poisson3d_3.h

Dolfin provide a high-performance linear algebra library

    const double d10 = J_02*J_21 - J_01*J_22;
    const double d11 = J_00*J_22 - J_02*J_20;
    const double d12 = J_01*J_20 - J_00*J_21;
    
    const double d20 = J_01*J_12 - J_02*J_11;
    const double d21 = J_02*J_10 - J_00*J_12;
    const double d22 = J_00*J_11 - J_01*J_10;
      
    // Compute determinant of Jacobian
    double detJ = J_00*d00 + J_10*d10 + J_20*d20;
    
    // Compute constants
    const double C0 = element_coordinates[3][0] + element_coordinates[2][0] \
                    + element_coordinates[1][0] - element_coordinates[0][0];
    const double C1 = element_coordinates[3][1] + element_coordinates[2][1] \
                    + element_coordinates[1][1] - element_coordinates[0][1];
    const double C2 = element_coordinates[3][2] + element_coordinates[2][2] \
                    + element_coordinates[1][2] - element_coordinates[0][2];
    
    // Get coordinates and map to the reference (FIAT) element
    double x = coordinates[0];
    double y = coordinates[1];
    double z = coordinates[2];
    
    x = (2.0*d00*x + 2.0*d10*y + 2.0*d20*z - d00*C0 - d10*C1 - d20*C2) / detJ;
    y = (2.0*d01*x + 2.0*d11*y + 2.0*d21*z - d01*C0 - d11*C1 - d21*C2) / detJ;
    z = (2.0*d02*x + 2.0*d12*y + 2.0*d22*z - d02*C0 - d12*C1 - d22*C2) / detJ;
    
    // Map coordinates to the reference cube
    if (std::abs(y + z) < 1e-14)
      x = 1.0;
    else
      x = -2.0 * (1.0 + x)/(y + z) - 1.0;
    if (std::abs(z - 1.0) < 1e-14)
      y = -1.0;
    else
      y = 2.0 * (1.0 + y)/(1.0 - z) - 1.0;
    
    // Compute number of derivatives
    unsigned int num_derivatives = 1;
    
    for (unsigned int j = 0; j < n; j++)
      num_derivatives *= 3;
    
    
    // Declare pointer to two dimensional array that holds combinations of derivatives and initialise
    unsigned int **combinations = new unsigned int *[num_derivatives];
        
    for (unsigned int j = 0; j < num_derivatives; j++)
    {
      combinations[j] = new unsigned int [n];
      for (unsigned int k = 0; k < n; k++)
        combinations[j][k] = 0;
    }
        
    // Generate combinations of derivatives
    for (unsigned int row = 1; row < num_derivatives; row++)
    {
      for (unsigned int num = 0; num < row; num++)
      {
        for (unsigned int col = n-1; col+1 > 0; col--)
        {
          if (combinations[row][col] + 1 > 2)
            combinations[row][col] = 0;
          else
          {
            combinations[row][col] += 1;
            break;
          }
        }
      }
    }
    
    // Compute inverse of Jacobian, components are scaled because of difference in FFC/FIAT reference elements
    const double Jinv[3][3] ={{2*d00 / detJ, 2*d10 / detJ, 2*d20 / detJ}, {2*d01 / detJ, 2*d11 / detJ, 2*d21 / detJ}, {2*d02 / detJ, 2*d12 / detJ, 2*d22 / detJ}};
    
    // Declare transformation matrix
    // Declare pointer to two dimensional array and initialise
    double **transform = new double *[num_derivatives];
        
    for (unsigned int j = 0; j < num_derivatives; j++)
    {
      transform[j] = new double [num_derivatives];
      for (unsigned int k = 0; k < num_derivatives; k++)
        transform[j][k] = 1;
    }
    
    // Construct transformation matrix
    for (unsigned int row = 0; row < num_derivatives; row++)
    {
      for (unsigned int col = 0; col < num_derivatives; col++)
      {
        for (unsigned int k = 0; k < n; k++)
          transform[row][col] *= Jinv[combinations[col][k]][combinations[row][k]];
      }
    }
    
    // Reset values
    for (unsigned int j = 0; j < 1*num_derivatives; j++)
      values[j] = 0;
    
    // Map degree of freedom to element degree of freedom
    const unsigned int dof = i;
    
    // Generate scalings
    const double scalings_y_0 = 1;
    const double scalings_y_1 = scalings_y_0*(0.5 - 0.5*y);
    const double scalings_y_2 = scalings_y_1*(0.5 - 0.5*y);
    const double scalings_y_3 = scalings_y_2*(0.5 - 0.5*y);
    const double scalings_z_0 = 1;
    const double scalings_z_1 = scalings_z_0*(0.5 - 0.5*z);
    const double scalings_z_2 = scalings_z_1*(0.5 - 0.5*z);
    const double scalings_z_3 = scalings_z_2*(0.5 - 0.5*z);
    
    // Compute psitilde_a
    const double psitilde_a_0 = 1;
    const double psitilde_a_1 = x;
    const double psitilde_a_2 = 1.5*x*psitilde_a_1 - 0.5*psitilde_a_0;
    const double psitilde_a_3 = 1.66666666666667*x*psitilde_a_2 - 0.666666666666667*psitilde_a_1;
    
    // Compute psitilde_bs
    const double psitilde_bs_0_0 = 1;
    const double psitilde_bs_0_1 = 1.5*y + 0.5;
    const double psitilde_bs_0_2 = 0.111111111111111*psitilde_bs_0_1 + 1.66666666666667*y*psitilde_bs_0_1 - 0.555555555555556*psitilde_bs_0_0;
    const double psitilde_bs_0_3 = 0.05*psitilde_bs_0_2 + 1.75*y*psitilde_bs_0_2 - 0.7*psitilde_bs_0_1;
    const double psitilde_bs_1_0 = 1;
    const double psitilde_bs_1_1 = 2.5*y + 1.5;
    const double psitilde_bs_1_2 = 0.54*psitilde_bs_1_1 + 2.1*y*psitilde_bs_1_1 - 0.56*psitilde_bs_1_0;
    const double psitilde_bs_2_0 = 1;
    const double psitilde_bs_2_1 = 3.5*y + 2.5;
    const double psitilde_bs_3_0 = 1;
    
    // Compute psitilde_cs
    const double psitilde_cs_00_0 = 1;
    const double psitilde_cs_00_1 = 2*z + 1;
    const double psitilde_cs_00_2 = 0.3125*psitilde_cs_00_1 + 1.875*z*psitilde_cs_00_1 - 0.5625*psitilde_cs_00_0;
    const double psitilde_cs_00_3 = 0.155555555555556*psitilde_cs_00_2 + 1.86666666666667*z*psitilde_cs_00_2 - 0.711111111111111*psitilde_cs_00_1;
    const double psitilde_cs_01_0 = 1;
    const double psitilde_cs_01_1 = 3*z + 2;