heat.h

finite element library for mathematic majored research

  /// 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 HeatBilinearForm_dof_map_1();
  }

};

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

class HeatBilinearForm_dof_map_2: public ufc::dof_map
{
private:

  unsigned int __global_dimension;

public:

  /// Constructor
  HeatBilinearForm_dof_map_2() : ufc::dof_map()
  {
    __global_dimension = 0;
  }

  /// Destructor
  virtual ~HeatBilinearForm_dof_map_2()
  {
    // 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 HeatBilinearForm_dof_map_2();
  }

};

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

class HeatBilinearForm_dof_map_3: public ufc::dof_map
{
private:

  unsigned int __global_dimension;

public:

  /// Constructor
  HeatBilinearForm_dof_map_3() : ufc::dof_map()
  {
    __global_dimension = 0;
  }

  /// Destructor
  virtual ~HeatBilinearForm_dof_map_3()
  {
    // 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
  }

  /// 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 1;
  }

  /// Return the number of dofs on each cell facet
  virtual unsigned int num_facet_dofs() const
  {
    return 0;
  }

  /// 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[2][0];
  }

  /// 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:
      
      break;
    case 1:
      
      break;
    case 2:
      
      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] = 0.3333333333*x[0][0] + 0.3333333333*x[1][0] + 0.3333333333*x[2][0];
    coordinates[0][1] = 0.3333333333*x[0][1] + 0.3333333333*x[1][1] + 0.3333333333*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 HeatBilinearForm_dof_map_3();
  }

};

/// This class defines the interface for the tabulation of the cell
/// tensor corresponding to the local contribution to a form from
/// the integral over a cell.

class HeatBilinearForm_cell_integral_0: public ufc::cell_integral
{
public:

  /// Constructor
  HeatBilinearForm_cell_integral_0() : ufc::cell_integral()
  {
    // Do nothing
  }

  /// Destructor
  virtual ~HeatBilinearForm_cell_integral_0()
  {
    // Do nothing
  }

  /// Tabulate the tensor for the contribution from a local cell
  virtual void tabulate_tensor(double* A,
                               const double * const * w,
                               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
    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;
    
    // Set scale factor
    const double det = std::abs(detJ);
    
    // Compute coefficients
    const double c1_1_0_0 = w[1][0];
    const double c0_1_1_0 = w[0][0];
    const double c0_1_1_1 = w[0][1];
    const double c0_1_1_2 = w[0][2];
    
    // Compute geometry tensors
    const double G0_ = det;
    const double G1_0_0_0_0 = det*c1_1_0_0*c0_1_1_0*(Jinv_00*Jinv_00 + Jinv_01*Jinv_01);
    const double G1_0_0_0_1 = det*c1_1_0_0*c0_1_1_0*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11);
    const double G1_0_0_1_0 = det*c1_1_0_0*c0_1_1_0*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01);
    const double G1_0_0_1_1 = det*c1_1_0_0*c0_1_1_0*(Jinv_10*Jinv_10 + Jinv_11*Jinv_11);
    const double G1_0_1_0_0 = det*c1_1_0_0*c0_1_1_1*(Jinv_00*Jinv_00 + Jinv_01*Jinv_01);
    const double G1_0_1_0_1 = det*c1_1_0_0*c0_1_1_1*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11);
    const double G1_0_1_1_0 = det*c1_1_0_0*c0_1_1_1*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01);
    const double G1_0_1_1_1 = det*c1_1_0_0*c0_1_1_1*(Jinv_10*Jinv_10 + Jinv_11*Jinv_11);
    const double G1_0_2_0_0 = det*c1_1_0_0*c0_1_1_2*(Jinv_00*Jinv_00 + Jinv_01*Jinv_01);
    const double G1_0_2_0_1 = det*c1_1_0_0*c0_1_1_2*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11);
    const double G1_0_2_1_0 = det*c1_1_0_0*c0_1_1_2*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01);
    const double G1_0_2_1_1 = det*c1_1_0_0*c0_1_1_2*(Jinv_10*Jinv_10 + Jinv