poisson3d_1.h

利用C

    const double J_01 = x[2][0] - x[0][0];
    const double J_02 = x[3][0] - x[0][0];
    const double J_10 = x[1][1] - x[0][1];
    const double J_11 = x[2][1] - x[0][1];
    const double J_12 = x[3][1] - x[0][1];
    const double J_20 = x[1][2] - x[0][2];
    const double J_21 = x[2][2] - x[0][2];
    const double J_22 = x[3][2] - x[0][2];
      
    // Compute sub determinants
    const double d_00 = J_11*J_22 - J_12*J_21;
    const double d_01 = J_12*J_20 - J_10*J_22;
    const double d_02 = J_10*J_21 - J_11*J_20;
    
    const double d_10 = J_02*J_21 - J_01*J_22;
    const double d_11 = J_00*J_22 - J_02*J_20;
    const double d_12 = J_01*J_20 - J_00*J_21;
    
    const double d_20 = J_01*J_12 - J_02*J_11;
    const double d_21 = J_02*J_10 - J_00*J_12;
    const double d_22 = J_00*J_11 - J_01*J_10;
      
    // Compute determinant of Jacobian
    double detJ = J_00*d_00 + J_10*d_10 + J_20*d_20;
      
    // Compute inverse of Jacobian
    const double Jinv_00 = d_00 / detJ;
    const double Jinv_01 = d_10 / detJ;
    const double Jinv_02 = d_20 / detJ;
    const double Jinv_10 = d_01 / detJ;
    const double Jinv_11 = d_11 / detJ;
    const double Jinv_12 = d_21 / detJ;
    const double Jinv_20 = d_02 / detJ;
    const double Jinv_21 = d_12 / detJ;
    const double Jinv_22 = d_22 / detJ;
    
    // Set scale factor
    const double det = std::abs(detJ);
    
    // Compute geometry tensors
    const double G0_0_0 = det*(Jinv_00*Jinv_00 + Jinv_01*Jinv_01 + Jinv_02*Jinv_02);
    const double G0_0_1 = det*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11 + Jinv_02*Jinv_12);
    const double G0_0_2 = det*(Jinv_00*Jinv_20 + Jinv_01*Jinv_21 + Jinv_02*Jinv_22);
    const double G0_1_0 = det*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01 + Jinv_12*Jinv_02);
    const double G0_1_1 = det*(Jinv_10*Jinv_10 + Jinv_11*Jinv_11 + Jinv_12*Jinv_12);
    const double G0_1_2 = det*(Jinv_10*Jinv_20 + Jinv_11*Jinv_21 + Jinv_12*Jinv_22);
    const double G0_2_0 = det*(Jinv_20*Jinv_00 + Jinv_21*Jinv_01 + Jinv_22*Jinv_02);
    const double G0_2_1 = det*(Jinv_20*Jinv_10 + Jinv_21*Jinv_11 + Jinv_22*Jinv_12);
    const double G0_2_2 = det*(Jinv_20*Jinv_20 + Jinv_21*Jinv_21 + Jinv_22*Jinv_22);
    
    // Compute element tensor
    A[0] = 0.166666666666666*G0_0_0 + 0.166666666666666*G0_0_1 + 0.166666666666666*G0_0_2 + 0.166666666666666*G0_1_0 + 0.166666666666666*G0_1_1 + 0.166666666666666*G0_1_2 + 0.166666666666666*G0_2_0 + 0.166666666666666*G0_2_1 + 0.166666666666666*G0_2_2;
    A[1] = -0.166666666666666*G0_0_0 - 0.166666666666666*G0_1_0 - 0.166666666666666*G0_2_0;
    A[2] = -0.166666666666666*G0_0_1 - 0.166666666666666*G0_1_1 - 0.166666666666666*G0_2_1;
    A[3] = -0.166666666666666*G0_0_2 - 0.166666666666666*G0_1_2 - 0.166666666666666*G0_2_2;
    A[4] = -0.166666666666666*G0_0_0 - 0.166666666666666*G0_0_1 - 0.166666666666666*G0_0_2;
    A[5] = 0.166666666666666*G0_0_0;
    A[6] = 0.166666666666666*G0_0_1;
    A[7] = 0.166666666666666*G0_0_2;
    A[8] = -0.166666666666666*G0_1_0 - 0.166666666666666*G0_1_1 - 0.166666666666666*G0_1_2;
    A[9] = 0.166666666666666*G0_1_0;
    A[10] = 0.166666666666666*G0_1_1;
    A[11] = 0.166666666666666*G0_1_2;
    A[12] = -0.166666666666666*G0_2_0 - 0.166666666666666*G0_2_1 - 0.166666666666666*G0_2_2;
    A[13] = 0.166666666666666*G0_2_0;
    A[14] = 0.166666666666666*G0_2_1;
    A[15] = 0.166666666666666*G0_2_2;
  }

};

/// This class defines the interface for the assembly of the global
/// tensor corresponding to a form with r + n arguments, that is, a
/// mapping
///
///     a : V1 x V2 x ... Vr x W1 x W2 x ... x Wn -> R
///
/// with arguments v1, v2, ..., vr, w1, w2, ..., wn. The rank r
/// global tensor A is defined by
///
///     A = a(V1, V2, ..., Vr, w1, w2, ..., wn),
///
/// where each argument Vj represents the application to the
/// sequence of basis functions of Vj and w1, w2, ..., wn are given
/// fixed functions (coefficients).

class UFC_Poisson3D_1BilinearForm: public ufc::form
{
public:

  /// Constructor
  UFC_Poisson3D_1BilinearForm() : ufc::form()
  {
    // Do nothing
  }

  /// Destructor
  virtual ~UFC_Poisson3D_1BilinearForm()
  {
    // Do nothing
  }

  /// Return a string identifying the form
  virtual const char* signature() const
  {
    return "(dXa0[0, 1, 2]/dxb0[0, 1, 2])(dXa1[0, 1, 2]/dxb0[0, 1, 2]) | ((d/dXa0[0, 1, 2])vi0[0, 1, 2, 3])*((d/dXa1[0, 1, 2])vi1[0, 1, 2, 3])*dX(0)";
  }

  /// Return the rank of the global tensor (r)
  virtual unsigned int rank() const
  {
    return 2;
  }

  /// Return the number of coefficients (n)
  virtual unsigned int num_coefficients() const
  {
    return 0;
  }

  /// Return the number of cell integrals
  virtual unsigned int num_cell_integrals() const
  {
    return 1;
  }
  
  /// Return the number of exterior facet integrals
  virtual unsigned int num_exterior_facet_integrals() const
  {
    return 0;
  }
  
  /// Return the number of interior facet integrals
  virtual unsigned int num_interior_facet_integrals() const
  {
    return 0;
  }
    
  /// Create a new finite element for argument function i
  virtual ufc::finite_element* create_finite_element(unsigned int i) const
  {
    switch ( i )
    {
    case 0:
      return new UFC_Poisson3D_1BilinearForm_finite_element_0();
      break;
    case 1:
      return new UFC_Poisson3D_1BilinearForm_finite_element_1();
      break;
    }
    return 0;
  }
  
  /// Create a new dof map for argument function i
  virtual ufc::dof_map* create_dof_map(unsigned int i) const
  {
    switch ( i )
    {
    case 0:
      return new UFC_Poisson3D_1BilinearForm_dof_map_0();
      break;
    case 1:
      return new UFC_Poisson3D_1BilinearForm_dof_map_1();
      break;
    }
    return 0;
  }

  /// Create a new cell integral on sub domain i
  virtual ufc::cell_integral* create_cell_integral(unsigned int i) const
  {
    return new UFC_Poisson3D_1BilinearForm_cell_integral_0();
  }

  /// Create a new exterior facet integral on sub domain i
  virtual ufc::exterior_facet_integral* create_exterior_facet_integral(unsigned int i) const
  {
    return 0;
  }

  /// Create a new interior facet integral on sub domain i
  virtual ufc::interior_facet_integral* create_interior_facet_integral(unsigned int i) const
  {
    return 0;
  }

};

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

class UFC_Poisson3D_1LinearForm_finite_element_0: public ufc::finite_element
{
public:

  /// Constructor
  UFC_Poisson3D_1LinearForm_finite_element_0() : ufc::finite_element()
  {
    // Do nothing
  }

  /// Destructor
  virtual ~UFC_Poisson3D_1LinearForm_finite_element_0()
  {
    // Do nothing
  }

  /// Return a string identifying the finite element
  virtual const char* signature() const
  {
    return "Lagrange finite element of degree 1 on a tetrahedron";
  }

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

  /// Return the dimension of the finite element function space
  virtual unsigned int space_dimension() const
  {
    return 4;
  }

  /// Return the rank of the value space
  virtual unsigned int value_rank() const
  {
    return 0;
  }

  /// Return the dimension of the value space for axis i
  virtual unsigned int value_dimension(unsigned int i) const
  {
    return 1;
  }

  /// 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_02 = element_coordinates[3][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];
    const double J_12 = element_coordinates[3][1] - element_coordinates[0][1];
    const double J_20 = element_coordinates[1][2] - element_coordinates[0][2];
    const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];
    const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];
      
    // Compute sub determinants
    const double d00 = J_11*J_22 - J_12*J_21;
    const double d01 = J_12*J_20 - J_10*J_22;
    const double d02 = J_10*J_21 - J_11*J_20;
    
    const double d10 = J_02*J_21 - J_01*J_22;
    const double d11 = J_00*J_22 - J_02*J_20;
    const double d12 = J_01*J_20 - J_00*J_21;
    
    const double d20 = J_01*J_12 - J_02*J_11;
    const double d21 = J_02*J_10 - J_00*J_12;
    const double d22 = J_00*J_11 - J_01*J_10;
      
    // Compute determinant of Jacobian
    double detJ = J_00*d00 + J_10*d10 + J_20*d20;
    
    // Compute inverse of Jacobian
    
    // Compute constants
    const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \
                    + d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \
                    + d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);
    
    const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \
                    + d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \
                    + d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);
    
    const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \
                    + d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \
                    + d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);
    
    // Get coordinates and map to the UFC reference element
    double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;
    double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;
    double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;
    
    // Map coordinates to the reference cube
    if (std::abs(y + z - 1.0) < 1e-14)
      x = 1.0;
    else
      x = -2.0 * x/(y + z - 1.0) - 1.0;
    if (std::abs(z - 1.0) < 1e-14)
      y = -1.0;
    else
      y = 2.0 * y/(1.0 - z) - 1.0;
    z = 2.0 * z - 1.0;
    
    // Reset values
    *values = 0;
    
    // 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_z_0 = 1;
    const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);
    
    // Compute psitilde_a
    const double psitilde_a_0 = 1;
    const double psitilde_a_1 = x;
    
    // 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_1_0 = 1;
    
    // Compute psitilde_cs
    const double psitilde_cs_00_0 = 1;
    const double psitilde_cs_00_1 = 2*z + 1;
    const double psitilde_cs_01_0 = 1;
    const double psitilde_cs_10_0 = 1;
    
    // Compute basisvalues
    const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
    const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;
    const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;
    const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;
    
    // Table(s) of coefficients
    const static double coefficients0[4][4] = \
    {{0.288675134594813, -0.182574185835055, -0.105409255338946, -0.074535599249993},
    {0.288675134594813, 0.182574185835055, -0.105409255338946, -0.074535599249993},
    {0.288675134594813, 0, 0.210818510677892, -0.074535599249993},
    {0.288675134594813, 0, 0, 0.223606797749979}};
    
    // 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];
    
    // Compute value(s)
    *values = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2 + coeff0_3*basisvalue3;
  }

  /// Evaluate all basis functions at given point in cell
  virtual void evaluate_basis_all(double* values,
                                  const double* coordinates,
                                  const ufc::cell& c) const
  {
    throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");
  }

  /// Evaluate order n de