ffc_26.h

Dolfin provide a high-performance linear algebra library

    double coeff0_1 = 0;
    double coeff0_2 = 0;
    double coeff1_0 = 0;
    double coeff1_1 = 0;
    double coeff1_2 = 0;
    
    // Declare new coefficients
    double new_coeff0_0 = 0;
    double new_coeff0_1 = 0;
    double new_coeff0_2 = 0;
    double new_coeff1_0 = 0;
    double new_coeff1_1 = 0;
    double new_coeff1_2 = 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_coeff1_0 = coefficients1[dof][0];
      new_coeff1_1 = coefficients1[dof][1];
      new_coeff1_2 = coefficients1[dof][2];
    
      // 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;
        coeff1_0 = new_coeff1_0;
        coeff1_1 = new_coeff1_1;
        coeff1_2 = new_coeff1_2;
    
        if(combinations[deriv_num][j] == 0)
        {
          new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0] + coeff0_2*dmats0[2][0];
          new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1] + coeff0_2*dmats0[2][1];
          new_coeff0_2 = coeff0_0*dmats0[0][2] + coeff0_1*dmats0[1][2] + coeff0_2*dmats0[2][2];
          new_coeff1_0 = coeff1_0*dmats0[0][0] + coeff1_1*dmats0[1][0] + coeff1_2*dmats0[2][0];
          new_coeff1_1 = coeff1_0*dmats0[0][1] + coeff1_1*dmats0[1][1] + coeff1_2*dmats0[2][1];
          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
      derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1 + new_coeff0_2*basisvalue2;
      derivatives[num_derivatives + deriv_num] = new_coeff1_0*basisvalue0 + new_coeff1_1*basisvalue1 + new_coeff1_2*basisvalue2;
    }
    
    // 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
    delete [] combinations;
    
  }

  /// 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
  {
    throw std::runtime_error("evaluate_dof not implemented for this type of element");
  }

  /// 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
    
    // Take absolute value of determinant
    detJ = std::abs(detJ);
    
    // Compute signs of edges (need to flip edge degrees of freedom)
    
    // Compute the edges
    const double e0_0 = x[2][0] - x[1][0];
    const double e0_1 = x[2][1] - x[1][1];
    const double e1_0 = x[2][0] - x[0][0];
    const double e1_1 = x[2][1] - x[0][1];
    const double e2_0 = x[1][0] - x[0][0];
    const double e2_1 = x[1][1] - x[0][1];
    
    // Compute edges normals by rotating edges 90 degrees clockwise
    const double n0_0 = e0_1;
    const double n0_1 = -e0_0;
    const double n1_0 = e1_1;
    const double n1_1 = -e1_0;
    const double n2_0 = e2_1;
    const double n2_1 = -e2_0;
    
    // Compute the orientation of the normals relative to the cell
    int sign_facet0 = n0_0*e2_0 + n0_1*e2_1 > 0 ? 1 : -1;
    int sign_facet1 = n1_0*e0_0 + n1_1*e0_1 > 0 ? 1 : -1;
    int sign_facet2 = n2_0*e1_0 + n2_1*e1_1 < 0 ? 1 : -1;
    
    // Evaluate at vertices and use Piola mapping
    vertex_values[0] = (1.0/detJ)*(sign_facet1*dof_values[2]*2*J_00 + sign_facet1*dof_values[3]*J_00 + sign_facet2*dof_values[4]*(-2*J_01) + sign_facet2*dof_values[5]*J_01);
    vertex_values[1] = (1.0/detJ)*(sign_facet0*dof_values[0]*2*J_00 + sign_facet0*dof_values[1]*J_00 + sign_facet2*dof_values[4]*(J_00 + J_01) + sign_facet2*dof_values[5]*(2*J_00 - 2*J_01));
    vertex_values[2] = (1.0/detJ)*(sign_facet0*dof_values[0]*J_01 + sign_facet0*dof_values[1]*2*J_01 + sign_facet1*dof_values[2]*(J_00 + J_01) + sign_facet1*dof_values[3]*(2*J_00 - 2*J_01));
    vertex_values[3] = (1.0/detJ)*(sign_facet1*dof_values[2]*2*J_10 + sign_facet1*dof_values[3]*J_10 + sign_facet2*dof_values[4]*(-2*J_11) + sign_facet2*dof_values[5]*J_11);
    vertex_values[4] = (1.0/detJ)*(sign_facet0*dof_values[0]*2*J_10 + sign_facet0*dof_values[1]*J_10 + sign_facet2*dof_values[4]*(J_10 + J_11) + sign_facet2*dof_values[5]*(2*J_10 - 2*J_11));
    vertex_values[5] = (1.0/detJ)*(sign_facet0*dof_values[0]*J_11 + sign_facet0*dof_values[1]*2*J_11 + sign_facet1*dof_values[2]*(J_10 + J_11) + sign_facet1*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 ffc_26_finite_element_0();
  }

};

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

class ffc_26_dof_map_0: public ufc::dof_map
{
private:

  unsigned int __global_dimension;

public:

  /// Constructor
  ffc_26_dof_map_0() : ufc::dof_map()
  {
    __global_dimension = 0;
  }

  /// Destructor
  virtual ~ffc_26_dof_map_0()
  {
    // Do nothing
  }

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

  /// 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 false;
      break;
    case 1:
      return true;
      break;
    case 2:
      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 = 2*m.num_entities[1];
    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 6;
  }

  /// Return the number of dofs on each cell facet
  virtual unsigned int num_facet_dofs() const
  {
    return 2;
  }

  /// 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] = 2*c.entity_indices[1][0];
    dofs[1] = 2*c.entity_indices[1][0] + 1;
    dofs[2] = 2*c.entity_indices[1][1];
    dofs[3] = 2*c.entity_indices[1][1] + 1;
    dofs[4] = 2*c.entity_indices[1][2];
    dofs[5] = 2*c.entity_indices[1][2] + 1;
  }

  /// 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] = 0;
      dofs[1] = 1;
      break;
    case 1:
      dofs[0] = 2;
      dofs[1] = 3;
      break;
    case 2:
      dofs[0] = 4;
      dofs[1] = 5;
      break;
    }
  }

  /// Tabulate the coordinates of all dofs on a cell
  virtual void tabulate_coordinates(double** coordinates,
                                    const ufc::cell& c) const
  {
    throw std::runtime_error("tabulate_coordinates not implemented for this type of element");
  }

  /// 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 ffc_26_dof_map_0();
  }

};

#endif