poisson.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 __POISSON_H
#define __POISSON_H

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

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

class UFC_PoissonBilinearForm_finite_element_0: public ufc::finite_element
{
public:

  /// Constructor
  UFC_PoissonBilinearForm_finite_element_0() : ufc::finite_element()
  {
    // Do nothing
  }

  /// Destructor
  virtual ~UFC_PoissonBilinearForm_finite_element_0()
  {
    // Do nothing
  }

  /// Return a string identifying the finite element
  virtual const char* signature() const
  {
    return "Lagrange finite element of degree 1 on a interval";
  }

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

  /// Return the dimension of the finite element function space
  virtual unsigned int space_dimension() const
  {
    return 2;
  }

  /// 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];
    
    // Get coordinates and map to the reference (UFC) element
    double x = (coordinates[0] - element_coordinates[0][0]) / J_00;
    
    // No mapping needed for 1D.
    
    // Reset values
    *values = 0;
    
    // Map degree of freedom to element degree of freedom
    const unsigned int dof = i;
    
    // Generate scalings not needed for 1D
    
    // Compute psitilde_a
    const double psitilde_a_0 = 1;
    const double psitilde_a_1 = x;
    
    // Compute basisvalues
    const double basisvalue0 = 0.707106781186548*psitilde_a_0;
    const double basisvalue1 = 1.22474487139159*psitilde_a_1;
    
    // Table(s) of coefficients
    const static double coefficients0[2][2] = \
    {{0.707106781186547, -0.408248290463863},
    {0.707106781186547, 0.408248290463863}};
    
    // Extract relevant coefficients
    const double coeff0_0 = coefficients0[dof][0];
    const double coeff0_1 = coefficients0[dof][1];
    
    // Compute value(s)
    *values = coeff0_0*basisvalue0 + coeff0_1*basisvalue1;
  }

  /// Evaluate all basis functions at given point in cell
  virtual void evaluate_basis_all(double* values,
                                  const double* coordinates,
                                  const ufc::cell& c) const
  {
    throw std::runtime_error("The vectorised version of evaluate_basis() is not yet implemented.");
  }

  /// Evaluate order n derivatives of basis function i at given point in cell
  virtual void evaluate_basis_derivatives(unsigned int i,
                                          unsigned int n,
                                          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];
    
    // Get coordinates and map to the reference (UFC) element
    double x = (coordinates[0] - element_coordinates[0][0]) / J_00;
    
    // No mapping needed for 1D.
    
    // Compute number of derivatives
    unsigned int num_derivatives = 1;
    
    for (unsigned int j = 0; j < n; j++)
      num_derivatives *= 1;
    
    
    // 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 > 0)
            combinations[row][col] = 0;
          else
          {
            combinations[row][col] += 1;
            break;
          }
        }
      }
    }
    
    // Compute inverse of Jacobian
    const double Jinv[1][1] =  {{1.0 / J_00}};
    
    // 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 not needed for 1D
    
    // Compute psitilde_a
    const double psitilde_a_0 = 1;
    const double psitilde_a_1 = x;
    
    // Compute basisvalues
    const double basisvalue0 = 0.707106781186548*psitilde_a_0;
    const double basisvalue1 = 1.22474487139159*psitilde_a_1;
    
    // Table(s) of coefficients
    const static double coefficients0[2][2] = \
    {{0.707106781186547, -0.408248290463863},
    {0.707106781186547, 0.408248290463863}};
    
    // Interesting (new) part
    // Tables of derivatives of the polynomial base (transpose)
    const static double dmats0[2][2] = \
    {{0, 0},
    {3.46410161513775, 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;
    
    // Declare new coefficients
    double new_coeff0_0 = 0;
    double new_coeff0_1 = 0;
    
    // Loop possible derivatives
    for (unsigned int deriv_num = 0; deriv_num < num_derivatives; deriv_num++)
    {
      // Get values from coefficients array
      new_coeff0_0 = coefficients0[dof][0];
      new_coeff0_1 = coefficients0[dof][1];
    
      // Loop derivative order
      for (unsigned int j = 0; j < n; j++)
      {
        // Update old coefficients
        coeff0_0 = new_coeff0_0;
        coeff0_1 = new_coeff0_1;
    
        if(combinations[deriv_num][j] == 0)
        {
          new_coeff0_0 = coeff0_0*dmats0[0][0] + coeff0_1*dmats0[1][0];
          new_coeff0_1 = coeff0_0*dmats0[0][1] + coeff0_1*dmats0[1][1];
        }
    
      }
      // Compute derivatives on reference element as dot product of coefficients and basisvalues
      derivatives[deriv_num] = new_coeff0_0*basisvalue0 + new_coeff0_1*basisvalue1;
    }
    
    // Transform derivatives back to physical element
    for (unsigned int row = 0; row < num_derivatives; row++)
    {
      for (unsigned int col = 0; col < num_derivatives; col++)
      {
        values[row] += transform[row][col]*derivatives[col];
      }
    }
    // Delete pointer to array of derivatives on FIAT element
    delete [] derivatives;
    
    // Delete pointer to array of combinations of derivatives and transform
    for (unsigned int row = 0; row < num_derivatives; row++)
    {
      delete [] combinations[row];
      delete [] transform[row];
    }
    
    delete [] combinations;
    delete [] transform;
  }

  /// Evaluate order n derivatives of all basis functions at given point in cell
  virtual void evaluate_basis_derivatives_all(unsigned int n,
                                              double* values,
                                              const double* coordinates,
                                              const ufc::cell& c) const
  {
    throw std::runtime_error("The vectorised version of evaluate_basis_derivatives() is not yet implemented.");
  }

  /// Evaluate linear functional for dof i on the function f
  virtual double evaluate_dof(unsigned int i,
                              const ufc::function& f,
                              const ufc::cell& c) const
  {
    // The reference points, direction and weights:
    const static double X[2][1][1] = {{{0}}, {{1}}};
    const static double W[2][1] = {{1}, {1}};
    const static double D[2][1][1] = {{{1}}, {{1}}};
    
    const double * const * x = c.coordinates;
    double result = 0.0;
    // Iterate over the points:
    // Evaluate basis functions for affine mapping
    const double w0 = 1.0 - X[i][0][0];
    const double w1 = X[i][0][0];
    
    // Compute affine mapping y = F(X)
    double y[1];
    y[0] = w0*x[0][0] + w1*x[1][0];
    
    // Evaluate function at physical points
    double values[1];
    f.evaluate(values, y, c);
    
    // Map function values using appropriate mapping
    // Affine map: Do nothing
    
    // Note that we do not map the weights (yet).
    
    // Take directional components
    for(int k = 0; k < 1; k++)
      result += values[k]*D[i][0][k];
    // Multiply by weights 
    result *= W[i][0];
    
    return result;
  }

  /// Evaluate linear functionals for all dofs on the function f
  virtual void evaluate_dofs(double* values,
                             const ufc::function& f,
                             const ufc::cell& c) const
  {
    throw std::runtime_error("Not implemented (introduced in UFC v1.1).");
  }

  /// Interpolate vertex values from dof values
  virtual void interpolate_vertex_values(double* vertex_values,
                                         const double* dof_values,
                                         const ufc::cell& c) const
  {
    // Evaluate at vertices and use affine mapping
    vertex_values[0] = dof_values[0];
    vertex_values[1] = dof_values[1];
  }

  /// Return the number of sub elements (for a mixed element)
  virtual unsigned int num_sub_elements() const
  {
    return 1;
  }

  /// Create a new finite element for sub element i (for a mixed element)
  virtual ufc::finite_element* create_sub_element(unsigned int i) const
  {
    return new UFC_PoissonBilinearForm_finite_element_0();
  }

};

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

class UFC_PoissonBilinearForm_finite_element_1: public ufc::finite_element
{
public:

  /// Constructor
  UFC_PoissonBilinearForm_finite_element_1() : ufc::finite_element()
  {
    // Do nothing
  }

  /// Destructor
  virtual ~UFC_PoissonBilinearForm_finite_element_1()
  {
    // Do nothing
  }

  /// Return a string identifying the finite element
  virtual const char* signature() const
  {
    return "Lagrange finite element of degree 1 on a interval";
  }

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

  /// Return the dimension of the finite element function space
  virtual unsigned int space_dimension() const
  {
    return 2;
  }

  /// 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];
    
    // Get coordinates and map to the reference (UFC) element
    double x = (coordinates[0] - element_coordinates[0][0]) / J_00;
    
    // No mapping needed for 1D.
    
    // Reset values
    *values = 0;
    
    // Map degree of freedom to element degree of freedom
    const unsigned int dof = i;
    
    // Generate scalings not needed for 1D
    
    // Compute psitilde_a
    const double psitilde_a_0 = 1;
    const double psitilde_a_1 = x;
    
    // Compute basisvalues
    const double basisvalue0 = 0.707106781186548*psitilde_a_0;
    const double basisvalue1 = 1.22474487139159*psitilde_a_1;
    
    // Table(s) of coefficients
    const static double coefficients0[2][2] = \
    {{0.707106781186547, -0.408248290463863},
    {0.707106781186547, 0.408248290463863}};
    
    // Extract relevant coefficients
    const double coeff0_0 = coefficients0[dof][0];
    const double coeff0_1 = coefficients0[dof][1];
    
    // Compute value(s)
    *values = coeff0_0*basisvalue0 + coeff0_1*basisvalue1;
  }

  /// Evaluate all basis functions at given point in cell
  virtual void evaluate_basis_all(double* values,
                                  const double* coordinates,