energynorm.h

finite element library for mathematic majored research

    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 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 EnergyNormFunctional_dof_map_0();
  }

};

/// 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 EnergyNormFunctional_cell_integral_0: public ufc::cell_integral
{
public:

  /// Constructor
  EnergyNormFunctional_cell_integral_0() : ufc::cell_integral()
  {
    // Do nothing
  }

  /// Destructor
  virtual ~EnergyNormFunctional_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_02 = x[3][0] - x[0][0];
    const double J_10 = x[1][1] - x[0][1];
    const double J_11 = x[2][1] - x[0][1];
    const double J_12 = x[3][1] - x[0][1];
    const double J_20 = x[1][2] - x[0][2];
    const double J_21 = x[2][2] - x[0][2];
    const double J_22 = x[3][2] - x[0][2];
      
    // Compute sub determinants
    const double d_00 = J_11*J_22 - J_12*J_21;
    const double d_01 = J_12*J_20 - J_10*J_22;
    const double d_02 = J_10*J_21 - J_11*J_20;
    
    const double d_10 = J_02*J_21 - J_01*J_22;
    const double d_11 = J_00*J_22 - J_02*J_20;
    const double d_12 = J_01*J_20 - J_00*J_21;
    
    const double d_20 = J_01*J_12 - J_02*J_11;
    const double d_21 = J_02*J_10 - J_00*J_12;
    const double d_22 = J_00*J_11 - J_01*J_10;
      
    // Compute determinant of Jacobian
    double detJ = J_00*d_00 + J_10*d_10 + J_20*d_20;
      
    // Compute inverse of Jacobian
    const double Jinv_00 = d_00 / detJ;
    const double Jinv_01 = d_10 / detJ;
    const double Jinv_02 = d_20 / detJ;
    const double Jinv_10 = d_01 / detJ;
    const double Jinv_11 = d_11 / detJ;
    const double Jinv_12 = d_21 / detJ;
    const double Jinv_20 = d_02 / detJ;
    const double Jinv_21 = d_12 / detJ;
    const double Jinv_22 = d_22 / detJ;
    
    // Set scale factor
    const double det = std::abs(detJ);
    
    // Compute coefficients
    const double c0_0_0_0 = w[0][0];
    const double c0_0_0_1 = w[0][1];
    const double c0_0_0_2 = w[0][2];
    const double c0_0_0_3 = w[0][3];
    const double c0_0_1_0 = w[0][0];
    const double c0_0_1_1 = w[0][1];
    const double c0_0_1_2 = w[0][2];
    const double c0_0_1_3 = w[0][3];
    const double c0_1_0_0 = w[0][0];
    const double c0_1_0_1 = w[0][1];
    const double c0_1_0_2 = w[0][2];
    const double c0_1_0_3 = w[0][3];
    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];
    const double c0_1_1_3 = w[0][3];
    
    // Compute geometry tensors
    const double G0_0_0 = det*c0_0_0_0*c0_0_1_0;
    const double G0_0_1 = det*c0_0_0_0*c0_0_1_1;
    const double G0_0_2 = det*c0_0_0_0*c0_0_1_2;
    const double G0_0_3 = det*c0_0_0_0*c0_0_1_3;
    const double G0_1_0 = det*c0_0_0_1*c0_0_1_0;
    const double G0_1_1 = det*c0_0_0_1*c0_0_1_1;
    const double G0_1_2 = det*c0_0_0_1*c0_0_1_2;
    const double G0_1_3 = det*c0_0_0_1*c0_0_1_3;
    const double G0_2_0 = det*c0_0_0_2*c0_0_1_0;
    const double G0_2_1 = det*c0_0_0_2*c0_0_1_1;
    const double G0_2_2 = det*c0_0_0_2*c0_0_1_2;
    const double G0_2_3 = det*c0_0_0_2*c0_0_1_3;
    const double G0_3_0 = det*c0_0_0_3*c0_0_1_0;
    const double G0_3_1 = det*c0_0_0_3*c0_0_1_1;
    const double G0_3_2 = det*c0_0_0_3*c0_0_1_2;
    const double G0_3_3 = det*c0_0_0_3*c0_0_1_3;
    const double G1_0_0_0_0 = det*c0_1_0_0*c0_1_1_0*(Jinv_00*Jinv_00 + Jinv_01*Jinv_01 + Jinv_02*Jinv_02);
    const double G1_0_0_0_1 = det*c0_1_0_0*c0_1_1_0*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11 + Jinv_02*Jinv_12);
    const double G1_0_0_0_2 = det*c0_1_0_0*c0_1_1_0*(Jinv_00*Jinv_20 + Jinv_01*Jinv_21 + Jinv_02*Jinv_22);
    const double G1_0_0_1_0 = det*c0_1_0_0*c0_1_1_1*(Jinv_00*Jinv_00 + Jinv_01*Jinv_01 + Jinv_02*Jinv_02);
    const double G1_0_0_2_1 = det*c0_1_0_0*c0_1_1_2*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11 + Jinv_02*Jinv_12);
    const double G1_0_0_3_2 = det*c0_1_0_0*c0_1_1_3*(Jinv_00*Jinv_20 + Jinv_01*Jinv_21 + Jinv_02*Jinv_22);
    const double G1_0_1_0_0 = det*c0_1_0_0*c0_1_1_0*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01 + Jinv_12*Jinv_02);
    const double G1_0_1_0_1 = det*c0_1_0_0*c0_1_1_0*(Jinv_10*Jinv_10 + Jinv_11*Jinv_11 + Jinv_12*Jinv_12);
    const double G1_0_1_0_2 = det*c0_1_0_0*c0_1_1_0*(Jinv_10*Jinv_20 + Jinv_11*Jinv_21 + Jinv_12*Jinv_22);
    const double G1_0_1_1_0 = det*c0_1_0_0*c0_1_1_1*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01 + Jinv_12*Jinv_02);
    const double G1_0_1_2_1 = det*c0_1_0_0*c0_1_1_2*(Jinv_10*Jinv_10 + Jinv_11*Jinv_11 + Jinv_12*Jinv_12);
    const double G1_0_1_3_2 = det*c0_1_0_0*c0_1_1_3*(Jinv_10*Jinv_20 + Jinv_11*Jinv_21 + Jinv_12*Jinv_22);
    const double G1_0_2_0_0 = det*c0_1_0_0*c0_1_1_0*(Jinv_20*Jinv_00 + Jinv_21*Jinv_01 + Jinv_22*Jinv_02);
    const double G1_0_2_0_1 = det*c0_1_0_0*c0_1_1_0*(Jinv_20*Jinv_10 + Jinv_21*Jinv_11 + Jinv_22*Jinv_12);
    const double G1_0_2_0_2 = det*c0_1_0_0*c0_1_1_0*(Jinv_20*Jinv_20 + Jinv_21*Jinv_21 + Jinv_22*Jinv_22);
    const double G1_0_2_1_0 = det*c0_1_0_0*c0_1_1_1*(Jinv_20*Jinv_00 + Jinv_21*Jinv_01 + Jinv_22*Jinv_02);
    const double G1_0_2_2_1 = det*c0_1_0_0*c0_1_1_2*(Jinv_20*Jinv_10 + Jinv_21*Jinv_11 + Jinv_22*Jinv_12);
    const double G1_0_2_3_2 = det*c0_1_0_0*c0_1_1_3*(Jinv_20*Jinv_20 + Jinv_21*Jinv_21 + Jinv_22*Jinv_22);
    const double G1_1_0_0_0 = det*c0_1_0_1*c0_1_1_0*(Jinv_00*Jinv_00 + Jinv_01*Jinv_01 + Jinv_02*Jinv_02);
    const double G1_1_0_0_1 = det*c0_1_0_1*c0_1_1_0*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11 + Jinv_02*Jinv_12);
    const double G1_1_0_0_2 = det*c0_1_0_1*c0_1_1_0*(Jinv_00*Jinv_20 + Jinv_01*Jinv_21 + Jinv_02*Jinv_22);
    const double G1_1_0_1_0 = det*c0_1_0_1*c0_1_1_1*(Jinv_00*Jinv_00 + Jinv_01*Jinv_01 + Jinv_02*Jinv_02);
    const double G1_1_0_2_1 = det*c0_1_0_1*c0_1_1_2*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11 + Jinv_02*Jinv_12);
    const double G1_1_0_3_2 = det*c0_1_0_1*c0_1_1_3*(Jinv_00*Jinv_20 + Jinv_01*Jinv_21 + Jinv_02*Jinv_22);
    const double G1_2_1_0_0 = det*c0_1_0_2*c0_1_1_0*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01 + Jinv_12*Jinv_02);
    const double G1_2_1_0_1 = det*c0_1_0_2*c0_1_1_0*(Jinv_10*Jinv_10 + Jinv_11*Jinv_11 + Jinv_12*Jinv_12);
    const double G1_2_1_0_2 = det*c0_1_0_2*c0_1_1_0*(Jinv_10*Jinv_20 + Jinv_11*Jinv_21 + Jinv_12*Jinv_22);
    const double G1_2_1_1_0 = det*c0_1_0_2*c0_1_1_1*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01 + Jinv_12*Jinv_02);
    const double G1_2_1_2_1 = det*c0_1_0_2*c0_1_1_2*(Jinv_10*Jinv_10 + Jinv_11*Jinv_11 + Jinv_12*Jinv_12);
    const double G1_2_1_3_2 = det*c0_1_0_2*c0_1_1_3*(Jinv_10*Jinv_20 + Jinv_11*Jinv_21 + Jinv_12*Jinv_22);
    const double G1_3_2_0_0 = det*c0_1_0_3*c0_1_1_0*(Jinv_20*Jinv_00 + Jinv_21*Jinv_01 + Jinv_22*Jinv_02);
    const double G1_3_2_0_1 = det*c0_1_0_3*c0_1_1_0*(Jinv_20*Jinv_10 + Jinv_21*Jinv_11 + Jinv_22*Jinv_12);
    const double G1_3_2_0_2 = det*c0_1_0_3*c0_1_1_0*(Jinv_20*Jinv_20 + Jinv_21*Jinv_21 + Jinv_22*Jinv_22);
    const double G1_3_2_1_0 = det*c0_1_0_3*c0_1_1_1*(Jinv_20*Jinv_00 + Jinv_21*Jinv_01 + Jinv_22*Jinv_02);
    const double G1_3_2_2_1 = det*c0_1_0_3*c0_1_1_2*(Jinv_20*Jinv_10 + Jinv_21*Jinv_11 + Jinv_22*Jinv_12);
    const double G1_3_2_3_2 = det*c0_1_0_3*c0_1_1_3*(Jinv_20*Jinv_20 + Jinv_21*Jinv_21 + Jinv_22*Jinv_22);
    
    // Compute element tensor
    A[0] = 0.01666666667*G0_0_0 + 0.008333333333*G0_0_1 + 0.008333333333*G0_0_2 + 0.008333333333*G0_0_3 + 0.008333333333*G0_1_0 + 0.01666666667*G0_1_1 + 0.008333333333*G0_1_2 + 0.008333333333*G0_1_3 + 0.008333333333*G0_2_0 + 0.008333333333*G0_2_1 + 0.01666666667*G0_2_2 + 0.008333333333*G0_2_3 + 0.008333333333*G0_3_0 + 0.008333333333*G0_3_1 + 0.008333333333*G0_3_2 + 0.01666666667*G0_3_3 + 0.1666666667*G1_0_0_0_0 + 0.1666666667*G1_0_0_0_1 + 0.1666666667*G1_0_0_0_2 - 0.1666666667*G1_0_0_1_0 - 0.1666666667*G1_0_0_2_1 - 0.1666666667*G1_0_0_3_2 + 0.1666666667*G1_0_1_0_0 + 0.1666666667*G1_0_1_0_1 + 0.1666666667*G1_0_1_0_2 - 0.1666666667*G1_0_1_1_0 - 0.1666666667*G1_0_1_2_1 - 0.1666666667*G1_0_1_3_2 + 0.1666666667*G1_0_2_0_0 + 0.1666666667*G1_0_2_0_1 + 0.1666666667*G1_0_2_0_2 - 0.1666666667*G1_0_2_1_0 - 0.1666666667*G1_0_2_2_1 - 0.1666666667*G1_0_2_3_2 - 0.1666666667*G1_1_0_0_0 - 0.1666666667*G1_1_0_0_1 - 0.1666666667*G1_1_0_0_2 + 0.1666666667*G1_1_0_1_0 + 0.1666666667*G1_1_0_2_1 + 0.1666666667*G1_1_0_3_2 - 0.1666666667*G1_2_1_0_0 - 0.1666666667*G1_2_1_0_1 - 0.1666666667*G1_2_1_0_2 + 0.1666666667*G1_2_1_1_0 + 0.1666666667*G1_2_1_2_1 + 0.1666666667*G1_2_1_3_2 - 0.1666666667*G1_3_2_0_0 - 0.1666666667*G1_3_2_0_1 - 0.1666666667*G1_3_2_0_2 + 0.1666666667*G1_3_2_1_0 + 0.1666666667*G1_3_2_2_1 + 0.1666666667*G1_3_2_3_2;
  }

};

/// This class defines the interface for the assembly of the global
/// tensor corresponding to a form with r + n arguments, that is, a
/// mapping
///
///     a : V1 x V2 x ... Vr x W1 x W2 x ... x Wn -> R
///
/// with arguments v1, v2, ..., vr, w1, w2, ..., wn. The rank r
/// global tensor A is defined by
///
///     A = a(V1, V2, ..., Vr, w1, w2, ..., wn),
///
/// where each argument Vj represents the application to the
/// sequence of basis functions of Vj and w1, w2, ..., wn are given
/// fixed functions (coefficients).

class EnergyNormFunctional: public ufc::form
{
public:

  /// Constructor
  EnergyNormFunctional() : ufc::form()
  {
    // Do nothing
  }

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

  /// Return a string identifying the form
  virtual const char* signature() const
  {
    return "w0_a0w0_a1 | va0*va1*dX(0) + w0_a0w0_a2(dXa1/dxb0)(dXa3/dxb0) | ((d/dXa1)va0)*((d/dXa3)va2)*dX(0)";
  }

  /// Return the rank of the global tensor (r)
  virtual unsigned int rank() const
  {
    return 0;
  }

  /// Return the number of coefficients (n)
  virtual unsigned int num_coefficients() const
  {
    return 1;
  }

  /// Return the number of cell integrals
  virtual unsigned int num_cell_integrals() const
  {
    return 1;
  }
  
  /// Return the number of exterior facet integrals
  virtual unsigned int num_exterior_facet_integrals() const
  {
    return 0;
  }
  
  /// Return the number of interior facet integrals
  virtual unsigned int num_interior_facet_integrals() const
  {
    return 0;
  }
    
  /// Create a new finite element for argument function i
  virtual ufc::finite_element* create_finite_element(unsigned int i) const
  {
    return new EnergyNormFunctional_finite_element_0();
  }
  
  /// Create a new dof map for argument function i
  virtual ufc::dof_map* create_dof_map(unsigned int i) const
  {
    return new EnergyNormFunctional_dof_map_0();
  }

  /// Create a new cell integral on sub domain i
  virtual ufc::cell_integral* create_cell_integral(unsigned int i) const
  {
    return new EnergyNormFunctional_cell_integral_0();
  }

  /// Create a new exterior facet integral on sub domain i
  virtual ufc::exterior_facet_integral* create_exterior_facet_integral(unsigned int i) const
  {
    return 0;
  }

  /// Create a new interior facet integral on sub domain i
  virtual ufc::interior_facet_integral* create_interior_facet_integral(unsigned int i) const
  {
    return 0;
  }

};

#endif