1
// 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_26_finite_element_0: public ufc::finite_element
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ffc_26_finite_element_0() : ufc::finite_element()
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virtual ~ffc_26_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 "Brezzi-Douglas-Marini finite element of degree 1 on a triangle";
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/// Return the cell shape
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virtual ufc::shape cell_shape() const
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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_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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// Compute determinant of Jacobian
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const double detJ = J_00*J_11 - J_01*J_10;
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// Compute inverse of Jacobian
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// Get coordinates and map to the reference (UFC) element
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double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
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element_coordinates[0][0]*element_coordinates[2][1] +\
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J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
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double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
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element_coordinates[1][0]*element_coordinates[0][1] -\
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J_10*coordinates[0] + J_00*coordinates[1]) / detJ;
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// Map coordinates to the reference square
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if (std::abs(y - 1.0) < 1e-14)
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x = 2.0 *x/(1.0 - y) - 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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// 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 basisvalues
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const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
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const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
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const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
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// Table(s) of coefficients
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const static double coefficients0[6][3] = \
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{{0.942809041582063, 0.577350269189626, -0.333333333333333},
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{-0.471404520791032, -0.288675134594813, 0.166666666666667},
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{0.471404520791032, -0.577350269189626, -0.666666666666667},
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{0.471404520791032, 0.288675134594813, 0.833333333333333},
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{-0.471404520791032, -0.288675134594813, 0.166666666666667},
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{0.942809041582064, 0.577350269189626, -0.333333333333333}};
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const static double coefficients1[6][3] = \
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{{-0.471404520791032, 0, -0.333333333333333},
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{0.942809041582063, 0, 0.666666666666667},
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{0.471404520791032, 0, 0.333333333333333},
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{-0.942809041582064, 0, -0.666666666666667},
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{-0.471404520791031, 0.866025403784439, 0.166666666666667},
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{-0.471404520791032, -0.866025403784439, 0.166666666666667}};
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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 coeff1_0 = coefficients1[dof][0];
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const double coeff1_1 = coefficients1[dof][1];
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const double coeff1_2 = coefficients1[dof][2];
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const double tmp0_0 = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2;
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const double tmp0_1 = coeff1_0*basisvalue0 + coeff1_1*basisvalue1 + coeff1_2*basisvalue2;
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// Using contravariant Piola transform to map values back to the physical element
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values[0] = (1.0/detJ)*(J_00*tmp0_0 + J_01*tmp0_1);
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values[1] = (1.0/detJ)*(J_10*tmp0_0 + J_11*tmp0_1);
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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_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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// Compute determinant of Jacobian
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const double detJ = J_00*J_11 - J_01*J_10;
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// Compute inverse of Jacobian
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// Get coordinates and map to the reference (UFC) element
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double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
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element_coordinates[0][0]*element_coordinates[2][1] +\
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J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
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double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
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element_coordinates[1][0]*element_coordinates[0][1] -\
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J_10*coordinates[0] + J_00*coordinates[1]) / detJ;
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// Map coordinates to the reference square
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if (std::abs(y - 1.0) < 1e-14)
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x = 2.0 *x/(1.0 - y) - 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 *= 2;
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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 > 1)
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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[2][2] = {{J_11 / detJ, -J_01 / detJ}, {-J_10 / detJ, J_00 / 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 < 2*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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// 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 basisvalues
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const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
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const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
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const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
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// Table(s) of coefficients
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const static double coefficients0[6][3] = \
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{{0.942809041582063, 0.577350269189626, -0.333333333333333},
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{-0.471404520791032, -0.288675134594813, 0.166666666666667},
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{0.471404520791032, -0.577350269189626, -0.666666666666667},
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{0.471404520791032, 0.288675134594813, 0.833333333333333},
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{-0.471404520791032, -0.288675134594813, 0.166666666666667},
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{0.942809041582064, 0.577350269189626, -0.333333333333333}};
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const static double coefficients1[6][3] = \
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{{-0.471404520791032, 0, -0.333333333333333},
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{0.942809041582063, 0, 0.666666666666667},
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{0.471404520791032, 0, 0.333333333333333},
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{-0.942809041582064, 0, -0.666666666666667},
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{-0.471404520791031, 0.866025403784439, 0.166666666666667},
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{-0.471404520791032, -0.866025403784439, 0.166666666666667}};
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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[3][3] = \
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{4.89897948556636, 0, 0},
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const static double dmats1[3][3] = \
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{2.44948974278318, 0, 0},
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{4.24264068711928, 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 [2*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_coeff1_0 = 0;
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double new_coeff1_1 = 0;
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double new_coeff1_2 = 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_coeff1_0 = coefficients1[dof][0];
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new_coeff1_1 = coefficients1[dof][1];
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new_coeff1_2 = coefficients1[dof][2];
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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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coeff1_0 = new_coeff1_0;
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coeff1_1 = new_coeff1_1;
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coeff1_2 = new_coeff1_2;
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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];
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new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1];
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new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2];
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new_coeff1_0 = coeff1_0*dmats0[0][0] + coeff1_1*dmats0[1][0] + coeff1_2*dmats0[2][0];
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new_coeff1_1 = coeff1_0*dmats0[0][1] + coeff1_1*dmats0[1][1] + coeff1_2*dmats0[2][1];
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new_coeff1_2 = coeff1_0*dmats0[0][2] + coeff1_1*dmats0[1][2] + coeff1_2*dmats0[2][2];
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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];
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new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1];
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new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2];
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new_coeff1_0 = coeff1_0*dmats1[0][0] + coeff1_1*dmats1[1][0] + coeff1_2*dmats1[2][0];
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new_coeff1_1 = coeff1_0*dmats1[0][1] + coeff1_1*dmats1[1][1] + coeff1_2*dmats1[2][1];
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new_coeff1_2 = coeff1_0*dmats1[0][2] + coeff1_1*dmats1[1][2] + coeff1_2*dmats1[2][2];
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// Compute derivatives on reference element as dot product of coefficients and basisvalues
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// Correct values by the contravariant Piola transform
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const double tmp0_0 = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2;
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const double tmp0_1 = new_coeff1_0*basisvalue0 + new_coeff1_1*basisvalue1 + new_coeff1_2*basisvalue2;
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derivatives[deriv_num] = (1.0/detJ)*(J_00*tmp0_0 + J_01*tmp0_1);
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derivatives[num_derivatives + deriv_num] = (1.0/detJ)*(J_10*tmp0_0 + J_11*tmp0_1);
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// 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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values[num_derivatives + row] += transform[row][col]*derivatives[num_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,
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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_derivatives() is not yet implemented.");
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/// Evaluate linear functional for dof i on the function f
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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:
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const static double X[6][1][2] = {{{0.666666666666667, 0.333333333333333}}, {{0.333333333333333, 0.666666666666667}}, {{0, 0.333333333333333}}, {{0, 0.666666666666667}}, {{0.333333333333333, 0}}, {{0.666666666666667, 0}}};
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const static double W[6][1] = {{1}, {1}, {1}, {1}, {1}, {1}};
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const static double D[6][1][2] = {{{1, 1}}, {{1, 1}}, {{1, 0}}, {{1, 0}}, {{0, -1}}, {{0, -1}}};
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// Extract vertex coordinates
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const double * const * x = c.coordinates;
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// Compute Jacobian of affine map from reference cell
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const double J_00 = x[1][0] - x[0][0];
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const double J_01 = x[2][0] - x[0][0];
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const double J_10 = x[1][1] - x[0][1];
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const double J_11 = x[2][1] - x[0][1];
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// Compute determinant of Jacobian
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double detJ = J_00*J_11 - J_01*J_10;
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// Compute inverse of Jacobian
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const double Jinv_00 = J_11 / detJ;
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const double Jinv_01 = -J_01 / detJ;
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const double Jinv_10 = -J_10 / detJ;
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const double Jinv_11 = J_00 / detJ;
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double copyofvalues[2];
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// Iterate over the points:
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// Evaluate basis functions for affine mapping
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const double w0 = 1.0 - X[i][0][0] - X[i][0][1];
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const double w1 = X[i][0][0];
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const double w2 = X[i][0][1];
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// Compute affine mapping y = F(X)
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y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0];
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y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1];
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// Evaluate function at physical points
454
f.evaluate(values, y, c);
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// Map function values using appropriate mapping
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copyofvalues[0] = values[0];
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copyofvalues[1] = values[1];
460
// Do the inverse of div piola
461
values[0] = detJ*(Jinv_00*copyofvalues[0]+Jinv_01*copyofvalues[1]);
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values[1] = detJ*(Jinv_10*copyofvalues[0]+Jinv_11*copyofvalues[1]);
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// Note that we do not map the weights (yet).
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// Take directional components
467
for(int k = 0; k < 2; k++)
468
result += values[k]*D[i][0][k];
469
// Multiply by weights
475
/// Evaluate linear functionals for all dofs on the function f
476
virtual void evaluate_dofs(double* values,
477
const ufc::function& f,
478
const ufc::cell& c) const
480
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
483
/// Interpolate vertex values from dof values
484
virtual void interpolate_vertex_values(double* vertex_values,
485
const double* dof_values,
486
const ufc::cell& c) const
488
// Extract vertex coordinates
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const double * const * x = c.coordinates;
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// Compute Jacobian of affine map from reference cell
492
const double J_00 = x[1][0] - x[0][0];
493
const double J_01 = x[2][0] - x[0][0];
494
const double J_10 = x[1][1] - x[0][1];
495
const double J_11 = x[2][1] - x[0][1];
497
// Compute determinant of Jacobian
498
double detJ = J_00*J_11 - J_01*J_10;
500
// Compute inverse of Jacobian
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// Evaluate at vertices and use Piola mapping
502
vertex_values[0] = (1.0/detJ)*(dof_values[2]*2*J_00 + dof_values[3]*J_00 + dof_values[4]*(-2*J_01) + dof_values[5]*J_01);
503
vertex_values[1] = (1.0/detJ)*(dof_values[0]*2*J_00 + dof_values[1]*J_00 + dof_values[4]*(J_00 + J_01) + dof_values[5]*(2*J_00 - 2*J_01));
504
vertex_values[2] = (1.0/detJ)*(dof_values[0]*J_01 + dof_values[1]*2*J_01 + dof_values[2]*(J_00 + J_01) + dof_values[3]*(2*J_00 - 2*J_01));
505
vertex_values[3] = (1.0/detJ)*(dof_values[2]*2*J_10 + dof_values[3]*J_10 + dof_values[4]*(-2*J_11) + dof_values[5]*J_11);
506
vertex_values[4] = (1.0/detJ)*(dof_values[0]*2*J_10 + dof_values[1]*J_10 + dof_values[4]*(J_10 + J_11) + dof_values[5]*(2*J_10 - 2*J_11));
507
vertex_values[5] = (1.0/detJ)*(dof_values[0]*J_11 + dof_values[1]*2*J_11 + dof_values[2]*(J_10 + J_11) + dof_values[3]*(2*J_10 - 2*J_11));
510
/// Return the number of sub elements (for a mixed element)
511
virtual unsigned int num_sub_elements() const
516
/// Create a new finite element for sub element i (for a mixed element)
517
virtual ufc::finite_element* create_sub_element(unsigned int i) const
519
return new ffc_26_finite_element_0();
524
/// This class defines the interface for a local-to-global mapping of
525
/// degrees of freedom (dofs).
527
class ffc_26_dof_map_0: public ufc::dof_map
531
unsigned int __global_dimension;
536
ffc_26_dof_map_0() : ufc::dof_map()
538
__global_dimension = 0;
542
virtual ~ffc_26_dof_map_0()
547
/// Return a string identifying the dof map
548
virtual const char* signature() const
550
return "FFC dof map for Brezzi-Douglas-Marini finite element of degree 1 on a triangle";
553
/// Return true iff mesh entities of topological dimension d are needed
554
virtual bool needs_mesh_entities(unsigned int d) const
571
/// Initialize dof map for mesh (return true iff init_cell() is needed)
572
virtual bool init_mesh(const ufc::mesh& m)
574
__global_dimension = 2*m.num_entities[1];
578
/// Initialize dof map for given cell
579
virtual void init_cell(const ufc::mesh& m,
585
/// Finish initialization of dof map for cells
586
virtual void init_cell_finalize()
591
/// Return the dimension of the global finite element function space
592
virtual unsigned int global_dimension() const
594
return __global_dimension;
597
/// Return the dimension of the local finite element function space
598
virtual unsigned int local_dimension() const
603
// Return the geometric dimension of the coordinates this dof map provides
604
virtual unsigned int geometric_dimension() const
606
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
609
/// Return the number of dofs on each cell facet
610
virtual unsigned int num_facet_dofs() const
615
/// Return the number of dofs associated with each cell entity of dimension d
616
virtual unsigned int num_entity_dofs(unsigned int d) const
618
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
621
/// Tabulate the local-to-global mapping of dofs on a cell
622
virtual void tabulate_dofs(unsigned int* dofs,
624
const ufc::cell& c) const
626
dofs[0] = 2*c.entity_indices[1][0];
627
dofs[1] = 2*c.entity_indices[1][0] + 1;
628
dofs[2] = 2*c.entity_indices[1][1];
629
dofs[3] = 2*c.entity_indices[1][1] + 1;
630
dofs[4] = 2*c.entity_indices[1][2];
631
dofs[5] = 2*c.entity_indices[1][2] + 1;
634
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
635
virtual void tabulate_facet_dofs(unsigned int* dofs,
636
unsigned int facet) const
655
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
656
virtual void tabulate_entity_dofs(unsigned int* dofs,
657
unsigned int d, unsigned int i) const
659
throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
662
/// Tabulate the coordinates of all dofs on a cell
663
virtual void tabulate_coordinates(double** coordinates,
664
const ufc::cell& c) const
666
const double * const * x = c.coordinates;
667
coordinates[0][0] = 0.666666666666667*x[1][0] + 0.333333333333333*x[2][0];
668
coordinates[0][1] = 0.666666666666667*x[1][1] + 0.333333333333333*x[2][1];
669
coordinates[1][0] = 0.333333333333333*x[1][0] + 0.666666666666667*x[2][0];
670
coordinates[1][1] = 0.333333333333333*x[1][1] + 0.666666666666667*x[2][1];
671
coordinates[2][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[2][0];
672
coordinates[2][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[2][1];
673
coordinates[3][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[2][0];
674
coordinates[3][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[2][1];
675
coordinates[4][0] = 0.666666666666667*x[0][0] + 0.333333333333333*x[1][0];
676
coordinates[4][1] = 0.666666666666667*x[0][1] + 0.333333333333333*x[1][1];
677
coordinates[5][0] = 0.333333333333333*x[0][0] + 0.666666666666667*x[1][0];
678
coordinates[5][1] = 0.333333333333333*x[0][1] + 0.666666666666667*x[1][1];
681
/// Return the number of sub dof maps (for a mixed element)
682
virtual unsigned int num_sub_dof_maps() const
687
/// Create a new dof_map for sub dof map i (for a mixed element)
688
virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
690
return new ffc_26_dof_map_0();
added
removed
src/kernel/elements/ffc_26.h
