ffc_15.h

Dolfin provide a high-performance linear algebra library

  {
    return 1;
  }

  /// Create a new finite element for sub element i (for a mixed element)
  virtual ufc::finite_element* create_sub_element(unsigned int i) const
  {
    return new ffc_15_finite_element_0_1();
  }

};

/// This class defines the interface for a finite element.

class ffc_15_finite_element_0: public ufc::finite_element
{
public:

  /// Constructor
  ffc_15_finite_element_0() : ufc::finite_element()
  {
    // Do nothing
  }

  /// Destructor
  virtual ~ffc_15_finite_element_0()
  {
    // Do nothing
  }

  /// Return a string identifying the finite element
  virtual const char* signature() const
  {
    return "Mixed finite element: [Lagrange finite element of degree 3 on a triangle, Lagrange finite element of degree 3 on a triangle]";
  }

  /// Return the cell shape
  virtual ufc::shape cell_shape() const
  {
    return ufc::triangle;
  }

  /// Return the dimension of the finite element function space
  virtual unsigned int space_dimension() const
  {
    return 20;
  }

  /// Return the rank of the value space
  virtual unsigned int value_rank() const
  {
    return 1;
  }

  /// Return the dimension of the value space for axis i
  virtual unsigned int value_dimension(unsigned int i) const
  {
    return 2;
  }

  /// Evaluate basis function i at given point in cell
  virtual void evaluate_basis(unsigned int i,
                              double* values,
                              const double* coordinates,
                              const ufc::cell& c) const
  {
    // Extract vertex coordinates
    const double * const * element_coordinates = c.coordinates;
    
    // Compute Jacobian of affine map from reference cell
    const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
    const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
    const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
    const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
      
    // Compute determinant of Jacobian
    const double detJ = J_00*J_11 - J_01*J_10;
    
    // Compute constants
    const double C0 = element_coordinates[1][0] + element_coordinates[2][0];
    const double C1 = element_coordinates[1][1] + element_coordinates[2][1];
    
    // Get coordinates and map to the reference (FIAT) element
    double x = (J_01*C1 - J_11*C0 + 2.0*J_11*coordinates[0] - 2.0*J_01*coordinates[1]) / detJ;
    double y = (J_10*C0 - J_00*C1 - 2.0*J_10*coordinates[0] + 2.0*J_00*coordinates[1]) / detJ;
    
    // Map coordinates to the reference square
    if (std::abs(y - 1.0) < 1e-14)
      x = -1.0;
    else
      x = 2.0 * (1.0 + x)/(1.0 - y) - 1.0;
    
    // Reset values
    values[0] = 0;
    values[1] = 0;
    
    if (0 <= i and i <= 9)
    {
      // Map degree of freedom to element degree of freedom
      const unsigned int dof = i;
    
      // Generate scalings
      const double scalings_y_0 = 1;
      const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
      const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);
      const double scalings_y_3 = scalings_y_2*(0.5 - 0.5*y);
    
      // Compute psitilde_a
      const double psitilde_a_0 = 1;
      const double psitilde_a_1 = x;
      const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;
      const double psitilde_a_3 = 1.66666666666667*x*psitilde_a_2 - 0.666666666666667*psitilde_a_1;
    
      // Compute psitilde_bs
      const double psitilde_bs_0_0 = 1;
      const double psitilde_bs_0_1 = 1.5*y + 0.5;
      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;
      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;
      const double psitilde_bs_1_0 = 1;
      const double psitilde_bs_1_1 = 2.5*y + 1.5;
      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;
      const double psitilde_bs_2_0 = 1;
      const double psitilde_bs_2_1 = 3.5*y + 2.5;
      const double psitilde_bs_3_0 = 1;
    
      // Compute basisvalues
      const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
      const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
      const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
      const double basisvalue3 = 2.73861278752583*psitilde_a_2*scalings_y_2*psitilde_bs_2_0;
      const double basisvalue4 = 2.12132034355964*psitilde_a_1*scalings_y_1*psitilde_bs_1_1;
      const double basisvalue5 = 1.22474487139159*psitilde_a_0*scalings_y_0*psitilde_bs_0_2;
      const double basisvalue6 = 3.74165738677394*psitilde_a_3*scalings_y_3*psitilde_bs_3_0;
      const double basisvalue7 = 3.16227766016838*psitilde_a_2*scalings_y_2*psitilde_bs_2_1;
      const double basisvalue8 = 2.44948974278318*psitilde_a_1*scalings_y_1*psitilde_bs_1_2;
      const double basisvalue9 = 1.4142135623731*psitilde_a_0*scalings_y_0*psitilde_bs_0_3;
    
      // Table(s) of coefficients
      const static double coefficients0[10][10] =   \
      {{0.0471404520791032, -0.0288675134594813, -0.0166666666666666, 0.0782460796435951, 0.0606091526731326, 0.0349927106111883, -0.0601337794302955, -0.0508223195384204, -0.0393667994375868, -0.0227284322524248},
      {0.0471404520791031, 0.0288675134594813, -0.0166666666666667, 0.0782460796435952, -0.0606091526731326, 0.0349927106111883, 0.0601337794302955, -0.0508223195384204, 0.0393667994375868, -0.0227284322524247},
      {0.0471404520791032, 0, 0.0333333333333334, 0, 0, 0.104978131833565, 0, 0, 0, 0.0909137290096989},
      {0.106066017177982, 0.259807621135332, -0.15, 0.117369119465393, 0.0606091526731326, -0.0787335988751736, 0, 0.101644639076841, -0.131222664791956, 0.090913729009699},
      {0.106066017177982, 0, 0.3, 0, 0.151522881682832, 0.0262445329583912, 0, 0, 0.131222664791956, -0.136370593514548},
      {0.106066017177982, -0.259807621135332, -0.15, 0.117369119465393, -0.0606091526731326, -0.0787335988751736, 0, 0.101644639076841, 0.131222664791956, 0.090913729009699},
      {0.106066017177982, 0, 0.3, 0, -0.151522881682832, 0.0262445329583912, 0, 0, -0.131222664791956, -0.136370593514548},
      {0.106066017177982, -0.259807621135332, -0.15, -0.0782460796435952, 0.090913729009699, 0.0962299541807677, 0.180401338290886, 0.0508223195384204, -0.0131222664791956, -0.0227284322524247},
      {0.106066017177982, 0.259807621135332, -0.15, -0.0782460796435952, -0.090913729009699, 0.0962299541807677, -0.180401338290886, 0.0508223195384204, 0.0131222664791956, -0.0227284322524247},
      {0.636396103067893, 0, 0, -0.234738238930785, 0, -0.262445329583912, 0, -0.203289278153682, 0, 0.090913729009699}};
    
      // Extract relevant coefficients
      const double coeff0_0 =   coefficients0[dof][0];
      const double coeff0_1 =   coefficients0[dof][1];
      const double coeff0_2 =   coefficients0[dof][2];
      const double coeff0_3 =   coefficients0[dof][3];
      const double coeff0_4 =   coefficients0[dof][4];
      const double coeff0_5 =   coefficients0[dof][5];
      const double coeff0_6 =   coefficients0[dof][6];
      const double coeff0_7 =   coefficients0[dof][7];
      const double coeff0_8 =   coefficients0[dof][8];
      const double coeff0_9 =   coefficients0[dof][9];
    
      // Compute value(s)
      values[0] = 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;
    }
    
    if (10 <= i and i <= 19)
    {
      // Map degree of freedom to element degree of freedom
      const unsigned int dof = i - 10;
    
      // Generate scalings
      const double scalings_y_0 = 1;
      const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
      const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);
      const double scalings_y_3 = scalings_y_2*(0.5 - 0.5*y);
    
      // Compute psitilde_a
      const double psitilde_a_0 = 1;
      const double psitilde_a_1 = x;
      const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;
      const double psitilde_a_3 = 1.66666666666667*x*psitilde_a_2 - 0.666666666666667*psitilde_a_1;
    
      // Compute psitilde_bs
      const double psitilde_bs_0_0 = 1;
      const double psitilde_bs_0_1 = 1.5*y + 0.5;
      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;
      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;
      const double psitilde_bs_1_0 = 1;
      const double psitilde_bs_1_1 = 2.5*y + 1.5;
      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;
      const double psitilde_bs_2_0 = 1;
      const double psitilde_bs_2_1 = 3.5*y + 2.5;
      const double psitilde_bs_3_0 = 1;
    
      // Compute basisvalues
      const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
      const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
      const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
      const double basisvalue3 = 2.73861278752583*psitilde_a_2*scalings_y_2*psitilde_bs_2_0;
      const double basisvalue4 = 2.12132034355964*psitilde_a_1*scalings_y_1*psitilde_bs_1_1;
      const double basisvalue5 = 1.22474487139159*psitilde_a_0*scalings_y_0*psitilde_bs_0_2;
      const double basisvalue6 = 3.74165738677394*psitilde_a_3*scalings_y_3*psitilde_bs_3_0;
      const double basisvalue7 = 3.16227766016838*psitilde_a_2*scalings_y_2*psitilde_bs_2_1;
      const double basisvalue8 = 2.44948974278318*psitilde_a_1*scalings_y_1*psitilde_bs_1_2;
      const double basisvalue9 = 1.4142135623731*psitilde_a_0*scalings_y_0*psitilde_bs_0_3;
    
      // Table(s) of coefficients
      const static double coefficients0[10][10] =   \
      {{0.0471404520791032, -0.0288675134594813, -0.0166666666666666, 0.0782460796435951, 0.0606091526731326, 0.0349927106111883, -0.0601337794302955, -0.0508223195384204, -0.0393667994375868, -0.0227284322524248},
      {0.0471404520791031, 0.0288675134594813, -0.0166666666666667, 0.0782460796435952, -0.0606091526731326, 0.0349927106111883, 0.0601337794302955, -0.0508223195384204, 0.0393667994375868, -0.0227284322524247},
      {0.0471404520791032, 0, 0.0333333333333334, 0, 0, 0.104978131833565, 0, 0, 0, 0.0909137290096989},
      {0.106066017177982, 0.259807621135332, -0.15, 0.117369119465393, 0.0606091526731326, -0.0787335988751736, 0, 0.101644639076841, -0.131222664791956, 0.090913729009699},
      {0.106066017177982, 0, 0.3, 0, 0.151522881682832, 0.0262445329583912, 0, 0, 0.131222664791956, -0.136370593514548},
      {0.106066017177982, -0.259807621135332, -0.15, 0.117369119465393, -0.0606091526731326, -0.0787335988751736, 0, 0.101644639076841, 0.131222664791956, 0.090913729009699},
      {0.106066017177982, 0, 0.3, 0, -0.151522881682832, 0.0262445329583912, 0, 0, -0.131222664791956, -0.136370593514548},
      {0.106066017177982, -0.259807621135332, -0.15, -0.0782460796435952, 0.090913729009699, 0.0962299541807677, 0.180401338290886, 0.0508223195384204, -0.0131222664791956, -0.0227284322524247},
      {0.106066017177982, 0.259807621135332, -0.15, -0.0782460796435952, -0.090913729009699, 0.0962299541807677, -0.180401338290886, 0.0508223195384204, 0.0131222664791956, -0.0227284322524247},
      {0.636396103067893, 0, 0, -0.234738238930785, 0, -0.262445329583912, 0, -0.203289278153682, 0, 0.090913729009699}};
    
      // Extract relevant coefficients
      const double coeff0_0 =   coefficients0[dof][0];
      const double coeff0_1 =   coefficients0[dof][1];
      const double coeff0_2 =   coefficients0[dof][2];
      const double coeff0_3 =   coefficients0[dof][3];
      const double coeff0_4 =   coefficients0[dof][4];
      const double coeff0_5 =   coefficients0[dof][5];
      const double coeff0_6 =   coefficients0[dof][6];
      const double coeff0_7 =   coefficients0[dof][7];
      const double coeff0_8 =   coefficients0[dof][8];
      const double coeff0_9 =   coefficients0[dof][9];
    
      // Compute value(s)
      values[1] = 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;
    }
    
  }

  /// Evaluate order n derivatives of basis function i at given point in cell
  virtual void evaluate_basis_derivatives(unsigned int i,
                                          unsigned int n,
                                          double* values,