0.00200892857142856*G0_2_2_2;
5406
A[271] = 0.00200892857142856*G0_0_0_0 + 0.00200892857142856*G0_0_0_1 - 0.00200892857142857*G0_0_0_2 + 0.00200892857142856*G0_1_1_0 + 0.00200892857142856*G0_1_1_1 - 0.00200892857142857*G0_1_1_2 + 0.00200892857142856*G0_2_2_0 + 0.00200892857142856*G0_2_2_1 - 0.00200892857142857*G0_2_2_2;
5407
A[272] = 0.00401785714285716*G0_0_0_0 - 0.00602678571428569*G0_0_0_1 + 0.00401785714285716*G0_0_0_2 + 0.00401785714285716*G0_1_1_0 - 0.00602678571428569*G0_1_1_1 + 0.00401785714285716*G0_1_1_2 + 0.00401785714285716*G0_2_2_0 - 0.00602678571428569*G0_2_2_1 + 0.00401785714285716*G0_2_2_2;
5408
A[273] = -0.0200892857142857*G0_0_0_0 - 0.0200892857142857*G0_0_0_2 - 0.0200892857142857*G0_1_1_0 - 0.0200892857142857*G0_1_1_2 - 0.0200892857142857*G0_2_2_0 - 0.0200892857142857*G0_2_2_2;
5409
A[274] = -0.00200892857142856*G0_0_0_0 + 0.00803571428571428*G0_0_0_1 + 0.00803571428571429*G0_0_0_2 - 0.00200892857142856*G0_1_1_0 + 0.00803571428571428*G0_1_1_1 + 0.00803571428571429*G0_1_1_2 - 0.00200892857142856*G0_2_2_0 + 0.00803571428571428*G0_2_2_1 + 0.00803571428571429*G0_2_2_2;
5410
A[275] = -0.00200892857142858*G0_0_0_0 + 0.00200892857142856*G0_0_0_1 + 0.00200892857142857*G0_0_0_2 - 0.00200892857142858*G0_1_1_0 + 0.00200892857142856*G0_1_1_1 + 0.00200892857142857*G0_1_1_2 - 0.00200892857142858*G0_2_2_0 + 0.00200892857142856*G0_2_2_1 + 0.00200892857142857*G0_2_2_2;
5411
A[276] = 0.00602678571428573*G0_0_0_0 - 0.00602678571428569*G0_0_0_1 + 0.00602678571428571*G0_0_0_2 + 0.00602678571428573*G0_1_1_0 - 0.00602678571428569*G0_1_1_1 + 0.00602678571428571*G0_1_1_2 + 0.00602678571428573*G0_2_2_0 - 0.00602678571428569*G0_2_2_1 + 0.00602678571428571*G0_2_2_2;
5412
A[277] = -0.00602678571428574*G0_0_0_0 - 0.0180803571428571*G0_0_0_1 + 0.00602678571428568*G0_0_0_2 - 0.00602678571428574*G0_1_1_0 - 0.0180803571428571*G0_1_1_1 + 0.00602678571428568*G0_1_1_2 - 0.00602678571428574*G0_2_2_0 - 0.0180803571428571*G0_2_2_1 + 0.00602678571428568*G0_2_2_2;
5413
A[278] = -0.00602678571428572*G0_0_0_0 + 0.00602678571428569*G0_0_0_1 - 0.00602678571428574*G0_0_0_2 - 0.00602678571428572*G0_1_1_0 + 0.00602678571428569*G0_1_1_1 - 0.00602678571428574*G0_1_1_2 - 0.00602678571428572*G0_2_2_0 + 0.00602678571428569*G0_2_2_1 - 0.00602678571428574*G0_2_2_2;
5414
A[279] = 0.0060267857142857*G0_0_0_0 - 0.0180803571428571*G0_0_0_1 - 0.00602678571428572*G0_0_0_2 + 0.0060267857142857*G0_1_1_0 - 0.0180803571428571*G0_1_1_1 - 0.00602678571428572*G0_1_1_2 + 0.0060267857142857*G0_2_2_0 - 0.0180803571428571*G0_2_2_1 - 0.00602678571428572*G0_2_2_2;
5415
A[280] = -0.00401785714285713*G0_0_0_0 - 0.00401785714285714*G0_0_0_1 - 0.00401785714285713*G0_0_0_2 - 0.00401785714285713*G0_1_1_0 - 0.00401785714285714*G0_1_1_1 - 0.00401785714285713*G0_1_1_2 - 0.00401785714285713*G0_2_2_0 - 0.00401785714285714*G0_2_2_1 - 0.00401785714285713*G0_2_2_2;
5416
A[281] = -0.00200892857142856*G0_0_0_0 - 0.00200892857142856*G0_1_1_0 - 0.00200892857142856*G0_2_2_0;
5417
A[282] = 0.00200892857142856*G0_0_0_1 + 0.00200892857142856*G0_1_1_1 + 0.00200892857142856*G0_2_2_1;
5418
A[283] = 0.00200892857142857*G0_0_0_2 + 0.00200892857142857*G0_1_1_2 + 0.00200892857142857*G0_2_2_2;
5419
A[284] = -0.00200892857142857*G0_0_0_1 - 0.00200892857142857*G0_0_0_2 - 0.00200892857142857*G0_1_1_1 - 0.00200892857142857*G0_1_1_2 - 0.00200892857142857*G0_2_2_1 - 0.00200892857142857*G0_2_2_2;
5420
A[285] = -0.00200892857142857*G0_0_0_1 - 0.00200892857142858*G0_0_0_2 - 0.00200892857142857*G0_1_1_1 - 0.00200892857142858*G0_1_1_2 - 0.00200892857142857*G0_2_2_1 - 0.00200892857142858*G0_2_2_2;
5421
A[286] = -0.00803571428571429*G0_0_0_0 - 0.0100446428571429*G0_0_0_2 - 0.00803571428571429*G0_1_1_0 - 0.0100446428571429*G0_1_1_2 - 0.00803571428571429*G0_2_2_0 - 0.0100446428571429*G0_2_2_2;
5422
A[287] = -0.00200892857142858*G0_0_0_0 - 0.00401785714285714*G0_0_0_2 - 0.00200892857142858*G0_1_1_0 - 0.00401785714285714*G0_1_1_2 - 0.00200892857142858*G0_2_2_0 - 0.00401785714285714*G0_2_2_2;
5423
A[288] = -0.00803571428571428*G0_0_0_0 - 0.0100446428571428*G0_0_0_1 - 0.00803571428571428*G0_1_1_0 - 0.0100446428571428*G0_1_1_1 - 0.00803571428571428*G0_2_2_0 - 0.0100446428571428*G0_2_2_1;
5424
A[289] = -0.00200892857142857*G0_0_0_0 - 0.00401785714285714*G0_0_0_1 - 0.00200892857142857*G0_1_1_0 - 0.00401785714285714*G0_1_1_1 - 0.00200892857142857*G0_2_2_0 - 0.00401785714285714*G0_2_2_1;
5425
A[290] = -0.0100446428571429*G0_0_0_0 - 0.0100446428571428*G0_0_0_1 + 0.0100446428571428*G0_0_0_2 - 0.0100446428571429*G0_1_1_0 - 0.0100446428571428*G0_1_1_1 + 0.0100446428571428*G0_1_1_2 - 0.0100446428571429*G0_2_2_0 - 0.0100446428571428*G0_2_2_1 + 0.0100446428571428*G0_2_2_2;
5426
A[291] = 0.00200892857142857*G0_0_0_0 + 0.00200892857142857*G0_0_0_1 - 0.00803571428571426*G0_0_0_2 + 0.00200892857142857*G0_1_1_0 + 0.00200892857142857*G0_1_1_1 - 0.00803571428571426*G0_1_1_2 + 0.00200892857142857*G0_2_2_0 + 0.00200892857142857*G0_2_2_1 - 0.00803571428571426*G0_2_2_2;
5427
A[292] = -0.0100446428571428*G0_0_0_0 + 0.0100446428571428*G0_0_0_1 - 0.0100446428571429*G0_0_0_2 - 0.0100446428571428*G0_1_1_0 + 0.0100446428571428*G0_1_1_1 - 0.0100446428571429*G0_1_1_2 - 0.0100446428571428*G0_2_2_0 + 0.0100446428571428*G0_2_2_1 - 0.0100446428571429*G0_2_2_2;
5428
A[293] = 0.00200892857142857*G0_0_0_0 - 0.00803571428571427*G0_0_0_1 + 0.00200892857142857*G0_0_0_2 + 0.00200892857142857*G0_1_1_0 - 0.00803571428571427*G0_1_1_1 + 0.00200892857142857*G0_1_1_2 + 0.00200892857142857*G0_2_2_0 - 0.00803571428571427*G0_2_2_1 + 0.00200892857142857*G0_2_2_2;
5429
A[294] = -0.0200892857142857*G0_0_0_1 - 0.0200892857142857*G0_0_0_2 - 0.0200892857142857*G0_1_1_1 - 0.0200892857142857*G0_1_1_2 - 0.0200892857142857*G0_2_2_1 - 0.0200892857142857*G0_2_2_2;
5430
A[295] = 0.00602678571428569*G0_0_0_0 + 0.0100446428571429*G0_0_0_1 + 0.0100446428571429*G0_0_0_2 + 0.00602678571428569*G0_1_1_0 + 0.0100446428571429*G0_1_1_1 + 0.0100446428571429*G0_1_1_2 + 0.00602678571428569*G0_2_2_0 + 0.0100446428571429*G0_2_2_1 + 0.0100446428571429*G0_2_2_2;
5431
A[296] = -0.00602678571428573*G0_0_0_0 - 0.0120535714285714*G0_0_0_1 - 0.0120535714285714*G0_0_0_2 - 0.00602678571428573*G0_1_1_0 - 0.0120535714285714*G0_1_1_1 - 0.0120535714285714*G0_1_1_2 - 0.00602678571428573*G0_2_2_0 - 0.0120535714285714*G0_2_2_1 - 0.0120535714285714*G0_2_2_2;
5432
A[297] = 0.00602678571428574*G0_0_0_0 + 0.0120535714285714*G0_0_0_1 + 0.0120535714285714*G0_0_0_2 + 0.00602678571428574*G0_1_1_0 + 0.0120535714285714*G0_1_1_1 + 0.0120535714285714*G0_1_1_2 + 0.00602678571428574*G0_2_2_0 + 0.0120535714285714*G0_2_2_1 + 0.0120535714285714*G0_2_2_2;
5433
A[298] = 0.0180803571428571*G0_0_0_0 + 0.0120535714285714*G0_0_0_1 + 0.0241071428571428*G0_0_0_2 + 0.0180803571428571*G0_1_1_0 + 0.0120535714285714*G0_1_1_1 + 0.0241071428571428*G0_1_1_2 + 0.0180803571428571*G0_2_2_0 + 0.0120535714285714*G0_2_2_1 + 0.0241071428571428*G0_2_2_2;
5434
A[299] = 0.0180803571428571*G0_0_0_0 + 0.0241071428571428*G0_0_0_1 + 0.0120535714285714*G0_0_0_2 + 0.0180803571428571*G0_1_1_0 + 0.0241071428571428*G0_1_1_1 + 0.0120535714285714*G0_1_1_2 + 0.0180803571428571*G0_2_2_0 + 0.0241071428571428*G0_2_2_1 + 0.0120535714285714*G0_2_2_2;
5435
A[300] = 0.00200892857142856*G0_0_0_0 + 0.00200892857142857*G0_0_0_1 + 0.00200892857142857*G0_0_0_2 + 0.00200892857142856*G0_1_1_0 + 0.00200892857142857*G0_1_1_1 + 0.00200892857142857*G0_1_1_2 + 0.00200892857142856*G0_2_2_0 + 0.00200892857142857*G0_2_2_1 + 0.00200892857142857*G0_2_2_2;
5436
A[301] = 0.00401785714285713*G0_0_0_0 + 0.00401785714285713*G0_1_1_0 + 0.00401785714285713*G0_2_2_0;
5437
A[302] = 0.00200892857142856*G0_0_0_1 + 0.00200892857142856*G0_1_1_1 + 0.00200892857142856*G0_2_2_1;
5438
A[303] = 0.00200892857142857*G0_0_0_2 + 0.00200892857142857*G0_1_1_2 + 0.00200892857142857*G0_2_2_2;
5439
A[304] = -0.00200892857142858*G0_0_0_1 - 0.00200892857142858*G0_0_0_2 - 0.00200892857142858*G0_1_1_1 - 0.00200892857142858*G0_1_1_2 - 0.00200892857142858*G0_2_2_1 - 0.00200892857142858*G0_2_2_2;
5440
A[305] = -0.00200892857142857*G0_0_0_1 - 0.00200892857142857*G0_0_0_2 - 0.00200892857142857*G0_1_1_1 - 0.00200892857142857*G0_1_1_2 - 0.00200892857142857*G0_2_2_1 - 0.00200892857142857*G0_2_2_2;
5441
A[306] = 0.0100446428571428*G0_0_0_0 + 0.0200892857142857*G0_0_0_2 + 0.0100446428571428*G0_1_1_0 + 0.0200892857142857*G0_1_1_2 + 0.0100446428571428*G0_2_2_0 + 0.0200892857142857*G0_2_2_2;
5442
A[307] = -0.00200892857142857*G0_0_0_0 - 0.0100446428571428*G0_0_0_2 - 0.00200892857142857*G0_1_1_0 - 0.0100446428571428*G0_1_1_2 - 0.00200892857142857*G0_2_2_0 - 0.0100446428571428*G0_2_2_2;
5443
A[308] = 0.0100446428571428*G0_0_0_0 + 0.0200892857142857*G0_0_0_1 + 0.0100446428571428*G0_1_1_0 + 0.0200892857142857*G0_1_1_1 + 0.0100446428571428*G0_2_2_0 + 0.0200892857142857*G0_2_2_1;
5444
A[309] = -0.00200892857142858*G0_0_0_0 - 0.0100446428571428*G0_0_0_1 - 0.00200892857142858*G0_1_1_0 - 0.0100446428571428*G0_1_1_1 - 0.00200892857142858*G0_2_2_0 - 0.0100446428571428*G0_2_2_1;
5445
A[310] = 0.00803571428571428*G0_0_0_0 + 0.00803571428571428*G0_0_0_1 - 0.00200892857142856*G0_0_0_2 + 0.00803571428571428*G0_1_1_0 + 0.00803571428571428*G0_1_1_1 - 0.00200892857142856*G0_1_1_2 + 0.00803571428571428*G0_2_2_0 + 0.00803571428571428*G0_2_2_1 - 0.00200892857142856*G0_2_2_2;
5446
A[311] = 0.00200892857142857*G0_0_0_0 + 0.00200892857142857*G0_0_0_1 - 0.00200892857142858*G0_0_0_2 + 0.00200892857142857*G0_1_1_0 + 0.00200892857142857*G0_1_1_1 - 0.00200892857142858*G0_1_1_2 + 0.00200892857142857*G0_2_2_0 + 0.00200892857142857*G0_2_2_1 - 0.00200892857142858*G0_2_2_2;
5447
A[312] = 0.00803571428571428*G0_0_0_0 - 0.00200892857142856*G0_0_0_1 + 0.00803571428571428*G0_0_0_2 + 0.00803571428571428*G0_1_1_0 - 0.00200892857142856*G0_1_1_1 + 0.00803571428571428*G0_1_1_2 + 0.00803571428571428*G0_2_2_0 - 0.00200892857142856*G0_2_2_1 + 0.00803571428571428*G0_2_2_2;
5448
A[313] = 0.00200892857142858*G0_0_0_0 - 0.00200892857142857*G0_0_0_1 + 0.00200892857142858*G0_0_0_2 + 0.00200892857142858*G0_1_1_0 - 0.00200892857142857*G0_1_1_1 + 0.00200892857142858*G0_1_1_2 + 0.00200892857142858*G0_2_2_0 - 0.00200892857142857*G0_2_2_1 + 0.00200892857142858*G0_2_2_2;
5449
A[314] = -0.0060267857142857*G0_0_0_0 + 0.00401785714285715*G0_0_0_1 + 0.00401785714285714*G0_0_0_2 - 0.0060267857142857*G0_1_1_0 + 0.00401785714285715*G0_1_1_1 + 0.00401785714285714*G0_1_1_2 - 0.0060267857142857*G0_2_2_0 + 0.00401785714285715*G0_2_2_1 + 0.00401785714285714*G0_2_2_2;
5450
A[315] = -0.0200892857142857*G0_0_0_1 - 0.0200892857142857*G0_0_0_2 - 0.0200892857142857*G0_1_1_1 - 0.0200892857142857*G0_1_1_2 - 0.0200892857142857*G0_2_2_1 - 0.0200892857142857*G0_2_2_2;
5451
A[316] = -0.00602678571428574*G0_0_0_0 + 0.00602678571428568*G0_0_0_1 + 0.00602678571428567*G0_0_0_2 - 0.00602678571428574*G0_1_1_0 + 0.00602678571428568*G0_1_1_1 + 0.00602678571428567*G0_1_1_2 - 0.00602678571428574*G0_2_2_0 + 0.00602678571428568*G0_2_2_1 + 0.00602678571428567*G0_2_2_2;
5452
A[317] = 0.00602678571428574*G0_0_0_0 - 0.00602678571428571*G0_0_0_1 - 0.00602678571428571*G0_0_0_2 + 0.00602678571428574*G0_1_1_0 - 0.00602678571428571*G0_1_1_1 - 0.00602678571428571*G0_1_1_2 + 0.00602678571428574*G0_2_2_0 - 0.00602678571428571*G0_2_2_1 - 0.00602678571428571*G0_2_2_2;
5453
A[318] = -0.0180803571428571*G0_0_0_0 - 0.00602678571428568*G0_0_0_1 + 0.00602678571428568*G0_0_0_2 - 0.0180803571428571*G0_1_1_0 - 0.00602678571428568*G0_1_1_1 + 0.00602678571428568*G0_1_1_2 - 0.0180803571428571*G0_2_2_0 - 0.00602678571428568*G0_2_2_1 + 0.00602678571428568*G0_2_2_2;
5454
A[319] = -0.0180803571428571*G0_0_0_0 + 0.00602678571428568*G0_0_0_1 - 0.00602678571428567*G0_0_0_2 - 0.0180803571428571*G0_1_1_0 + 0.00602678571428568*G0_1_1_1 - 0.00602678571428567*G0_1_1_2 - 0.0180803571428571*G0_2_2_0 + 0.00602678571428568*G0_2_2_1 - 0.00602678571428567*G0_2_2_2;
5455
A[320] = -0.00736607142857145*G0_0_0_0 - 0.00736607142857145*G0_0_0_1 - 0.00736607142857145*G0_0_0_2 - 0.00736607142857145*G0_1_1_0 - 0.00736607142857145*G0_1_1_1 - 0.00736607142857145*G0_1_1_2 - 0.00736607142857145*G0_2_2_0 - 0.00736607142857145*G0_2_2_1 - 0.00736607142857145*G0_2_2_2;
5456
A[321] = -0.0046875*G0_0_0_0 - 0.0046875*G0_1_1_0 - 0.0046875*G0_2_2_0;
5457
A[322] = -0.0046875*G0_0_0_1 - 0.0046875*G0_1_1_1 - 0.0046875*G0_2_2_1;
5458
A[323] = -0.0046875*G0_0_0_2 - 0.0046875*G0_1_1_2 - 0.0046875*G0_2_2_2;
5459
A[324] = 0.0241071428571429*G0_0_0_1 + 0.00602678571428571*G0_0_0_2 + 0.0241071428571429*G0_1_1_1 + 0.00602678571428571*G0_1_1_2 + 0.0241071428571429*G0_2_2_1 + 0.00602678571428571*G0_2_2_2;
5460
A[325] = 0.00602678571428571*G0_0_0_1 + 0.0241071428571428*G0_0_0_2 + 0.00602678571428571*G0_1_1_1 + 0.0241071428571428*G0_1_1_2 + 0.00602678571428571*G0_2_2_1 + 0.0241071428571428*G0_2_2_2;
5461
A[326] = 0.0241071428571429*G0_0_0_0 + 0.00602678571428573*G0_0_0_2 + 0.0241071428571429*G0_1_1_0 + 0.00602678571428573*G0_1_1_2 + 0.0241071428571429*G0_2_2_0 + 0.00602678571428573*G0_2_2_2;
5462
A[327] = 0.0060267857142857*G0_0_0_0 + 0.0241071428571429*G0_0_0_2 + 0.0060267857142857*G0_1_1_0 + 0.0241071428571429*G0_1_1_2 + 0.0060267857142857*G0_2_2_0 + 0.0241071428571429*G0_2_2_2;
5463
A[328] = 0.0241071428571428*G0_0_0_0 + 0.00602678571428571*G0_0_0_1 + 0.0241071428571428*G0_1_1_0 + 0.00602678571428571*G0_1_1_1 + 0.0241071428571428*G0_2_2_0 + 0.00602678571428571*G0_2_2_1;
5464
A[329] = 0.00602678571428572*G0_0_0_0 + 0.0241071428571428*G0_0_0_1 + 0.00602678571428572*G0_1_1_0 + 0.0241071428571428*G0_1_1_1 + 0.00602678571428572*G0_2_2_0 + 0.0241071428571428*G0_2_2_1;
5465
A[330] = 0.0120535714285714*G0_0_0_0 + 0.0120535714285714*G0_0_0_1 + 0.00602678571428577*G0_0_0_2 + 0.0120535714285714*G0_1_1_0 + 0.0120535714285714*G0_1_1_1 + 0.00602678571428577*G0_1_1_2 + 0.0120535714285714*G0_2_2_0 + 0.0120535714285714*G0_2_2_1 + 0.00602678571428577*G0_2_2_2;
5466
A[331] = -0.00602678571428569*G0_0_0_0 - 0.00602678571428569*G0_0_0_1 + 0.0060267857142857*G0_0_0_2 - 0.00602678571428569*G0_1_1_0 - 0.00602678571428569*G0_1_1_1 + 0.0060267857142857*G0_1_1_2 - 0.00602678571428569*G0_2_2_0 - 0.00602678571428569*G0_2_2_1 + 0.0060267857142857*G0_2_2_2;
5467
A[332] = 0.0120535714285714*G0_0_0_0 + 0.00602678571428576*G0_0_0_1 + 0.0120535714285714*G0_0_0_2 + 0.0120535714285714*G0_1_1_0 + 0.00602678571428576*G0_1_1_1 + 0.0120535714285714*G0_1_1_2 + 0.0120535714285714*G0_2_2_0 + 0.00602678571428576*G0_2_2_1 + 0.0120535714285714*G0_2_2_2;
5468
A[333] = -0.0060267857142857*G0_0_0_0 + 0.00602678571428572*G0_0_0_1 - 0.00602678571428569*G0_0_0_2 - 0.0060267857142857*G0_1_1_0 + 0.00602678571428572*G0_1_1_1 - 0.00602678571428569*G0_1_1_2 - 0.0060267857142857*G0_2_2_0 + 0.00602678571428572*G0_2_2_1 - 0.00602678571428569*G0_2_2_2;
5469
A[334] = 0.00602678571428576*G0_0_0_0 + 0.0120535714285714*G0_0_0_1 + 0.0120535714285714*G0_0_0_2 + 0.00602678571428576*G0_1_1_0 + 0.0120535714285714*G0_1_1_1 + 0.0120535714285714*G0_1_1_2 + 0.00602678571428576*G0_2_2_0 + 0.0120535714285714*G0_2_2_1 + 0.0120535714285714*G0_2_2_2;
5470
A[335] = 0.00602678571428568*G0_0_0_0 - 0.00602678571428573*G0_0_0_1 - 0.00602678571428573*G0_0_0_2 + 0.00602678571428568*G0_1_1_0 - 0.00602678571428573*G0_1_1_1 - 0.00602678571428573*G0_1_1_2 + 0.00602678571428568*G0_2_2_0 - 0.00602678571428573*G0_2_2_1 - 0.00602678571428573*G0_2_2_2;
5471
A[336] = 0.0723214285714285*G0_0_0_0 + 0.0723214285714285*G0_0_0_1 + 0.0723214285714285*G0_0_0_2 + 0.0723214285714285*G0_1_1_0 + 0.0723214285714285*G0_1_1_1 + 0.0723214285714285*G0_1_1_2 + 0.0723214285714285*G0_2_2_0 + 0.0723214285714285*G0_2_2_1 + 0.0723214285714285*G0_2_2_2;
5472
A[337] = -0.0723214285714286*G0_0_0_0 - 0.0361607142857143*G0_0_0_1 - 0.0361607142857143*G0_0_0_2 - 0.0723214285714286*G0_1_1_0 - 0.0361607142857143*G0_1_1_1 - 0.0361607142857143*G0_1_1_2 - 0.0723214285714286*G0_2_2_0 - 0.0361607142857143*G0_2_2_1 - 0.0361607142857143*G0_2_2_2;
5473
A[338] = -0.0361607142857143*G0_0_0_0 - 0.0723214285714285*G0_0_0_1 - 0.0361607142857143*G0_0_0_2 - 0.0361607142857143*G0_1_1_0 - 0.0723214285714285*G0_1_1_1 - 0.0361607142857143*G0_1_1_2 - 0.0361607142857143*G0_2_2_0 - 0.0723214285714285*G0_2_2_1 - 0.0361607142857143*G0_2_2_2;
5474
A[339] = -0.0361607142857143*G0_0_0_0 - 0.0361607142857143*G0_0_0_1 - 0.0723214285714286*G0_0_0_2 - 0.0361607142857143*G0_1_1_0 - 0.0361607142857143*G0_1_1_1 - 0.0723214285714286*G0_1_1_2 - 0.0361607142857143*G0_2_2_0 - 0.0361607142857143*G0_2_2_1 - 0.0723214285714286*G0_2_2_2;
5475
A[340] = 0.0046875*G0_0_0_0 + 0.00468749999999999*G0_0_0_1 + 0.00468749999999999*G0_0_0_2 + 0.0046875*G0_1_1_0 + 0.00468749999999999*G0_1_1_1 + 0.00468749999999999*G0_1_1_2 + 0.0046875*G0_2_2_0 + 0.00468749999999999*G0_2_2_1 + 0.00468749999999999*G0_2_2_2;
5476
A[341] = 0.00736607142857143*G0_0_0_0 + 0.00736607142857143*G0_1_1_0 + 0.00736607142857143*G0_2_2_0;
5477
A[342] = -0.0046875*G0_0_0_1 - 0.0046875*G0_1_1_1 - 0.0046875*G0_2_2_1;
5478
A[343] = -0.0046875*G0_0_0_2 - 0.0046875*G0_1_1_2 - 0.0046875*G0_2_2_2;
5479
A[344] = 0.0241071428571428*G0_0_0_1 + 0.00602678571428569*G0_0_0_2 + 0.0241071428571428*G0_1_1_1 + 0.00602678571428569*G0_1_1_2 + 0.0241071428571428*G0_2_2_1 + 0.00602678571428569*G0_2_2_2;
5480
A[345] = 0.0060267857142857*G0_0_0_1 + 0.0241071428571428*G0_0_0_2 + 0.0060267857142857*G0_1_1_1 + 0.0241071428571428*G0_1_1_2 + 0.0060267857142857*G0_2_2_1 + 0.0241071428571428*G0_2_2_2;
5481
A[346] = -0.0120535714285714*G0_0_0_0 - 0.00602678571428572*G0_0_0_2 - 0.0120535714285714*G0_1_1_0 - 0.00602678571428572*G0_1_1_2 - 0.0120535714285714*G0_2_2_0 - 0.00602678571428572*G0_2_2_2;
5482
A[347] = 0.0060267857142857*G0_0_0_0 + 0.0120535714285714*G0_0_0_2 + 0.0060267857142857*G0_1_1_0 + 0.0120535714285714*G0_1_1_2 + 0.0060267857142857*G0_2_2_0 + 0.0120535714285714*G0_2_2_2;
5483
A[348] = -0.0120535714285714*G0_0_0_0 - 0.00602678571428571*G0_0_0_1 - 0.0120535714285714*G0_1_1_0 - 0.00602678571428571*G0_1_1_1 - 0.0120535714285714*G0_2_2_0 - 0.00602678571428571*G0_2_2_1;
5484
A[349] = 0.00602678571428571*G0_0_0_0 + 0.0120535714285714*G0_0_0_1 + 0.00602678571428571*G0_1_1_0 + 0.0120535714285714*G0_1_1_1 + 0.00602678571428571*G0_2_2_0 + 0.0120535714285714*G0_2_2_1;
5485
A[350] = -0.0241071428571429*G0_0_0_0 - 0.0241071428571428*G0_0_0_1 - 0.0180803571428571*G0_0_0_2 - 0.0241071428571429*G0_1_1_0 - 0.0241071428571428*G0_1_1_1 - 0.0180803571428571*G0_1_1_2 - 0.0241071428571429*G0_2_2_0 - 0.0241071428571428*G0_2_2_1 - 0.0180803571428571*G0_2_2_2;
5486
A[351] = -0.0060267857142857*G0_0_0_0 - 0.00602678571428569*G0_0_0_1 + 0.0180803571428571*G0_0_0_2 - 0.0060267857142857*G0_1_1_0 - 0.00602678571428569*G0_1_1_1 + 0.0180803571428571*G0_1_1_2 - 0.0060267857142857*G0_2_2_0 - 0.00602678571428569*G0_2_2_1 + 0.0180803571428571*G0_2_2_2;
5487
A[352] = -0.0241071428571429*G0_0_0_0 - 0.0180803571428571*G0_0_0_1 - 0.0241071428571429*G0_0_0_2 - 0.0241071428571429*G0_1_1_0 - 0.0180803571428571*G0_1_1_1 - 0.0241071428571429*G0_1_1_2 - 0.0241071428571429*G0_2_2_0 - 0.0180803571428571*G0_2_2_1 - 0.0241071428571429*G0_2_2_2;
5488
A[353] = -0.00602678571428569*G0_0_0_0 + 0.0180803571428571*G0_0_0_1 - 0.00602678571428569*G0_0_0_2 - 0.00602678571428569*G0_1_1_0 + 0.0180803571428571*G0_1_1_1 - 0.00602678571428569*G0_1_1_2 - 0.00602678571428569*G0_2_2_0 + 0.0180803571428571*G0_2_2_1 - 0.00602678571428569*G0_2_2_2;
5489
A[354] = -0.00602678571428569*G0_0_0_0 - 0.0120535714285714*G0_0_0_1 - 0.0120535714285714*G0_0_0_2 - 0.00602678571428569*G0_1_1_0 - 0.0120535714285714*G0_1_1_1 - 0.0120535714285714*G0_1_1_2 - 0.00602678571428569*G0_2_2_0 - 0.0120535714285714*G0_2_2_1 - 0.0120535714285714*G0_2_2_2;
5490
A[355] = -0.00602678571428574*G0_0_0_0 + 0.00602678571428571*G0_0_0_1 + 0.00602678571428571*G0_0_0_2 - 0.00602678571428574*G0_1_1_0 + 0.00602678571428571*G0_1_1_1 + 0.00602678571428571*G0_1_1_2 - 0.00602678571428574*G0_2_2_0 + 0.00602678571428571*G0_2_2_1 + 0.00602678571428571*G0_2_2_2;
5491
A[356] = 0.0723214285714285*G0_0_0_0 + 0.0361607142857143*G0_0_0_1 + 0.0361607142857143*G0_0_0_2 + 0.0723214285714285*G0_1_1_0 + 0.0361607142857143*G0_1_1_1 + 0.0361607142857143*G0_1_1_2 + 0.0723214285714285*G0_2_2_0 + 0.0361607142857143*G0_2_2_1 + 0.0361607142857143*G0_2_2_2;
5492
A[357] = -0.0723214285714285*G0_0_0_0 - 0.0723214285714285*G0_1_1_0 - 0.0723214285714285*G0_2_2_0;
5493
A[358] = 0.0361607142857143*G0_0_0_0 - 0.0361607142857142*G0_0_0_1 + 0.0361607142857143*G0_1_1_0 - 0.0361607142857142*G0_1_1_1 + 0.0361607142857143*G0_2_2_0 - 0.0361607142857142*G0_2_2_1;
5494
A[359] = 0.0361607142857143*G0_0_0_0 - 0.0361607142857143*G0_0_0_2 + 0.0361607142857143*G0_1_1_0 - 0.0361607142857143*G0_1_1_2 + 0.0361607142857143*G0_2_2_0 - 0.0361607142857143*G0_2_2_2;
5495
A[360] = 0.00468749999999999*G0_0_0_0 + 0.00468749999999998*G0_0_0_1 + 0.00468749999999999*G0_0_0_2 + 0.00468749999999999*G0_1_1_0 + 0.00468749999999998*G0_1_1_1 + 0.00468749999999999*G0_1_1_2 + 0.00468749999999999*G0_2_2_0 + 0.00468749999999998*G0_2_2_1 + 0.00468749999999999*G0_2_2_2;
5496
A[361] = -0.0046875*G0_0_0_0 - 0.0046875*G0_1_1_0 - 0.0046875*G0_2_2_0;
5497
A[362] = 0.00736607142857139*G0_0_0_1 + 0.00736607142857139*G0_1_1_1 + 0.00736607142857139*G0_2_2_1;
5498
A[363] = -0.0046875*G0_0_0_2 - 0.0046875*G0_1_1_2 - 0.0046875*G0_2_2_2;
5499
A[364] = -0.0120535714285714*G0_0_0_1 - 0.00602678571428572*G0_0_0_2 - 0.0120535714285714*G0_1_1_1 - 0.00602678571428572*G0_1_1_2 - 0.0120535714285714*G0_2_2_1 - 0.00602678571428572*G0_2_2_2;
5500
A[365] = 0.0060267857142857*G0_0_0_1 + 0.0120535714285714*G0_0_0_2 + 0.0060267857142857*G0_1_1_1 + 0.0120535714285714*G0_1_1_2 + 0.0060267857142857*G0_2_2_1 + 0.0120535714285714*G0_2_2_2;
5501
A[366] = 0.0241071428571428*G0_0_0_0 + 0.00602678571428569*G0_0_0_2 + 0.0241071428571428*G0_1_1_0 + 0.00602678571428569*G0_1_1_2 + 0.0241071428571428*G0_2_2_0 + 0.00602678571428569*G0_2_2_2;
5502
A[367] = 0.00602678571428568*G0_0_0_0 + 0.0241071428571428*G0_0_0_2 + 0.00602678571428568*G0_1_1_0 + 0.0241071428571428*G0_1_1_2 + 0.00602678571428568*G0_2_2_0 + 0.0241071428571428*G0_2_2_2;
5503
A[368] = 0.0120535714285714*G0_0_0_0 + 0.00602678571428569*G0_0_0_1 + 0.0120535714285714*G0_1_1_0 + 0.00602678571428569*G0_1_1_1 + 0.0120535714285714*G0_2_2_0 + 0.00602678571428569*G0_2_2_1;
5504
A[369] = -0.00602678571428571*G0_0_0_0 - 0.0120535714285714*G0_0_0_1 - 0.00602678571428571*G0_1_1_0 - 0.0120535714285714*G0_1_1_1 - 0.00602678571428571*G0_2_2_0 - 0.0120535714285714*G0_2_2_1;
5505
A[370] = -0.0241071428571428*G0_0_0_0 - 0.0241071428571428*G0_0_0_1 - 0.0180803571428571*G0_0_0_2 - 0.0241071428571428*G0_1_1_0 - 0.0241071428571428*G0_1_1_1 - 0.0180803571428571*G0_1_1_2 - 0.0241071428571428*G0_2_2_0 - 0.0241071428571428*G0_2_2_1 - 0.0180803571428571*G0_2_2_2;
5506
A[371] = -0.00602678571428568*G0_0_0_0 - 0.00602678571428568*G0_0_0_1 + 0.0180803571428571*G0_0_0_2 - 0.00602678571428568*G0_1_1_0 - 0.00602678571428568*G0_1_1_1 + 0.0180803571428571*G0_1_1_2 - 0.00602678571428568*G0_2_2_0 - 0.00602678571428568*G0_2_2_1 + 0.0180803571428571*G0_2_2_2;
5507
A[372] = -0.0120535714285715*G0_0_0_0 - 0.0060267857142857*G0_0_0_1 - 0.0120535714285715*G0_0_0_2 - 0.0120535714285715*G0_1_1_0 - 0.0060267857142857*G0_1_1_1 - 0.0120535714285715*G0_1_1_2 - 0.0120535714285715*G0_2_2_0 - 0.0060267857142857*G0_2_2_1 - 0.0120535714285715*G0_2_2_2;
5508
A[373] = 0.00602678571428572*G0_0_0_0 - 0.00602678571428569*G0_0_0_1 + 0.00602678571428573*G0_0_0_2 + 0.00602678571428572*G0_1_1_0 - 0.00602678571428569*G0_1_1_1 + 0.00602678571428573*G0_1_1_2 + 0.00602678571428572*G0_2_2_0 - 0.00602678571428569*G0_2_2_1 + 0.00602678571428573*G0_2_2_2;
5509
A[374] = -0.0180803571428571*G0_0_0_0 - 0.0241071428571428*G0_0_0_1 - 0.0241071428571429*G0_0_0_2 - 0.0180803571428571*G0_1_1_0 - 0.0241071428571428*G0_1_1_1 - 0.0241071428571429*G0_1_1_2 - 0.0180803571428571*G0_2_2_0 - 0.0241071428571428*G0_2_2_1 - 0.0241071428571429*G0_2_2_2;
5510
A[375] = 0.0180803571428571*G0_0_0_0 - 0.00602678571428569*G0_0_0_1 - 0.0060267857142857*G0_0_0_2 + 0.0180803571428571*G0_1_1_0 - 0.00602678571428569*G0_1_1_1 - 0.0060267857142857*G0_1_1_2 + 0.0180803571428571*G0_2_2_0 - 0.00602678571428569*G0_2_2_1 - 0.0060267857142857*G0_2_2_2;
5511
A[376] = 0.0361607142857142*G0_0_0_0 + 0.0723214285714285*G0_0_0_1 + 0.0361607142857143*G0_0_0_2 + 0.0361607142857142*G0_1_1_0 + 0.0723214285714285*G0_1_1_1 + 0.0361607142857143*G0_1_1_2 + 0.0361607142857142*G0_2_2_0 + 0.0723214285714285*G0_2_2_1 + 0.0361607142857143*G0_2_2_2;
5512
A[377] = -0.0361607142857143*G0_0_0_0 + 0.0361607142857142*G0_0_0_1 - 0.0361607142857143*G0_1_1_0 + 0.0361607142857142*G0_1_1_1 - 0.0361607142857143*G0_2_2_0 + 0.0361607142857142*G0_2_2_1;
5513
A[378] = -0.0723214285714285*G0_0_0_1 - 0.0723214285714285*G0_1_1_1 - 0.0723214285714285*G0_2_2_1;
5514
A[379] = 0.0361607142857143*G0_0_0_1 - 0.0361607142857143*G0_0_0_2 + 0.0361607142857143*G0_1_1_1 - 0.0361607142857143*G0_1_1_2 + 0.0361607142857143*G0_2_2_1 - 0.0361607142857143*G0_2_2_2;
5515
A[380] = 0.00468749999999999*G0_0_0_0 + 0.00468749999999999*G0_0_0_1 + 0.0046875*G0_0_0_2 + 0.00468749999999999*G0_1_1_0 + 0.00468749999999999*G0_1_1_1 + 0.0046875*G0_1_1_2 + 0.00468749999999999*G0_2_2_0 + 0.00468749999999999*G0_2_2_1 + 0.0046875*G0_2_2_2;
5516
A[381] = -0.0046875*G0_0_0_0 - 0.0046875*G0_1_1_0 - 0.0046875*G0_2_2_0;
5517
A[382] = -0.00468750000000001*G0_0_0_1 - 0.00468750000000001*G0_1_1_1 - 0.00468750000000001*G0_2_2_1;
5518
A[383] = 0.00736607142857142*G0_0_0_2 + 0.00736607142857142*G0_1_1_2 + 0.00736607142857142*G0_2_2_2;
5519
A[384] = 0.0120535714285714*G0_0_0_1 + 0.00602678571428569*G0_0_0_2 + 0.0120535714285714*G0_1_1_1 + 0.00602678571428569*G0_1_1_2 + 0.0120535714285714*G0_2_2_1 + 0.00602678571428569*G0_2_2_2;
5520
A[385] = -0.00602678571428573*G0_0_0_1 - 0.0120535714285714*G0_0_0_2 - 0.00602678571428573*G0_1_1_1 - 0.0120535714285714*G0_1_1_2 - 0.00602678571428573*G0_2_2_1 - 0.0120535714285714*G0_2_2_2;
5521
A[386] = 0.0120535714285714*G0_0_0_0 + 0.00602678571428568*G0_0_0_2 + 0.0120535714285714*G0_1_1_0 + 0.00602678571428568*G0_1_1_2 + 0.0120535714285714*G0_2_2_0 + 0.00602678571428568*G0_2_2_2;
5522
A[387] = -0.00602678571428573*G0_0_0_0 - 0.0120535714285714*G0_0_0_2 - 0.00602678571428573*G0_1_1_0 - 0.0120535714285714*G0_1_1_2 - 0.00602678571428573*G0_2_2_0 - 0.0120535714285714*G0_2_2_2;
5523
A[388] = 0.0241071428571428*G0_0_0_0 + 0.00602678571428569*G0_0_0_1 + 0.0241071428571428*G0_1_1_0 + 0.00602678571428569*G0_1_1_1 + 0.0241071428571428*G0_2_2_0 + 0.00602678571428569*G0_2_2_1;
5524
A[389] = 0.00602678571428569*G0_0_0_0 + 0.0241071428571428*G0_0_0_1 + 0.00602678571428569*G0_1_1_0 + 0.0241071428571428*G0_1_1_1 + 0.00602678571428569*G0_2_2_0 + 0.0241071428571428*G0_2_2_1;
5525
A[390] = -0.0120535714285714*G0_0_0_0 - 0.0120535714285714*G0_0_0_1 - 0.00602678571428569*G0_0_0_2 - 0.0120535714285714*G0_1_1_0 - 0.0120535714285714*G0_1_1_1 - 0.00602678571428569*G0_1_1_2 - 0.0120535714285714*G0_2_2_0 - 0.0120535714285714*G0_2_2_1 - 0.00602678571428569*G0_2_2_2;
5526
A[391] = 0.00602678571428574*G0_0_0_0 + 0.00602678571428573*G0_0_0_1 - 0.00602678571428571*G0_0_0_2 + 0.00602678571428574*G0_1_1_0 + 0.00602678571428573*G0_1_1_1 - 0.00602678571428571*G0_1_1_2 + 0.00602678571428574*G0_2_2_0 + 0.00602678571428573*G0_2_2_1 - 0.00602678571428571*G0_2_2_2;
5527
A[392] = -0.0241071428571429*G0_0_0_0 - 0.0180803571428571*G0_0_0_1 - 0.0241071428571429*G0_0_0_2 - 0.0241071428571429*G0_1_1_0 - 0.0180803571428571*G0_1_1_1 - 0.0241071428571429*G0_1_1_2 - 0.0241071428571429*G0_2_2_0 - 0.0180803571428571*G0_2_2_1 - 0.0241071428571429*G0_2_2_2;
5528
A[393] = -0.00602678571428568*G0_0_0_0 + 0.0180803571428571*G0_0_0_1 - 0.00602678571428566*G0_0_0_2 - 0.00602678571428568*G0_1_1_0 + 0.0180803571428571*G0_1_1_1 - 0.00602678571428566*G0_1_1_2 - 0.00602678571428568*G0_2_2_0 + 0.0180803571428571*G0_2_2_1 - 0.00602678571428566*G0_2_2_2;
5529
A[394] = -0.0180803571428571*G0_0_0_0 - 0.0241071428571429*G0_0_0_1 - 0.0241071428571429*G0_0_0_2 - 0.0180803571428571*G0_1_1_0 - 0.0241071428571429*G0_1_1_1 - 0.0241071428571429*G0_1_1_2 - 0.0180803571428571*G0_2_2_0 - 0.0241071428571429*G0_2_2_1 - 0.0241071428571429*G0_2_2_2;
5530
A[395] = 0.0180803571428571*G0_0_0_0 - 0.0060267857142857*G0_0_0_1 - 0.00602678571428569*G0_0_0_2 + 0.0180803571428571*G0_1_1_0 - 0.0060267857142857*G0_1_1_1 - 0.00602678571428569*G0_1_1_2 + 0.0180803571428571*G0_2_2_0 - 0.0060267857142857*G0_2_2_1 - 0.00602678571428569*G0_2_2_2;
5531
A[396] = 0.0361607142857142*G0_0_0_0 + 0.0361607142857142*G0_0_0_1 + 0.0723214285714285*G0_0_0_2 + 0.0361607142857142*G0_1_1_0 + 0.0361607142857142*G0_1_1_1 + 0.0723214285714285*G0_1_1_2 + 0.0361607142857142*G0_2_2_0 + 0.0361607142857142*G0_2_2_1 + 0.0723214285714285*G0_2_2_2;
5532
A[397] = -0.0361607142857142*G0_0_0_0 + 0.0361607142857143*G0_0_0_2 - 0.0361607142857142*G0_1_1_0 + 0.0361607142857143*G0_1_1_2 - 0.0361607142857142*G0_2_2_0 + 0.0361607142857143*G0_2_2_2;
5533
A[398] = -0.0361607142857142*G0_0_0_1 + 0.0361607142857143*G0_0_0_2 - 0.0361607142857142*G0_1_1_1 + 0.0361607142857143*G0_1_1_2 - 0.0361607142857142*G0_2_2_1 + 0.0361607142857143*G0_2_2_2;
5534
A[399] = -0.0723214285714284*G0_0_0_2 - 0.0723214285714284*G0_1_1_2 - 0.0723214285714284*G0_2_2_2;
5535
}
5536
5537
};
5538
5539
/// This class defines the interface for the assembly of the global
5540
/// tensor corresponding to a form with r + n arguments, that is, a
5541
/// mapping
5542
///
5543
/// a : V1 x V2 x ... Vr x W1 x W2 x ... x Wn -> R
5544
///
5545
/// with arguments v1, v2, ..., vr, w1, w2, ..., wn. The rank r
5546
/// global tensor A is defined by
5547
///
5548
/// A = a(V1, V2, ..., Vr, w1, w2, ..., wn),
5549
///
5550
/// where each argument Vj represents the application to the
5551
/// sequence of basis functions of Vj and w1, w2, ..., wn are given
5552
/// fixed functions (coefficients).
5553
5554
class UFC_AdvectionBilinearForm: public ufc::form
5555
{
5556
public:
5557
5558
/// Constructor
5559
UFC_AdvectionBilinearForm() : ufc::form()
5560
{
5561
// Do nothing
5562
}
5563
5564
/// Destructor
5565
virtual ~UFC_AdvectionBilinearForm()
5566
{
5567
// Do nothing
5568
}
5569
5570
/// Return a string identifying the form
5571
virtual const char* signature() const
5572
{
5573
return "w0_a1[0, 1, 2](dXa2[0, 1, 2]/dxa0[0, 1, 2]) | vi0[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]*va1[0, 1, 2][a0[0, 1, 2]]*((d/dXa2[0, 1, 2])vi1[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19])*dX(0)";
5574
}
5575
5576
/// Return the rank of the global tensor (r)
5577
virtual unsigned int rank() const
5578
{
5579
return 2;
5580
}
5581
5582
/// Return the number of coefficients (n)
5583
virtual unsigned int num_coefficients() const
5584
{
5585
return 1;
5586
}
5587
5588
/// Return the number of cell integrals
5589
virtual unsigned int num_cell_integrals() const
5590
{
5591
return 1;
5592
}
5593
5594
/// Return the number of exterior facet integrals
5595
virtual unsigned int num_exterior_facet_integrals() const
5596
{
5597
return 0;
5598
}
5599
5600
/// Return the number of interior facet integrals
5601
virtual unsigned int num_interior_facet_integrals() const
5602
{
5603
return 0;
5604
}
5605
5606
/// Create a new finite element for argument function i
5607
virtual ufc::finite_element* create_finite_element(unsigned int i) const
5608
{
5609
switch ( i )
5610
{
5611
case 0:
5612
return new UFC_AdvectionBilinearForm_finite_element_0();
5613
break;
5614
case 1:
5615
return new UFC_AdvectionBilinearForm_finite_element_1();
5616
break;
5617
case 2:
5618
return new UFC_AdvectionBilinearForm_finite_element_2();
5619
break;
5620
}
5621
return 0;
5622
}
5623
5624
/// Create a new dof map for argument function i
5625
virtual ufc::dof_map* create_dof_map(unsigned int i) const
5626
{
5627
switch ( i )
5628
{
5629
case 0:
5630
return new UFC_AdvectionBilinearForm_dof_map_0();
5631
break;
5632
case 1:
5633
return new UFC_AdvectionBilinearForm_dof_map_1();
5634
break;
5635
case 2:
5636
return new UFC_AdvectionBilinearForm_dof_map_2();
5637
break;
5638
}
5639
return 0;
5640
}
5641
5642
/// Create a new cell integral on sub domain i
5643
virtual ufc::cell_integral* create_cell_integral(unsigned int i) const
5644
{
5645
return new UFC_AdvectionBilinearForm_cell_integral_0();
5646
}
5647
5648
/// Create a new exterior facet integral on sub domain i
5649
virtual ufc::exterior_facet_integral* create_exterior_facet_integral(unsigned int i) const
5650
{
5651
return 0;
5652
}
5653
5654
/// Create a new interior facet integral on sub domain i
5655
virtual ufc::interior_facet_integral* create_interior_facet_integral(unsigned int i) const
5656
{
5657
return 0;
5658
}
5659
5660
};
5661
5662
// DOLFIN wrappers
5663
5664
#include <dolfin/fem/Form.h>
5665
5666
class AdvectionBilinearForm : public dolfin::Form
5667
{
5668
public:
5669
5670
AdvectionBilinearForm(dolfin::Function& w0) : dolfin::Form()
5671
{
5672
__coefficients.push_back(&w0);
5673
}
5674
5675
/// Return UFC form
5676
virtual const ufc::form& form() const
5677
{
5678
return __form;
5679
}
5680
5681
/// Return array of coefficients
5682
virtual const dolfin::Array<dolfin::Function*>& coefficients() const
5683
{
5684
return __coefficients;
5685
}
5686
5687
private:
5688
5689
// UFC form
5690
UFC_AdvectionBilinearForm __form;
5691
5692
/// Array of coefficients
5693
dolfin::Array<dolfin::Function*> __coefficients;
5694
5695
};
5696
5697
#endif
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