drag.h

Dolfin provide a high-performance linear algebra library

      // 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}};
    
      // Interesting (new) part
      // Tables of derivatives of the polynomial base (transpose)
      const static double dmats0[1][1] =   \
      {{0}};
    
      const static double dmats1[1][1] =   \
      {{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;
    
      // Declare new coefficients
      double new_coeff0_0 = 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];
    
        // Loop derivative order
        for (unsigned int j = 0; j < n; j++)
        {
          // Update old coefficients
          coeff0_0 = new_coeff0_0;
    
          if(combinations[deriv_num][j] == 0)
          {
            new_coeff0_0 = coeff0_0*dmats0[0][0];
          }
          if(combinations[deriv_num][j] == 1)
          {
            new_coeff0_0 = coeff0_0*dmats1[0][0];
          }
    
        }
        // Compute derivatives on reference element as dot product of coefficients and basisvalues
        derivatives[deriv_num] = new_coeff0_0*basisvalue0;
      }
    
      // 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
      delete [] combinations;
    
    }
    
    if (1 <= i and i <= 1)
    {
      // Map degree of freedom to element degree of freedom
      const unsigned int dof = i - 1;
    
      // 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}};
    
      // Interesting (new) part
      // Tables of derivatives of the polynomial base (transpose)
      const static double dmats0[1][1] =   \
      {{0}};
    
      const static double dmats1[1][1] =   \
      {{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;
    
      // Declare new coefficients
      double new_coeff0_0 = 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];
    
        // Loop derivative order
        for (unsigned int j = 0; j < n; j++)
        {
          // Update old coefficients
          coeff0_0 = new_coeff0_0;
    
          if(combinations[deriv_num][j] == 0)
          {
            new_coeff0_0 = coeff0_0*dmats0[0][0];
          }
          if(combinations[deriv_num][j] == 1)
          {
            new_coeff0_0 = coeff0_0*dmats1[0][0];
          }
    
        }
        // Compute derivatives on reference element as dot product of coefficients and basisvalues
        derivatives[deriv_num] = new_coeff0_0*basisvalue0;
      }
    
      // 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[num_derivatives + 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
      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
  {
    double values[2];
    double coordinates[2];
    
    // Nodal coordinates on reference cell
    static double X[2][2] = {{0.333333333333333, 0.333333333333333}, {0.333333333333333, 0.333333333333333}};
    
    // Components for each dof
    static unsigned int components[2] = {0, 1};
    
    // 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];
    const double w1 = X[i][0];
    const double w2 = X[i][1];
    
    // Compute affine mapping x = F(X)
    coordinates[0] = w0*x[0][0] + w1*x[1][0] + w2*x[2][0];
    coordinates[1] = w0*x[0][1] + w1*x[1][1] + w2*x[2][1];
    
    // Evaluate function at coordinates
    f.evaluate(values, coordinates, c);
    
    // Pick component for evaluation
    return values[components[i]];
  }

  /// 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[0];
    vertex_values[2] = dof_values[0];
    // Evaluate at vertices and use affine mapping
    vertex_values[3] = dof_values[1];
    vertex_values[4] = dof_values[1];
    vertex_values[5] = dof_values[1];
  }

  /// Return the number of sub elements (for a mixed element)
  virtual unsigned int num_sub_elements() const
  {
    return 2;
  }

  /// Create a new finite element for sub element i (for a mixed element)
  virtual ufc::finite_element* create_sub_element(unsigned int i) const
  {
    switch ( i )
    {
    case 0:
      return new UFC_DragFunctional_finite_element_1_0();
      break;
    case 1:
      return new UFC_DragFunctional_finite_element_1_1();
      break;
    }
    return 0;
  }

};

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

class UFC_DragFunctional_dof_map_0: public ufc::dof_map
{
private:

  unsigned int __global_dimension;

public:

  /// Constructor
  UFC_DragFunctional_dof_map_0() : ufc::dof_map()
  {
    __global_dimension = 0;
  }

  /// Destructor
  virtual ~UFC_DragFunctional_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 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 true;
      break;
    case 1:
      return false;
      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 = 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 3;
  }

  /// 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] = c.entity_indices[0][0];
    dofs[1] = c.entity_indices[0][1];
    dofs[2] = c.entity_indices[0][2];
  }

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

  /// 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[1][0] = x[1][0];
    coordinates[1][1] = x[1][1];
    coordinates[2][0] = x[2][0];
    coordinates[2][1] = x[2][1];
  }

  /// 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_DragFunctional_dof_map_0();
  }

};

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

class UFC_DragFunctional_dof_map_1_0: public ufc::dof_map
{
private:

  unsigned int __global_dimension;

public:

  /// Constructor
  UFC_DragFunctional_dof_map_1_0() : ufc::dof_map()
  {
    __global_dimension = 0;
  }

  /// Destructor
  virtual ~UFC_DragFunctional_dof_map_1_0()
  {
    // Do nothing
  }

  /// Return a string identifying the dof map
  virtual const char* signature() const
  {
    return "FFC dof map for Discontinuous Lagrange finite element of degree 0 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 false;
      break;
    case 2:
      return true;
      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[2];
    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
  }