energynorm.h

Dolfin provide a high-performance linear algebra library

  /// Constructor
  UFC_EnergyNormFunctional_cell_integral_0() : ufc::cell_integral()
  {
    // Do nothing
  }

  /// Destructor
  virtual ~UFC_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_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;
    
    // Take absolute value of determinant
    detJ = std::abs(detJ);
    
    // Set scale factor
    const double det = 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_0_4 = w[0][4];
    const double c0_0_0_5 = w[0][5];
    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_0_1_4 = w[0][4];
    const double c0_0_1_5 = w[0][5];
    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_0_4 = w[0][4];
    const double c0_1_0_5 = w[0][5];
    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];
    const double c0_1_1_4 = w[0][4];
    const double c0_1_1_5 = w[0][5];
    
    // 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_4 = det*c0_0_0_1*c0_0_1_4;
    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_5 = det*c0_0_0_2*c0_0_1_5;
    const double G0_3_0 = det*c0_0_0_3*c0_0_1_0;
    const double G0_3_3 = det*c0_0_0_3*c0_0_1_3;
    const double G0_3_4 = det*c0_0_0_3*c0_0_1_4;
    const double G0_3_5 = det*c0_0_0_3*c0_0_1_5;
    const double G0_4_1 = det*c0_0_0_4*c0_0_1_1;
    const double G0_4_3 = det*c0_0_0_4*c0_0_1_3;
    const double G0_4_4 = det*c0_0_0_4*c0_0_1_4;
    const double G0_4_5 = det*c0_0_0_4*c0_0_1_5;
    const double G0_5_2 = det*c0_0_0_5*c0_0_1_2;
    const double G0_5_3 = det*c0_0_0_5*c0_0_1_3;
    const double G0_5_4 = det*c0_0_0_5*c0_0_1_4;
    const double G0_5_5 = det*c0_0_0_5*c0_0_1_5;
    const double G1_0_0_0_0 = det*c0_1_0_0*c0_1_1_0*(Jinv_00*Jinv_00 + Jinv_01*Jinv_01);
    const double G1_0_0_0_1 = det*c0_1_0_0*c0_1_1_0*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11);
    const double G1_0_0_1_0 = det*c0_1_0_0*c0_1_1_1*(Jinv_00*Jinv_00 + Jinv_01*Jinv_01);
    const double G1_0_0_2_1 = det*c0_1_0_0*c0_1_1_2*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11);
    const double G1_0_0_4_1 = det*c0_1_0_0*c0_1_1_4*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11);
    const double G1_0_0_5_0 = det*c0_1_0_0*c0_1_1_5*(Jinv_00*Jinv_00 + Jinv_01*Jinv_01);
    const double G1_0_1_0_0 = det*c0_1_0_0*c0_1_1_0*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01);
    const double G1_0_1_0_1 = det*c0_1_0_0*c0_1_1_0*(Jinv_10*Jinv_10 + Jinv_11*Jinv_11);
    const double G1_0_1_1_0 = det*c0_1_0_0*c0_1_1_1*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01);
    const double G1_0_1_2_1 = det*c0_1_0_0*c0_1_1_2*(Jinv_10*Jinv_10 + Jinv_11*Jinv_11);
    const double G1_0_1_4_1 = det*c0_1_0_0*c0_1_1_4*(Jinv_10*Jinv_10 + Jinv_11*Jinv_11);
    const double G1_0_1_5_0 = det*c0_1_0_0*c0_1_1_5*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01);
    const double G1_1_0_0_0 = det*c0_1_0_1*c0_1_1_0*(Jinv_00*Jinv_00 + Jinv_01*Jinv_01);
    const double G1_1_0_0_1 = det*c0_1_0_1*c0_1_1_0*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11);
    const double G1_1_0_1_0 = det*c0_1_0_1*c0_1_1_1*(Jinv_00*Jinv_00 + Jinv_01*Jinv_01);
    const double G1_1_0_2_1 = det*c0_1_0_1*c0_1_1_2*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11);
    const double G1_1_0_3_1 = det*c0_1_0_1*c0_1_1_3*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11);
    const double G1_1_0_5_0 = det*c0_1_0_1*c0_1_1_5*(Jinv_00*Jinv_00 + Jinv_01*Jinv_01);
    const double G1_1_0_5_1 = det*c0_1_0_1*c0_1_1_5*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11);
    const double G1_2_1_0_0 = det*c0_1_0_2*c0_1_1_0*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01);
    const double G1_2_1_0_1 = det*c0_1_0_2*c0_1_1_0*(Jinv_10*Jinv_10 + Jinv_11*Jinv_11);
    const double G1_2_1_1_0 = det*c0_1_0_2*c0_1_1_1*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01);
    const double G1_2_1_2_1 = det*c0_1_0_2*c0_1_1_2*(Jinv_10*Jinv_10 + Jinv_11*Jinv_11);
    const double G1_2_1_3_0 = det*c0_1_0_2*c0_1_1_3*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01);
    const double G1_2_1_4_0 = det*c0_1_0_2*c0_1_1_4*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01);
    const double G1_2_1_4_1 = det*c0_1_0_2*c0_1_1_4*(Jinv_10*Jinv_10 + Jinv_11*Jinv_11);
    const double G1_3_0_2_1 = det*c0_1_0_3*c0_1_1_2*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11);
    const double G1_3_0_3_0 = det*c0_1_0_3*c0_1_1_3*(Jinv_00*Jinv_00 + Jinv_01*Jinv_01);
    const double G1_3_0_3_1 = det*c0_1_0_3*c0_1_1_3*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11);
    const double G1_3_0_4_0 = det*c0_1_0_3*c0_1_1_4*(Jinv_00*Jinv_00 + Jinv_01*Jinv_01);
    const double G1_3_0_4_1 = det*c0_1_0_3*c0_1_1_4*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11);
    const double G1_3_0_5_1 = det*c0_1_0_3*c0_1_1_5*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11);
    const double G1_3_1_1_0 = det*c0_1_0_3*c0_1_1_1*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01);
    const double G1_3_1_3_0 = det*c0_1_0_3*c0_1_1_3*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01);
    const double G1_3_1_3_1 = det*c0_1_0_3*c0_1_1_3*(Jinv_10*Jinv_10 + Jinv_11*Jinv_11);
    const double G1_3_1_4_0 = det*c0_1_0_3*c0_1_1_4*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01);
    const double G1_3_1_5_0 = det*c0_1_0_3*c0_1_1_5*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01);
    const double G1_3_1_5_1 = det*c0_1_0_3*c0_1_1_5*(Jinv_10*Jinv_10 + Jinv_11*Jinv_11);
    const double G1_4_0_2_1 = det*c0_1_0_4*c0_1_1_2*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11);
    const double G1_4_0_3_0 = det*c0_1_0_4*c0_1_1_3*(Jinv_00*Jinv_00 + Jinv_01*Jinv_01);
    const double G1_4_0_3_1 = det*c0_1_0_4*c0_1_1_3*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11);
    const double G1_4_0_4_0 = det*c0_1_0_4*c0_1_1_4*(Jinv_00*Jinv_00 + Jinv_01*Jinv_01);
    const double G1_4_0_4_1 = det*c0_1_0_4*c0_1_1_4*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11);
    const double G1_4_0_5_1 = det*c0_1_0_4*c0_1_1_5*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11);
    const double G1_4_1_0_0 = det*c0_1_0_4*c0_1_1_0*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01);
    const double G1_4_1_0_1 = det*c0_1_0_4*c0_1_1_0*(Jinv_10*Jinv_10 + Jinv_11*Jinv_11);
    const double G1_4_1_2_1 = det*c0_1_0_4*c0_1_1_2*(Jinv_10*Jinv_10 + Jinv_11*Jinv_11);
    const double G1_4_1_3_0 = det*c0_1_0_4*c0_1_1_3*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01);
    const double G1_4_1_4_0 = det*c0_1_0_4*c0_1_1_4*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01);
    const double G1_4_1_4_1 = det*c0_1_0_4*c0_1_1_4*(Jinv_10*Jinv_10 + Jinv_11*Jinv_11);
    const double G1_4_1_5_0 = det*c0_1_0_4*c0_1_1_5*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01);
    const double G1_5_0_0_0 = det*c0_1_0_5*c0_1_1_0*(Jinv_00*Jinv_00 + Jinv_01*Jinv_01);
    const double G1_5_0_0_1 = det*c0_1_0_5*c0_1_1_0*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11);
    const double G1_5_0_1_0 = det*c0_1_0_5*c0_1_1_1*(Jinv_00*Jinv_00 + Jinv_01*Jinv_01);
    const double G1_5_0_3_1 = det*c0_1_0_5*c0_1_1_3*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11);
    const double G1_5_0_4_1 = det*c0_1_0_5*c0_1_1_4*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11);
    const double G1_5_0_5_0 = det*c0_1_0_5*c0_1_1_5*(Jinv_00*Jinv_00 + Jinv_01*Jinv_01);
    const double G1_5_0_5_1 = det*c0_1_0_5*c0_1_1_5*(Jinv_00*Jinv_10 + Jinv_01*Jinv_11);
    const double G1_5_1_1_0 = det*c0_1_0_5*c0_1_1_1*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01);
    const double G1_5_1_3_0 = det*c0_1_0_5*c0_1_1_3*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01);
    const double G1_5_1_3_1 = det*c0_1_0_5*c0_1_1_3*(Jinv_10*Jinv_10 + Jinv_11*Jinv_11);
    const double G1_5_1_4_0 = det*c0_1_0_5*c0_1_1_4*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01);
    const double G1_5_1_5_0 = det*c0_1_0_5*c0_1_1_5*(Jinv_10*Jinv_00 + Jinv_11*Jinv_01);
    const double G1_5_1_5_1 = det*c0_1_0_5*c0_1_1_5*(Jinv_10*Jinv_10 + Jinv_11*Jinv_11);
    
    // Compute element tensor
    A[0] = 0.0166666666666667*G0_0_0 - 0.00277777777777777*G0_0_1 - 0.00277777777777778*G0_0_2 - 0.0111111111111111*G0_0_3 - 0.00277777777777777*G0_1_0 + 0.0166666666666667*G0_1_1 - 0.00277777777777778*G0_1_2 - 0.0111111111111111*G0_1_4 - 0.00277777777777778*G0_2_0 - 0.00277777777777778*G0_2_1 + 0.0166666666666667*G0_2_2 - 0.0111111111111111*G0_2_5 - 0.0111111111111111*G0_3_0 + 0.0888888888888888*G0_3_3 + 0.0444444444444444*G0_3_4 + 0.0444444444444444*G0_3_5 - 0.0111111111111111*G0_4_1 + 0.0444444444444444*G0_4_3 + 0.0888888888888888*G0_4_4 + 0.0444444444444444*G0_4_5 - 0.0111111111111111*G0_5_2 + 0.0444444444444444*G0_5_3 + 0.0444444444444444*G0_5_4 + 0.0888888888888888*G0_5_5 + 0.499999999999999*G1_0_0_0_0 + 0.499999999999999*G1_0_0_0_1 + 0.166666666666666*G1_0_0_1_0 + 0.166666666666667*G1_0_0_2_1 - 0.666666666666666*G1_0_0_4_1 - 0.666666666666666*G1_0_0_5_0 + 0.499999999999999*G1_0_1_0_0 + 0.499999999999999*G1_0_1_0_1 + 0.166666666666666*G1_0_1_1_0 + 0.166666666666666*G1_0_1_2_1 - 0.666666666666666*G1_0_1_4_1 - 0.666666666666666*G1_0_1_5_0 + 0.166666666666666*G1_1_0_0_0 + 0.166666666666666*G1_1_0_0_1 + 0.499999999999999*G1_1_0_1_0 - 0.166666666666666*G1_1_0_2_1 + 0.666666666666665*G1_1_0_3_1 - 0.666666666666665*G1_1_0_5_0 - 0.666666666666666*G1_1_0_5_1 + 0.166666666666667*G1_2_1_0_0 + 0.166666666666667*G1_2_1_0_1 - 0.166666666666666*G1_2_1_1_0 + 0.499999999999999*G1_2_1_2_1 + 0.666666666666665*G1_2_1_3_0 - 0.666666666666665*G1_2_1_4_0 - 0.666666666666666*G1_2_1_4_1 + 0.666666666666665*G1_3_0_2_1 + 1.33333333333333*G1_3_0_3_0 + 0.666666666666665*G1_3_0_3_1 - 1.33333333333333*G1_3_0_4_0 - 0.666666666666666*G1_3_0_4_1 - 0.666666666666665*G1_3_0_5_1 + 0.666666666666665*G1_3_1_1_0 + 0.666666666666665*G1_3_1_3_0 + 1.33333333333333*G1_3_1_3_1 - 0.666666666666665*G1_3_1_4_0 - 0.666666666666665*G1_3_1_5_0 - 1.33333333333333*G1_3_1_5_1 - 0.666666666666665*G1_4_0_2_1 - 1.33333333333333*G1_4_0_3_0 - 0.666666666666665*G1_4_0_3_1 + 1.33333333333333*G1_4_0_4_0 + 0.666666666666666*G1_4_0_4_1 + 0.666666666666665*G1_4_0_5_1 - 0.666666666666666*G1_4_1_0_0 - 0.666666666666666*G1_4_1_0_1 - 0.666666666666666*G1_4_1_2_1 - 0.666666666666666*G1_4_1_3_0 + 0.666666666666666*G1_4_1_4_0 + 1.33333333333333*G1_4_1_4_1 + 0.666666666666666*G1_4_1_5_0 - 0.666666666666666*G1_5_0_0_0 - 0.666666666666666*G1_5_0_0_1 - 0.666666666666665*G1_5_0_1_0 - 0.666666666666665*G1_5_0_3_1 + 0.666666666666666*G1_5_0_4_1 + 1.33333333333333*G1_5_0_5_0 + 0.666666666666666*G1_5_0_5_1 - 0.666666666666666*G1_5_1_1_0 - 0.666666666666665*G1_5_1_3_0 - 1.33333333333333*G1_5_1_3_1 + 0.666666666666665*G1_5_1_4_0 + 0.666666666666666*G1_5_1_5_0 + 1.33333333333333*G1_5_1_5_1;
  }

};

/// 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 UFC_EnergyNormFunctional: public ufc::form
{
public:

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

  /// Destructor
  virtual ~UFC_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 UFC_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 UFC_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 UFC_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;
  }

};

// DOLFIN wrappers

#include <dolfin/Form.h>

class EnergyNormFunctional : public dolfin::Form
{
public:

  EnergyNormFunctional(dolfin::Function& w0) : dolfin::Form()
  {
    __coefficients.push_back(&w0);
  }

  /// Return UFC form
  virtual const ufc::form& form() const
  {
    return __form;
  }
  
  /// Return array of coefficients
  virtual const dolfin::Array<dolfin::Function*>& coefficients() const
  {
    return __coefficients;
  }

private:

  // UFC form
  UFC_EnergyNormFunctional __form;

  /// Array of coefficients
  dolfin::Array<dolfin::Function*> __coefficients;

};

#endif