poisson2d.h

利用C

    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}};
    
    // Interesting (new) part
    // Tables of derivatives of the polynomial base (transpose)
    const static double dmats0[4][4] = \
    {{0, 0, 0, 0},
    {6.32455532033676, 0, 0, 0},
    {0, 0, 0, 0},
    {0, 0, 0, 0}};
    
    const static double dmats1[4][4] = \
    {{0, 0, 0, 0},
    {3.16227766016838, 0, 0, 0},
    {5.47722557505166, 0, 0, 0},
    {0, 0, 0, 0}};
    
    const static double dmats2[4][4] = \
    {{0, 0, 0, 0},
    {3.16227766016838, 0, 0, 0},
    {1.82574185835055, 0, 0, 0},
    {5.16397779494322, 0, 0, 0}};
    
    // Compute reference derivatives
    // Declare pointer to array of derivatives on FIAT element
    double *derivatives = new double [num_derivatives];
    
    // Declare coefficients
    double coeff0_0 = 0;
    double coeff0_1 = 0;
    double coeff0_2 = 0;
    double coeff0_3 = 0;
    
    // Declare new coefficients
    double new_coeff0_0 = 0;
    double new_coeff0_1 = 0;
    double new_coeff0_2 = 0;
    double new_coeff0_3 = 0;
    
    // Loop possible derivatives
    for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
    {
      // Get values from coefficients array
      new_coeff0_0 = coefficients0[dof][0];
      new_coeff0_1 = coefficients0[dof][1];
      new_coeff0_2 = coefficients0[dof][2];
      new_coeff0_3 = coefficients0[dof][3];
    
      // Loop derivative order
      for (unsigned int j = 0; j < n; j++)
      {
        // Update old coefficients
        coeff0_0 = new_coeff0_0;
        coeff0_1 = new_coeff0_1;
        coeff0_2 = new_coeff0_2;
        coeff0_3 = new_coeff0_3;
    
        if(combinations[deriv_num][j] == 0)
        {
          new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0] + coeff0_3*dmats0[3][0];
          new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1] + coeff0_3*dmats0[3][1];
          new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2] + coeff0_3*dmats0[3][2];
          new_coeff0_3 = coeff0_0*dmats0[0][3] + coeff0_1*dmats0[1][3] + coeff0_2*dmats0[2][3] + coeff0_3*dmats0[3][3];
        }
        if(combinations[deriv_num][j] == 1)
        {
          new_coeff0_0 = coeff0_0*dmats1[0][0] + coeff0_1*dmats1[1][0] + coeff0_2*dmats1[2][0] + coeff0_3*dmats1[3][0];
          new_coeff0_1 = coeff0_0*dmats1[0][1] + coeff0_1*dmats1[1][1] + coeff0_2*dmats1[2][1] + coeff0_3*dmats1[3][1];
          new_coeff0_2 = coeff0_0*dmats1[0][2] + coeff0_1*dmats1[1][2] + coeff0_2*dmats1[2][2] + coeff0_3*dmats1[3][2];
          new_coeff0_3 = coeff0_0*dmats1[0][3] + coeff0_1*dmats1[1][3] + coeff0_2*dmats1[2][3] + coeff0_3*dmats1[3][3];
        }
        if(combinations[deriv_num][j] == 2)
        {
          new_coeff0_0 = coeff0_0*dmats2[0][0] + coeff0_1*dmats2[1][0] + coeff0_2*dmats2[2][0] + coeff0_3*dmats2[3][0];
          new_coeff0_1 = coeff0_0*dmats2[0][1] + coeff0_1*dmats2[1][1] + coeff0_2*dmats2[2][1] + coeff0_3*dmats2[3][1];
          new_coeff0_2 = coeff0_0*dmats2[0][2] + coeff0_1*dmats2[1][2] + coeff0_2*dmats2[2][2] + coeff0_3*dmats2[3][2];
          new_coeff0_3 = coeff0_0*dmats2[0][3] + coeff0_1*dmats2[1][3] + coeff0_2*dmats2[2][3] + coeff0_3*dmats2[3][3];
        }
    
      }
      // Compute derivatives on reference element as dot product of coefficients and basisvalues
      derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2 + new_coeff0_3*basisvalue3;
    }
    
    // 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];
      }
    }
    // 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 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
  {
    double values[1];
    double coordinates[3];
    
    // Nodal coordinates on reference cell
    static double X[4][3] = {{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}};
    
    // Components for each dof
    static unsigned int components[4] = {0, 0, 0, 0};
    
    // Extract vertex coordinates
    const double * const * x = c.coordinates;
    
    // Evaluate basis functions for affine mapping
    const double w0 = 1.0 - X[i][0] - X[i][1] - X[i][2];
    const double w1 = X[i][0];
    const double w2 = X[i][1];
    const double w3 = X[i][2];
    
    // Compute affine mapping x = F(X)
    coordinates[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0] + w3*x[3][0];
    coordinates[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1] + w3*x[3][1];
    coordinates[2] = w0*x[0][2] + w1*x[1][2] + w2*x[2][2] + w3*x[3][2];
    
    // Evaluate function at coordinates
    f.evaluate(values, coordinates, c);
    
    // Pick component for evaluation
    return values[components[i]];
  }

  /// 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
  {
    // Evaluate at vertices and use affine mapping
    vertex_values[0] = dof_values[0];
    vertex_values[1] = dof_values[1];
    vertex_values[2] = dof_values[2];
    vertex_values[3] = dof_values[3];
  }

  /// 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_Poisson2DBilinearForm_finite_element_1();
  }

};

/// This class defines the interface for a local-to-global mapping of
/// degrees of freedom (dofs).

class UFC_Poisson2DBilinearForm_dof_map_0: public ufc::dof_map
{
private:

  unsigned int __global_dimension;

public:

  /// Constructor
  UFC_Poisson2DBilinearForm_dof_map_0() : ufc::dof_map()
  {
    __global_dimension = 0;
  }

  /// Destructor
  virtual ~UFC_Poisson2DBilinearForm_dof_map_0()
  {
    // Do nothing
  }

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

  /// Return true iff mesh entities of topological dimension d are needed
  virtual bool needs_mesh_entities(unsigned int d) const
  {
    switch ( d )
    {
    case 0:
      return true;
      break;
    case 1:
      return false;
      break;
    case 2:
      return false;
      break;
    case 3:
      return false;
      break;
    }
    return false;
  }

  /// Initialize dof map for mesh (return true iff init_cell() is needed)
  virtual bool init_mesh(const ufc::mesh& m)
  {
    __global_dimension = m.num_entities[0];
    return false;
  }

  /// Initialize dof map for given cell
  virtual void init_cell(const ufc::mesh& m,
                         const ufc::cell& c)
  {
    // Do nothing
  }

  /// Finish initialization of dof map for cells
  virtual void init_cell_finalize()
  {
    // Do nothing
  }

  /// Return the dimension of the global finite element function space
  virtual unsigned int global_dimension() const
  {
    return __global_dimension;
  }

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

  // Return the geometric dimension of the coordinates this dof map provides
  virtual unsigned int geometric_dimension() const
  {
    throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
  }

  /// Return the number of dofs on each cell facet
  virtual unsigned int num_facet_dofs() const
  {
    return 3;
  }

  /// Return the number of dofs associated with each cell entity of dimension d
  virtual unsigned int num_entity_dofs(unsigned int d) const
  {
    throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
  }

  /// Tabulate the local-to-global mapping of dofs on a cell
  virtual void tabulate_dofs(unsigned int* dofs,
                             const ufc::mesh& m,
                             const ufc::cell& c) const
  {
    dofs[0] = c.entity_indices[0][0];
    dofs[1] = c.entity_indices[0][1];
    dofs[2] = c.entity_indices[0][2];
    dofs[3] = c.entity_indices[0][3];
  }

  /// Tabulate the local-to-local mapping from facet dofs to cell dofs
  virtual void tabulate_facet_dofs(unsigned int* dofs,
                                   unsigned int facet) const
  {
    switch ( facet )
    {
    case 0:
      dofs[0] = 1;
      dofs[1] = 2;
      dofs[2] = 3;
      break;
    case 1:
      dofs[0] = 0;
      dofs[1] = 2;
      dofs[2] = 3;
      break;
    case 2:
      dofs[0] = 0;
      dofs[1] = 1;
      dofs[2] = 3;
      break;
    case 3:
      dofs[0] = 0;
      dofs[1] = 1;
      dofs[2] = 2;
      break;
    }
  }

  /// Tabulate the local-to-local mapping from dofs associated with mesh entity i of dimension d to cell dofs
  virtual void tabulate_entity_dofs(unsigned int* dofs,
                                    unsigned int d, unsigned int i) const
  {
    throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
  }

  /// Tabulate the coordinates of all dofs on a cell
  virtual void tabulate_coordinates(double** coordinates,
                                    const ufc::cell& c) const
  {
    const double * const * x = c.coordinates;
    coordinates[0][0] = x[0][0];
    coordinates[0][1] = x[0][1];
    coordinates[0][2] = x[0][2];
    coordinates[1][0] = x[1][0];
    coordinates[1][1] = x[1][1];
    coordinates[1][2] = x[1][2];
    coordinates[2][0] = x[2][0];
    coordinates[2][1] = x[2][1];
    coordinates[2][2] = x[2][2];
    coordinates[3][0] = x[3][0];
    coordinates[3][1] = x[3][1];
    coordinates[3][2] = x[3][2];
  }

  /// Return the number of sub dof maps (for a mixed element)
  virtual unsigned int num_sub_dof_maps() const
  {
    return 1;
  }

  /// Create a new dof_map for sub dof map i (for a mixed element)
  virtual ufc::dof_map* create_sub_dof_map(unsigned int i) const
  {
    return new UFC_Poisson2DBilinearForm_dof_map_0();
  }

};

/// This class defines the interface for a local-to-global mapping of
/// degrees of freedom (dofs).

class UFC_Poisson2DBilinearForm_dof_map_1: public ufc::dof_map
{
private:

  unsigned int __global_dimension;

public:

  /// Constructor
  UFC_Poisson2DBilinearForm_dof_map_1() : ufc::dof_map()
  {
    __global_dimension = 0;
  }

  /// Destructor
  virtual ~UFC_Poisson2DBilinearForm_dof_map_1()
  {
    // Do nothing
  }

  /// Return a string identifying the dof map
  virtual const char* signature() const
  {