projection.h

利用C

    const double J_21 = element_coordinates[2][2] - element_coordinates[0][2];
    const double J_22 = element_coordinates[3][2] - element_coordinates[0][2];
      
    // Compute sub determinants
    const double d00 = J_11*J_22 - J_12*J_21;
    const double d01 = J_12*J_20 - J_10*J_22;
    const double d02 = J_10*J_21 - J_11*J_20;
    
    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 inverse of Jacobian
    
    // Compute constants
    const double C0 = d00*(element_coordinates[0][0] - element_coordinates[2][0] - element_coordinates[3][0]) \
                    + d10*(element_coordinates[0][1] - element_coordinates[2][1] - element_coordinates[3][1]) \
                    + d20*(element_coordinates[0][2] - element_coordinates[2][2] - element_coordinates[3][2]);
    
    const double C1 = d01*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[3][0]) \
                    + d11*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[3][1]) \
                    + d21*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[3][2]);
    
    const double C2 = d02*(element_coordinates[0][0] - element_coordinates[1][0] - element_coordinates[2][0]) \
                    + d12*(element_coordinates[0][1] - element_coordinates[1][1] - element_coordinates[2][1]) \
                    + d22*(element_coordinates[0][2] - element_coordinates[1][2] - element_coordinates[2][2]);
    
    // Get coordinates and map to the UFC reference element
    double x = (C0 + d00*coordinates[0] + d10*coordinates[1] + d20*coordinates[2]) / detJ;
    double y = (C1 + d01*coordinates[0] + d11*coordinates[1] + d21*coordinates[2]) / detJ;
    double z = (C2 + d02*coordinates[0] + d12*coordinates[1] + d22*coordinates[2]) / detJ;
    
    // Map coordinates to the reference cube
    if (std::abs(y + z - 1.0) < 1e-14)
      x = 1.0;
    else
      x = -2.0 * x/(y + z - 1.0) - 1.0;
    if (std::abs(z - 1.0) < 1e-14)
      y = -1.0;
    else
      y = 2.0 * y/(1.0 - z) - 1.0;
    z = 2.0 * 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
    const double Jinv[3][3] ={{d00 / detJ, d10 / detJ, d20 / detJ}, {d01 / detJ, d11 / detJ, d21 / detJ}, {d02 / detJ, d12 / detJ, 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_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);
    
    // 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;
    
    // 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_1_0 = 1;
    const double psitilde_bs_1_1 = 2.5*y + 1.5;
    const double psitilde_bs_2_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_01_0 = 1;
    const double psitilde_cs_01_1 = 3*z + 2;
    const double psitilde_cs_02_0 = 1;
    const double psitilde_cs_10_0 = 1;
    const double psitilde_cs_10_1 = 3*z + 2;
    const double psitilde_cs_11_0 = 1;
    const double psitilde_cs_20_0 = 1;
    
    // Compute basisvalues
    const double basisvalue0 = 0.866025403784439*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_0;
    const double basisvalue1 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_0;
    const double basisvalue2 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_0;
    const double basisvalue3 = 1.11803398874989*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_1;
    const double basisvalue4 = 5.1234753829798*psitilde_a_2*scalings_y_2*psitilde_bs_2_0*scalings_z_2*psitilde_cs_20_0;
    const double basisvalue5 = 3.96862696659689*psitilde_a_1*scalings_y_1*psitilde_bs_1_1*scalings_z_2*psitilde_cs_11_0;
    const double basisvalue6 = 2.29128784747792*psitilde_a_0*scalings_y_0*psitilde_bs_0_2*scalings_z_2*psitilde_cs_02_0;
    const double basisvalue7 = 3.24037034920393*psitilde_a_1*scalings_y_1*psitilde_bs_1_0*scalings_z_1*psitilde_cs_10_1;
    const double basisvalue8 = 1.87082869338697*psitilde_a_0*scalings_y_0*psitilde_bs_0_1*scalings_z_1*psitilde_cs_01_1;
    const double basisvalue9 = 1.3228756555323*psitilde_a_0*scalings_y_0*psitilde_bs_0_0*scalings_z_0*psitilde_cs_00_2;
    
    // Table(s) of coefficients
    const static double coefficients0[10][10] = \
    {{-0.0577350269189625, -0.0608580619450185, -0.0351364184463153, -0.0248451997499977, 0.0650600048632355, 0.050395263067897, 0.0290957186981323, 0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
    {-0.0577350269189625, 0.0608580619450185, -0.0351364184463153, -0.0248451997499976, 0.0650600048632355, -0.050395263067897, 0.0290957186981323, -0.0411475599898912, 0.0237565548366599, 0.0167984210226323},
    {-0.0577350269189626, 0, 0.0702728368926306, -0.0248451997499976, 0, 0, 0.087287156094397, 0, -0.0475131096733199, 0.0167984210226323},
    {-0.0577350269189626, 0, 0, 0.074535599249993, 0, 0, 0, 0, 0, 0.100790526135794},
    {0.23094010767585, 0, 0.140545673785261, 0.0993807989999906, 0, 0, 0, 0, 0.1187827741833, -0.0671936840905293},
    {0.23094010767585, 0.121716123890037, -0.0702728368926306, 0.0993807989999907, 0, 0, 0, 0.102868899974728, -0.0593913870916499, -0.0671936840905293},
    {0.23094010767585, 0.121716123890037, 0.0702728368926307, -0.0993807989999907, 0, 0.100790526135794, -0.087287156094397, -0.0205737799949456, -0.01187827741833, 0.0167984210226323},
    {0.23094010767585, -0.121716123890037, -0.0702728368926307, 0.0993807989999906, 0, 0, 0, -0.102868899974728, -0.0593913870916499, -0.0671936840905293},
    {0.23094010767585, -0.121716123890037, 0.0702728368926306, -0.0993807989999907, 0, -0.100790526135794, -0.0872871560943969, 0.0205737799949456, -0.01187827741833, 0.0167984210226323},
    {0.23094010767585, 0, -0.140545673785261, -0.0993807989999906, -0.130120009726471, 0, 0.0290957186981323, 0, 0.02375655483666, 0.0167984210226323}};
    
    // Interesting (new) part
    // Tables of derivatives of the polynomial base (transpose)
    const static double dmats0[10][10] = \
    {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {6.32455532033676, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 11.2249721603218, 0, 0, 0, 0, 0, 0, 0, 0},
    {4.58257569495584, 0, 8.36660026534076, -1.18321595661992, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {3.74165738677394, 0, 0, 8.69482604771366, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};
    
    const static double dmats1[10][10] = \
    {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {5.47722557505166, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825973, 0, 0, 0, 0, 0, 0},
    {2.29128784747792, 7.24568837309472, 4.18330013267038, -0.591607978309962, 0, 0, 0, 0, 0, 0},
    {-2.64575131106459, 0, 9.66091783079296, 0.683130051063974, 0, 0, 0, 0, 0, 0},
    {1.87082869338697, 0, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0},
    {3.24037034920393, 0, 0, 7.52994023880668, 0, 0, 0, 0, 0, 0},
    {0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};
    
    const static double dmats2[10][10] = \
    {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {3.16227766016838, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {1.82574185835055, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {5.16397779494322, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {2.95803989154981, 5.61248608016091, -1.08012344973464, -0.763762615825973, 0, 0, 0, 0, 0, 0},
    {2.29128784747792, 1.44913767461894, 4.18330013267038, -0.591607978309962, 0, 0, 0, 0, 0, 0},
    {1.32287565553229, 0, 3.86436713231718, -0.341565025531986, 0, 0, 0, 0, 0, 0},
    {1.87082869338697, 7.09929573971954, 0, 4.34741302385683, 0, 0, 0, 0, 0, 0},
    {1.08012344973464, 0, 7.09929573971954, 2.50998007960223, 0, 0, 0, 0, 0, 0},
    {-3.81881307912986, 0, 0, 8.87411967464942, 0, 0, 0, 0, 0, 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;
    double coeff0_1 = 0;
    double coeff0_2 = 0;
    double coeff0_3 = 0;
    double coeff0_4 = 0;
    double coeff0_5 = 0;
    double coeff0_6 = 0;
    double coeff0_7 = 0;
    double coeff0_8 = 0;
    double coeff0_9 = 0;
    
    // Declare new coefficients
    double new_coeff0_0 = 0;
    double new_coeff0_1 = 0;
    double new_coeff0_2 = 0;
    double new_coeff0_3 = 0;
    double new_coeff0_4 = 0;
    double new_coeff0_5 = 0;