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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 0.4.3.
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/// This class defines the interface for a finite element.
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class ffc_03_finite_element_0: public ufc::finite_element
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ffc_03_finite_element_0() : ufc::finite_element()
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virtual ~ffc_03_finite_element_0()
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/// Return a string identifying the finite element
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virtual const char* signature() const
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return "Lagrange finite element of degree 1 on a tetrahedron";
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/// Return the cell shape
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virtual ufc::shape cell_shape() const
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return ufc::tetrahedron;
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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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/// Return the rank of the value space
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virtual unsigned int value_rank() const
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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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/// Evaluate basis function i at given point in cell
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virtual void evaluate_basis(unsigned int i,
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const double* coordinates,
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const ufc::cell& c) const
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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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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 = -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 = 2.0 * y/(1.0 - z) - 1.0;
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// Map degree of freedom to element degree of freedom
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const unsigned int dof = i;
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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_z_0 = 1;
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const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);
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// Compute psitilde_a
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const double psitilde_a_0 = 1;
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const double psitilde_a_1 = x;
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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_1_0 = 1;
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// Compute psitilde_cs
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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_01_0 = 1;
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const double psitilde_cs_10_0 = 1;
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// Compute basisvalues
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const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
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const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;
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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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// Table(s) of coefficients
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const static double coefficients0[4][4] = \
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{{0.288675134594813, -0.182574185835055, -0.105409255338946, -0.074535599249993},
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{0.288675134594813, 0.182574185835055, -0.105409255338946, -0.074535599249993},
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{0.288675134594813, 0, 0.210818510677892, -0.074535599249993},
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{0.288675134594813, 0, 0, 0.223606797749979}};
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// Extract relevant coefficients
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const double coeff0_0 = coefficients0[dof][0];
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const double coeff0_1 = coefficients0[dof][1];
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const double coeff0_2 = coefficients0[dof][2];
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const double coeff0_3 = coefficients0[dof][3];
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*values = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2 + coeff0_3*basisvalue3;
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/// Evaluate all basis functions at given point in cell
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virtual void evaluate_basis_all(double* values,
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const double* coordinates,
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const ufc::cell& c) const
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throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");
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/// Evaluate order n derivatives of basis function i at given point in cell
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virtual void evaluate_basis_derivatives(unsigned int i,
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const double* coordinates,
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const ufc::cell& c) const
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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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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 = -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 = 2.0 * y/(1.0 - z) - 1.0;
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// Compute number of derivatives
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unsigned int num_derivatives = 1;
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for (unsigned int j = 0; j < n; j++)
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num_derivatives *= 3;
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// Declare pointer to two dimensional array that holds combinations of derivatives and initialise
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unsigned int **combinations = new unsigned int *[num_derivatives];
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for (unsigned int j = 0; j < num_derivatives; j++)
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combinations[j] = new unsigned int [n];
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for (unsigned int k = 0; k < n; k++)
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combinations[j][k] = 0;
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// Generate combinations of derivatives
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for (unsigned int row = 1; row < num_derivatives; row++)
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for (unsigned int num = 0; num < row; num++)
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for (unsigned int col = n-1; col+1 > 0; col--)
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if (combinations[row][col] + 1 > 2)
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combinations[row][col] = 0;
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combinations[row][col] += 1;
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// Compute inverse of Jacobian
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const double Jinv[3][3] ={{d00 / detJ, d10 / detJ, d20 / detJ}, {d01 / detJ, d11 / detJ, d21 / detJ}, {d02 / detJ, d12 / detJ, d22 / detJ}};
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// Declare transformation matrix
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// Declare pointer to two dimensional array and initialise
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double **transform = new double *[num_derivatives];
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for (unsigned int j = 0; j < num_derivatives; j++)
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transform[j] = new double [num_derivatives];
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for (unsigned int k = 0; k < num_derivatives; k++)
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// Construct transformation matrix
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for (unsigned int row = 0; row < num_derivatives; row++)
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for (unsigned int col = 0; col < num_derivatives; col++)
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for (unsigned int k = 0; k < n; k++)
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transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
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for (unsigned int j = 0; j < 1*num_derivatives; j++)
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// Map degree of freedom to element degree of freedom
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const unsigned int dof = i;
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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_z_0 = 1;
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const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);
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// Compute psitilde_a
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const double psitilde_a_0 = 1;
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const double psitilde_a_1 = x;
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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_1_0 = 1;
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// Compute psitilde_cs
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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_01_0 = 1;
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const double psitilde_cs_10_0 = 1;
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// Compute basisvalues
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const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
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const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;
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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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// Table(s) of coefficients
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const static double coefficients0[4][4] = \
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{{0.288675134594813, -0.182574185835055, -0.105409255338946, -0.074535599249993},
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{0.288675134594813, 0.182574185835055, -0.105409255338946, -0.074535599249993},
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{0.288675134594813, 0, 0.210818510677892, -0.074535599249993},
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{0.288675134594813, 0, 0, 0.223606797749979}};
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// Interesting (new) part
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// Tables of derivatives of the polynomial base (transpose)
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const static double dmats0[4][4] = \
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{6.32455532033676, 0, 0, 0},
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const static double dmats1[4][4] = \
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{3.16227766016838, 0, 0, 0},
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{5.47722557505166, 0, 0, 0},
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const static double dmats2[4][4] = \
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{3.16227766016838, 0, 0, 0},
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{1.82574185835055, 0, 0, 0},
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{5.16397779494322, 0, 0, 0}};
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// Compute reference derivatives
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// Declare pointer to array of derivatives on FIAT element
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double *derivatives = new double [num_derivatives];
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// Declare coefficients
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// Declare new coefficients
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double new_coeff0_0 = 0;
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double new_coeff0_1 = 0;
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double new_coeff0_2 = 0;
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double new_coeff0_3 = 0;
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// Loop possible derivatives
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for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
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// Get values from coefficients array
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new_coeff0_0 = coefficients0[dof][0];
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new_coeff0_1 = coefficients0[dof][1];
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new_coeff0_2 = coefficients0[dof][2];
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new_coeff0_3 = coefficients0[dof][3];
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// Loop derivative order
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for (unsigned int j = 0; j < n; j++)
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// Update old coefficients
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coeff0_0 = new_coeff0_0;
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coeff0_1 = new_coeff0_1;
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coeff0_2 = new_coeff0_2;
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coeff0_3 = new_coeff0_3;
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if(combinations[deriv_num][j] == 0)
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new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0] + coeff0_3*dmats0[3][0];
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new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1] + coeff0_3*dmats0[3][1];
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new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2] + coeff0_3*dmats0[3][2];
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new_coeff0_3 = coeff0_0*dmats0[0][3] + coeff0_1*dmats0[1][3] + coeff0_2*dmats0[2][3] + coeff0_3*dmats0[3][3];
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if(combinations[deriv_num][j] == 1)
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new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0] + coeff0_3*dmats1[3][0];
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new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1] + coeff0_3*dmats1[3][1];
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new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2] + coeff0_3*dmats1[3][2];
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new_coeff0_3 = coeff0_0*dmats1[0][3] + coeff0_1*dmats1[1][3] + coeff0_2*dmats1[2][3] + coeff0_3*dmats1[3][3];
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if(combinations[deriv_num][j] == 2)
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new_coeff0_0 = coeff0_0*dmats2[0][0] + coeff0_1*dmats2[1][0] + coeff0_2*dmats2[2][0] + coeff0_3*dmats2[3][0];
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new_coeff0_1 = coeff0_0*dmats2[0][1] + coeff0_1*dmats2[1][1] + coeff0_2*dmats2[2][1] + coeff0_3*dmats2[3][1];
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new_coeff0_2 = coeff0_0*dmats2[0][2] + coeff0_1*dmats2[1][2] + coeff0_2*dmats2[2][2] + coeff0_3*dmats2[3][2];
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new_coeff0_3 = coeff0_0*dmats2[0][3] + coeff0_1*dmats2[1][3] + coeff0_2*dmats2[2][3] + coeff0_3*dmats2[3][3];
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// Compute derivatives on reference element as dot product of coefficients and basisvalues
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derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2 + new_coeff0_3*basisvalue3;
433
// Transform derivatives back to physical element
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for (unsigned int row = 0; row < num_derivatives; row++)
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for (unsigned int col = 0; col < num_derivatives; col++)
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values[row] += transform[row][col]*derivatives[col];
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// Delete pointer to array of derivatives on FIAT element
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delete [] derivatives;
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// Delete pointer to array of combinations of derivatives and transform
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for (unsigned int row = 0; row < num_derivatives; row++)
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delete [] combinations[row];
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delete [] transform[row];
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delete [] combinations;
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/// Evaluate order n derivatives of all basis functions at given point in cell
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virtual void evaluate_basis_derivatives_all(unsigned int n,
458
const double* coordinates,
459
const ufc::cell& c) const
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throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");
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/// Evaluate linear functional for dof i on the function f
465
virtual double evaluate_dof(unsigned int i,
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const ufc::function& f,
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const ufc::cell& c) const
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// The reference points, direction and weights:
470
const static double X[4][1][3] = {{{0, 0, 0}}, {{1, 0, 0}}, {{0, 1, 0}}, {{0, 0, 1}}};
471
const static double W[4][1] = {{1}, {1}, {1}, {1}};
472
const static double D[4][1][1] = {{{1}}, {{1}}, {{1}}, {{1}}};
474
const double * const * x = c.coordinates;
476
// Iterate over the points:
477
// Evaluate basis functions for affine mapping
478
const double w0 = 1.0 - X[i][0][0] - X[i][0][1] - X[i][0][2];
479
const double w1 = X[i][0][0];
480
const double w2 = X[i][0][1];
481
const double w3 = X[i][0][2];
483
// Compute affine mapping y = F(X)
485
y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0] + w3*x[3][0];
486
y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1] + w3*x[3][1];
487
y[2] = w0*x[0][2] + w1*x[1][2] + w2*x[2][2] + w3*x[3][2];
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// Evaluate function at physical points
491
f.evaluate(values, y, c);
493
// Map function values using appropriate mapping
494
// Affine map: Do nothing
496
// Note that we do not map the weights (yet).
498
// Take directional components
499
for(int k = 0; k < 1; k++)
500
result += values[k]*D[i][0][k];
501
// Multiply by weights
507
/// Evaluate linear functionals for all dofs on the function f
508
virtual void evaluate_dofs(double* values,
509
const ufc::function& f,
510
const ufc::cell& c) const
512
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
515
/// Interpolate vertex values from dof values
516
virtual void interpolate_vertex_values(double* vertex_values,
517
const double* dof_values,
518
const ufc::cell& c) const
520
// Evaluate at vertices and use affine mapping
521
vertex_values[0] = dof_values[0];
522
vertex_values[1] = dof_values[1];
523
vertex_values[2] = dof_values[2];
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vertex_values[3] = dof_values[3];
527
/// Return the number of sub elements (for a mixed element)
528
virtual unsigned int num_sub_elements() const
533
/// Create a new finite element for sub element i (for a mixed element)
534
virtual ufc::finite_element* create_sub_element(unsigned int i) const
536
return new ffc_03_finite_element_0();
541
/// This class defines the interface for a local-to-global mapping of
542
/// degrees of freedom (dofs).
544
class ffc_03_dof_map_0: public ufc::dof_map
548
unsigned int __global_dimension;
553
ffc_03_dof_map_0() : ufc::dof_map()
555
__global_dimension = 0;
559
virtual ~ffc_03_dof_map_0()
564
/// Return a string identifying the dof map
565
virtual const char* signature() const
567
return "FFC dof map for Lagrange finite element of degree 1 on a tetrahedron";
570
/// Return true iff mesh entities of topological dimension d are needed
571
virtual bool needs_mesh_entities(unsigned int d) const
591
/// Initialize dof map for mesh (return true iff init_cell() is needed)
592
virtual bool init_mesh(const ufc::mesh& m)
594
__global_dimension = m.num_entities[0];
598
/// Initialize dof map for given cell
599
virtual void init_cell(const ufc::mesh& m,
605
/// Finish initialization of dof map for cells
606
virtual void init_cell_finalize()
611
/// Return the dimension of the global finite element function space
612
virtual unsigned int global_dimension() const
614
return __global_dimension;
617
/// Return the dimension of the local finite element function space
618
virtual unsigned int local_dimension() const
623
// Return the geometric dimension of the coordinates this dof map provides
624
virtual unsigned int geometric_dimension() const
626
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
629
/// Return the number of dofs on each cell facet
630
virtual unsigned int num_facet_dofs() const
635
/// Return the number of dofs associated with each cell entity of dimension d
636
virtual unsigned int num_entity_dofs(unsigned int d) const
638
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
641
/// Tabulate the local-to-global mapping of dofs on a cell
642
virtual void tabulate_dofs(unsigned int* dofs,
644
const ufc::cell& c) const
646
dofs[0] = c.entity_indices[0][0];
647
dofs[1] = c.entity_indices[0][1];
648
dofs[2] = c.entity_indices[0][2];
649
dofs[3] = c.entity_indices[0][3];
652
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
653
virtual void tabulate_facet_dofs(unsigned int* dofs,
654
unsigned int facet) const
681
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
682
virtual void tabulate_entity_dofs(unsigned int* dofs,
683
unsigned int d, unsigned int i) const
685
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
688
/// Tabulate the coordinates of all dofs on a cell
689
virtual void tabulate_coordinates(double** coordinates,
690
const ufc::cell& c) const
692
const double * const * x = c.coordinates;
693
coordinates[0][0] = x[0][0];
694
coordinates[0][1] = x[0][1];
695
coordinates[0][2] = x[0][2];
696
coordinates[1][0] = x[1][0];
697
coordinates[1][1] = x[1][1];
698
coordinates[1][2] = x[1][2];
699
coordinates[2][0] = x[2][0];
700
coordinates[2][1] = x[2][1];
701
coordinates[2][2] = x[2][2];
702
coordinates[3][0] = x[3][0];
703
coordinates[3][1] = x[3][1];
704
coordinates[3][2] = x[3][2];
707
/// Return the number of sub dof maps (for a mixed element)
708
virtual unsigned int num_sub_dof_maps() const
713
/// Create a new dof_map for sub dof map i (for a mixed element)
714
virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
716
return new ffc_03_dof_map_0();