mixedpoisson.h

利用C

          new_coeff1_2 = coeff1_0*dmats0[0][2] + coeff1_1*dmats0[1][2] + coeff1_2*dmats0[2][2];
        }
        if(combinations[deriv_num][j] == 1)
        {
          new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0];
          new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1];
          new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2];
          new_coeff1_0 = coeff1_0*dmats1[0][0] + coeff1_1*dmats1[1][0] + coeff1_2*dmats1[2][0];
          new_coeff1_1 = coeff1_0*dmats1[0][1] + coeff1_1*dmats1[1][1] + coeff1_2*dmats1[2][1];
          new_coeff1_2 = coeff1_0*dmats1[0][2] + coeff1_1*dmats1[1][2] + coeff1_2*dmats1[2][2];
        }
    
      }
      // Compute derivatives on reference element as dot product of coefficients and basisvalues
      // Correct values by the contravariant Piola transform
      const double tmp0_0 = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2;
      const double tmp0_1 = new_coeff1_0*basisvalue0 + new_coeff1_1*basisvalue1 + new_coeff1_2*basisvalue2;
      derivatives[deriv_num] = (1.0/detJ)*(J_00*tmp0_0 + J_01*tmp0_1);
      derivatives[num_derivatives + deriv_num] = (1.0/detJ)*(J_10*tmp0_0 + J_11*tmp0_1);
    }
    
    // Transform derivatives back to physical element
    for (unsigned int row = 0; row < num_derivatives; row++)
    {
      for (unsigned int col = 0; col < num_derivatives; col++)
      {
        values[row] += transform[row][col]*derivatives[col];
        values[num_derivatives + row] += transform[row][col]*derivatives[num_derivatives + col];
      }
    }
    // Delete pointer to array of derivatives on FIAT element
    delete [] derivatives;
    
    // Delete pointer to array of combinations of derivatives and transform
    for (unsigned int row = 0; row < num_derivatives; row++)
    {
      delete [] combinations[row];
      delete [] transform[row];
    }
    
    delete [] combinations;
    delete [] transform;
  }

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

  /// Evaluate linear functional for dof i on the function f
  virtual double evaluate_dof(unsigned int i,
                              const ufc::function& f,
                              const ufc::cell& c) const
  {
    // The reference points, direction and weights:
    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}}};
    const static double W[6][1] = {{1}, {1}, {1}, {1}, {1}, {1}};
    const static double D[6][1][2] = {{{1, 1}}, {{1, 1}}, {{1, 0}}, {{1, 0}}, {{0, -1}}, {{0, -1}}};
    
    // Extract vertex coordinates
    const double * const * x = c.coordinates;
    
    // Compute Jacobian of affine map from reference cell
    const double J_00 = x[1][0] - x[0][0];
    const double J_01 = x[2][0] - x[0][0];
    const double J_10 = x[1][1] - x[0][1];
    const double J_11 = x[2][1] - x[0][1];
      
    // Compute determinant of Jacobian
    double detJ = J_00*J_11 - J_01*J_10;
      
    // Compute inverse of Jacobian
    const double Jinv_00 =  J_11 / detJ;
    const double Jinv_01 = -J_01 / detJ;
    const double Jinv_10 = -J_10 / detJ;
    const double Jinv_11 =  J_00 / detJ;
    
    double copyofvalues[2];
    double result = 0.0;
    // Iterate over the points:
    // Evaluate basis functions for affine mapping
    const double w0 = 1.0 - X[i][0][0] - X[i][0][1];
    const double w1 = X[i][0][0];
    const double w2 = X[i][0][1];
    
    // Compute affine mapping y = F(X)
    double y[2];
    y[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0];
    y[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1];
    
    // Evaluate function at physical points
    double values[2];
    f.evaluate(values, y, c);
    
    // Map function values using appropriate mapping
    // Copy old values:
    copyofvalues[0] = values[0];
    copyofvalues[1] = values[1];
    // Do the inverse of div piola 
    values[0] = detJ*(Jinv_00*copyofvalues[0]+Jinv_01*copyofvalues[1]);
    values[1] = detJ*(Jinv_10*copyofvalues[0]+Jinv_11*copyofvalues[1]);
    
    // Note that we do not map the weights (yet).
    
    // Take directional components
    for(int k = 0; k < 2; k++)
      result += values[k]*D[i][0][k];
    // Multiply by weights 
    result *= W[i][0];
    
    return result;
  }

  /// Evaluate linear functionals for all dofs on the function f
  virtual void evaluate_dofs(double* values,
                             const ufc::function& f,
                             const ufc::cell& c) const
  {
    throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
  }

  /// Interpolate vertex values from dof values
  virtual void interpolate_vertex_values(double* vertex_values,
                                         const double* dof_values,
                                         const ufc::cell& c) const
  {
    // Extract vertex coordinates
    const double * const * x = c.coordinates;
    
    // Compute Jacobian of affine map from reference cell
    const double J_00 = x[1][0] - x[0][0];
    const double J_01 = x[2][0] - x[0][0];
    const double J_10 = x[1][1] - x[0][1];
    const double J_11 = x[2][1] - x[0][1];
      
    // Compute determinant of Jacobian
    double detJ = J_00*J_11 - J_01*J_10;
      
    // Compute inverse of Jacobian
    // Evaluate at vertices and use Piola mapping
    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);
    vertex_values[2] = (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));
    vertex_values[4] = (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));
    vertex_values[1] = (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);
    vertex_values[3] = (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));
    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));
  }

  /// Return the number of sub elements (for a mixed element)
  virtual unsigned int num_sub_elements() const
  {
    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 UFC_MixedPoissonBilinearForm_finite_element_0_0();
  }

};

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

class UFC_MixedPoissonBilinearForm_finite_element_0_1: public ufc::finite_element
{
public:

  /// Constructor
  UFC_MixedPoissonBilinearForm_finite_element_0_1() : ufc::finite_element()
  {
    // Do nothing
  }

  /// Destructor
  virtual ~UFC_MixedPoissonBilinearForm_finite_element_0_1()
  {
    // Do nothing
  }

  /// Return a string identifying the finite element
  virtual const char* signature() const
  {
    return "Discontinuous Lagrange finite element of degree 0 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 1;
  }

  /// 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_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 inverse of Jacobian
    
    // Get coordinates and map to the reference (UFC) element
    double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
                element_coordinates[0][0]*element_coordinates[2][1] +\
                J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
    double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
                element_coordinates[1][0]*element_coordinates[0][1] -\
                J_10*coordinates[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 *x/(1.0 - y) - 1.0;
    y = 2.0*y - 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;
    
    // Compute psitilde_a
    const double psitilde_a_0 = 1;
    
    // Compute psitilde_bs
    const double psitilde_bs_0_0 = 1;
    
    // Compute basisvalues
    const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
    
    // Table(s) of coefficients
    const static double coefficients0[1][1] = \
    {{1.41421356237309}};
    
    // Extract relevant coefficients
    const double coeff0_0 = coefficients0[dof][0];
    
    // Compute value(s)
    *values = coeff0_0*basisvalue0;
  }

  /// 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 derivatives of basis function i at given point in cell
  virtual void evaluate_basis_derivatives(unsigned int i,
                                          unsigned int n,
                                          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 inverse of Jacobian
    
    // Get coordinates and map to the reference (UFC) element
    double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
                element_coordinates[0][0]*element_coordinates[2][1] +\
                J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
    double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
                element_coordinates[1][0]*element_coordinates[0][1] -\
                J_10*coordinates[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 *x/(1.0 - y) - 1.0;
    y = 2.0*y - 1.0;
    
    // Compute number of derivatives
    unsigned int num_derivatives = 1;
    
    for (unsigned int j = 0; j < n; j++)
      num_derivatives *= 2;
    
    
    // Declare pointer to two dimensional array that holds combinations of derivatives and initialise
    unsigned int **combinations = new unsigned int *[num_derivatives];
        
    for (unsigned int j = 0; j < num_derivatives; j++)
    {
      combinations[j] = new unsigned int [n];
      for (unsigned int k = 0; k < n; k++)
        combinations[j][k] = 0;
    }
        
    // Generate combinations of derivatives
    for (unsigned int row = 1; row < num_derivatives; row++)
    {
      for (unsigned int num = 0; num < row; num++)
      {
        for (unsigned int col = n-1; col+1 > 0; col--)
        {
          if (combinations[row][col] + 1 > 1)
            combinations[row][col] = 0;
          else
          {
            combinations[row][col] += 1;
            break;
          }
        }
      }
    }
    
    // Compute inverse of Jacobian
    const double Jinv[2][2] =  {{J_11 / detJ, -J_01 / detJ}, {-J_10 / detJ, J_00 / detJ}};
    
    // Declare transformation matrix