poisson2d_4.h

利用C

// This code conforms with the UFC specification version 1.0
// and was automatically generated by FFC version 0.5.0.
//
// Warning: This code was generated with the option '-l dolfin'
// and contains DOLFIN-specific wrappers that depend on DOLFIN.

#ifndef __POISSON2D_4_H
#define __POISSON2D_4_H

#include <cmath>
#include <stdexcept>
#include <fstream>
#include <ufc.h>

/// This class defines the interface for a finite element.

class UFC_Poisson2D_4BilinearForm_finite_element_0: public ufc::finite_element
{
public:

  /// Constructor
  UFC_Poisson2D_4BilinearForm_finite_element_0() : ufc::finite_element()
  {
    // Do nothing
  }

  /// Destructor
  virtual ~UFC_Poisson2D_4BilinearForm_finite_element_0()
  {
    // Do nothing
  }

  /// Return a string identifying the finite element
  virtual const char* signature() const
  {
    return "Lagrange finite element of degree 4 on a triangle";
  }

  /// Return the cell shape
  virtual ufc::shape cell_shape() const
  {
    return ufc::triangle;
  }

  /// Return the dimension of the finite element function space
  virtual unsigned int space_dimension() const
  {
    return 15;
  }

  /// Return the rank of the value space
  virtual unsigned int value_rank() const
  {
    return 0;
  }

  /// Return the dimension of the value space for axis i
  virtual unsigned int value_dimension(unsigned int i) const
  {
    return 1;
  }

  /// Evaluate basis function i at given point in cell
  virtual void evaluate_basis(unsigned int i,
                              double* values,
                              const double* coordinates,
                              const ufc::cell& c) const
  {
    // Extract vertex coordinates
    const double * const * element_coordinates = c.coordinates;
    
    // Compute Jacobian of affine map from reference cell
    const double J_00 = element_coordinates[1][0] - element_coordinates[0][0];
    const double J_01 = element_coordinates[2][0] - element_coordinates[0][0];
    const double J_10 = element_coordinates[1][1] - element_coordinates[0][1];
    const double J_11 = element_coordinates[2][1] - element_coordinates[0][1];
      
    // Compute determinant of Jacobian
    const double detJ = J_00*J_11 - J_01*J_10;
    
    // Compute inverse of Jacobian
    
    // Get coordinates and map to the reference (UFC) element
    double x = (element_coordinates[0][1]*element_coordinates[2][0] -\
                element_coordinates[0][0]*element_coordinates[2][1] +\
                J_11*coordinates[0] - J_01*coordinates[1]) / detJ;
    double y = (element_coordinates[1][1]*element_coordinates[0][0] -\
                element_coordinates[1][0]*element_coordinates[0][1] -\
                J_10*coordinates[0] + J_00*coordinates[1]) / detJ;
    
    // Map coordinates to the reference square
    if (std::abs(y - 1.0) < 1e-14)
      x = -1.0;
    else
      x = 2.0 *x/(1.0 - y) - 1.0;
    y = 2.0*y - 1.0;
    
    // Reset values
    *values = 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_y_4 = scalings_y_3*(0.5 - 0.5*y);
    
    // 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;
    const double psitilde_a_4 = 1.75*x*psitilde_a_3 - 0.75*psitilde_a_2;
    
    // 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_0_4 = 0.0285714285714286*psitilde_bs_0_3 + 1.8*y*psitilde_bs_0_3 - 0.771428571428571*psitilde_bs_0_2;
    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_1_3 = 0.285714285714286*psitilde_bs_1_2 + 2*y*psitilde_bs_1_2 - 0.714285714285714*psitilde_bs_1_1;
    const double psitilde_bs_2_0 = 1;
    const double psitilde_bs_2_1 = 3.5*y + 2.5;
    const double psitilde_bs_2_2 = 1.02040816326531*psitilde_bs_2_1 + 2.57142857142857*y*psitilde_bs_2_1 - 0.551020408163265*psitilde_bs_2_0;
    const double psitilde_bs_3_0 = 1;
    const double psitilde_bs_3_1 = 4.5*y + 3.5;
    const double psitilde_bs_4_0 = 1;
    
    // Compute basisvalues
    const double basisvalue0 = 0.707106781186548*psitilde_a_0*scalings_y_0*psitilde_bs_0_0;
    const double basisvalue1 = 1.73205080756888*psitilde_a_1*scalings_y_1*psitilde_bs_1_0;
    const double basisvalue2 = psitilde_a_0*scalings_y_0*psitilde_bs_0_1;
    const double basisvalue3 = 2.73861278752583*psitilde_a_2*scalings_y_2*psitilde_bs_2_0;
    const double basisvalue4 = 2.12132034355964*psitilde_a_1*scalings_y_1*psitilde_bs_1_1;
    const double basisvalue5 = 1.22474487139159*psitilde_a_0*scalings_y_0*psitilde_bs_0_2;
    const double basisvalue6 = 3.74165738677394*psitilde_a_3*scalings_y_3*psitilde_bs_3_0;
    const double basisvalue7 = 3.16227766016838*psitilde_a_2*scalings_y_2*psitilde_bs_2_1;
    const double basisvalue8 = 2.44948974278318*psitilde_a_1*scalings_y_1*psitilde_bs_1_2;
    const double basisvalue9 = 1.4142135623731*psitilde_a_0*scalings_y_0*psitilde_bs_0_3;
    const double basisvalue10 = 4.74341649025257*psitilde_a_4*scalings_y_4*psitilde_bs_4_0;
    const double basisvalue11 = 4.18330013267038*psitilde_a_3*scalings_y_3*psitilde_bs_3_1;
    const double basisvalue12 = 3.53553390593274*psitilde_a_2*scalings_y_2*psitilde_bs_2_2;
    const double basisvalue13 = 2.73861278752583*psitilde_a_1*scalings_y_1*psitilde_bs_1_3;
    const double basisvalue14 = 1.58113883008419*psitilde_a_0*scalings_y_0*psitilde_bs_0_4;
    
    // Table(s) of coefficients
    const static double coefficients0[15][15] = \
    {{0, -0.0412393049421161, -0.0238095238095238, 0.0289800294976279, 0.0224478343233825, 0.012960263189329, -0.0395942580610999, -0.0334632556631574, -0.025920526378658, -0.014965222882255, 0.0321247254366312, 0.0283313448138523, 0.0239443566116079, 0.0185472188784818, 0.0107082418122104},
    {0, 0.0412393049421161, -0.0238095238095238, 0.0289800294976278, -0.0224478343233825, 0.012960263189329, 0.0395942580610999, -0.0334632556631574, 0.025920526378658, -0.014965222882255, 0.0321247254366312, -0.0283313448138523, 0.023944356611608, -0.0185472188784818, 0.0107082418122104},
    {0, 0, 0.0476190476190476, 0, 0, 0.0388807895679869, 0, 0, 0, 0.0598608915290199, 0, 0, 0, 0, 0.0535412090610519},
    {0.125707872210942, 0.131965775814772, -0.0253968253968254, 0.139104141588614, -0.0718330698348239, 0.0311046316543895, 0.0633508128977598, 0.0267706045305259, -0.0622092633087792, 0.0478887132232159, 0, 0.0566626896277046, -0.0838052481406279, 0.0834624849531681, -0.0535412090610519},
    {-0.0314269680527355, 0.0109971479845644, 0.00634920634920629, 0, 0.188561808316413, -0.163299316185545, 0, 0.0936971158568409, 0, -0.0419026240703139, 0, 0, 0.0838052481406278, -0.139104141588614, 0.107082418122104},
    {0.125707872210942, 0.0439885919382572, 0.126984126984127, 0, 0.0359165349174119, 0.155523158271948, 0, 0, 0.103682105514632, -0.011972178305804, 0, 0, 0, 0.0927360943924091, -0.107082418122104},
    {0.125707872210942, -0.131965775814772, -0.0253968253968255, 0.139104141588614, 0.0718330698348238, 0.0311046316543895, -0.0633508128977598, 0.0267706045305259, 0.0622092633087791, 0.047888713223216, 0, -0.0566626896277046, -0.0838052481406278, -0.0834624849531682, -0.0535412090610519},
    {-0.0314269680527357, -0.0109971479845642, 0.00634920634920626, 0, -0.188561808316413, -0.163299316185545, 0, 0.0936971158568409, 0, -0.0419026240703139, 0, 0, 0.0838052481406278, 0.139104141588614, 0.107082418122104},
    {0.125707872210942, -0.0439885919382573, 0.126984126984127, 0, -0.035916534917412, 0.155523158271948, 0, 0, -0.103682105514632, -0.011972178305804, 0, 0, 0, -0.0927360943924091, -0.107082418122104},
    {0.125707872210942, -0.0879771838765143, -0.101587301587302, 0.0927360943924091, 0.107749604752236, 0.0725774738602423, 0.0791885161221998, -0.013385302265263, -0.0518410527573159, -0.0419026240703139, -0.128498901746525, -0.0566626896277046, -0.011972178305804, 0.00927360943924092, 0.0107082418122104},
    {-0.0314269680527355, 0, -0.0126984126984127, -0.243432247780074, 0, 0.0544331053951818, 0, 0.0936971158568408, 0, -0.0419026240703139, 0.192748352619787, 0, -0.0239443566116079, 0, 0.0107082418122103},
    {0.125707872210942, 0.0879771838765144, -0.101587301587302, 0.0927360943924091, -0.107749604752236, 0.0725774738602423, -0.0791885161221998, -0.013385302265263, 0.0518410527573159, -0.0419026240703139, -0.128498901746525, 0.0566626896277045, -0.011972178305804, -0.0092736094392409, 0.0107082418122104},
    {0.251415744421884, -0.351908735506058, -0.203174603174603, -0.139104141588614, -0.107749604752236, -0.0622092633087791, 0.19005243869328, -0.0267706045305259, 0.124418526617558, 0.155638317975452, 0, 0.169988068883114, 0.0838052481406278, -0.0278208283177228, -0.0535412090610519},
    {0.251415744421884, 0.351908735506058, -0.203174603174603, -0.139104141588614, 0.107749604752236, -0.0622092633087791, -0.19005243869328, -0.026770604530526, -0.124418526617558, 0.155638317975452, 0, -0.169988068883114, 0.0838052481406279, 0.0278208283177227, -0.0535412090610519},
    {0.251415744421884, 0, 0.406349206349206, 0, 0, -0.186627789926337, 0, -0.187394231713682, 0, -0.203527031198668, 0, 0, -0.167610496281256, 0, 0.107082418122104}};
    
    // Extract relevant coefficients
    const double coeff0_0 = coefficients0[dof][0];
    const double coeff0_1 = coefficients0[dof][1];
    const double coeff0_2 = coefficients0[dof][2];
    const double coeff0_3 = coefficients0[dof][3];
    const double coeff0_4 = coefficients0[dof][4];
    const double coeff0_5 = coefficients0[dof][5];
    const double coeff0_6 = coefficients0[dof][6];
    const double coeff0_7 = coefficients0[dof][7];
    const double coeff0_8 = coefficients0[dof][8];
    const double coeff0_9 = coefficients0[dof][9];
    const double coeff0_10 = coefficients0[dof][10];
    const double coeff0_11 = coefficients0[dof][11];
    const double coeff0_12 = coefficients0[dof][12];
    const double coeff0_13 = coefficients0[dof][13];
    const double coeff0_14 = coefficients0[dof][14];
    
    // Compute value(s)
    *values = coeff0_0*basisvalue0 + coeff0_1*basisvalue1 + coeff0_2*basisvalue2 + coeff0_3*basisvalue3 + coeff0_4*basisvalue4 + coeff0_5*basisvalue5 + coeff0_6*basisvalue6 + coeff0_7*basisvalue7 + coeff0_8*basisvalue8 + coeff0_9*basisvalue9 + coeff0_10*basisvalue10 + coeff0_11*basisvalue11 + coeff0_12*basisvalue12 + coeff0_13*basisvalue13 + coeff0_14*basisvalue14;
  }

  /// Evaluate all basis functions at given point in cell
  virtual void evaluate_basis_all(double* values,
                                  const double* coordinates,
                                  const ufc::cell& c) const
  {