/usr/include/dolfin/ale/Poisson3D.h is in libdolfin1.0-dev 1.0.0-1.
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// and was automatically generated by FFC version 1.0.0.
//
// This code was generated with the option '-l dolfin' and
// contains DOLFIN-specific wrappers that depend on DOLFIN.
//
// This code was generated with the following parameters:
//
// cache_dir: ''
// convert_exceptions_to_warnings: False
// cpp_optimize: False
// cpp_optimize_flags: '-O2'
// epsilon: 1e-14
// error_control: False
// form_postfix: True
// format: 'dolfin'
// log_level: 10
// log_prefix: ''
// no_ferari: True
// optimize: True
// output_dir: '.'
// precision: 15
// quadrature_degree: 'auto'
// quadrature_rule: 'auto'
// representation: 'auto'
// split: False
// swig_binary: 'swig'
// swig_path: ''
#ifndef __POISSON3D_H
#define __POISSON3D_H
#include <cmath>
#include <stdexcept>
#include <fstream>
#include <ufc.h>
/// This class defines the interface for a finite element.
class poisson3d_finite_element_0: public ufc::finite_element
{
public:
/// Constructor
poisson3d_finite_element_0() : ufc::finite_element()
{
// Do nothing
}
/// Destructor
virtual ~poisson3d_finite_element_0()
{
// Do nothing
}
/// Return a string identifying the finite element
virtual const char* signature() const
{
return "FiniteElement('Lagrange', Cell('tetrahedron', Space(3)), 1, None)";
}
/// Return the cell shape
virtual ufc::shape cell_shape() const
{
return ufc::tetrahedron;
}
/// Return the topological dimension of the cell shape
virtual unsigned int topological_dimension() const
{
return 3;
}
/// Return the geometric dimension of the cell shape
virtual unsigned int geometric_dimension() const
{
return 3;
}
/// Return the dimension of the finite element function space
virtual unsigned int space_dimension() const
{
return 4;
}
/// 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 * 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_02 = x[3][0] - x[0][0];
const double J_10 = x[1][1] - x[0][1];
const double J_11 = x[2][1] - x[0][1];
const double J_12 = x[3][1] - x[0][1];
const double J_20 = x[1][2] - x[0][2];
const double J_21 = x[2][2] - x[0][2];
const double J_22 = x[3][2] - x[0][2];
// Compute sub determinants
const double d_00 = J_11*J_22 - J_12*J_21;
const double d_01 = J_12*J_20 - J_10*J_22;
const double d_02 = J_10*J_21 - J_11*J_20;
const double d_10 = J_02*J_21 - J_01*J_22;
const double d_11 = J_00*J_22 - J_02*J_20;
const double d_12 = J_01*J_20 - J_00*J_21;
const double d_20 = J_01*J_12 - J_02*J_11;
const double d_21 = J_02*J_10 - J_00*J_12;
const double d_22 = J_00*J_11 - J_01*J_10;
// Compute determinant of Jacobian
double detJ = J_00*d_00 + J_10*d_10 + J_20*d_20;
// Compute inverse of Jacobian
// Compute constants
const double C0 = x[3][0] + x[2][0] + x[1][0] - x[0][0];
const double C1 = x[3][1] + x[2][1] + x[1][1] - x[0][1];
const double C2 = x[3][2] + x[2][2] + x[1][2] - x[0][2];
// Get coordinates and map to the reference (FIAT) element
double X = (d_00*(2.0*coordinates[0] - C0) + d_10*(2.0*coordinates[1] - C1) + d_20*(2.0*coordinates[2] - C2)) / detJ;
double Y = (d_01*(2.0*coordinates[0] - C0) + d_11*(2.0*coordinates[1] - C1) + d_21*(2.0*coordinates[2] - C2)) / detJ;
double Z = (d_02*(2.0*coordinates[0] - C0) + d_12*(2.0*coordinates[1] - C1) + d_22*(2.0*coordinates[2] - C2)) / detJ;
// Reset values.
*values = 0.0;
switch (i)
{
case 0:
{
// Array of basisvalues.
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
// Declare helper variables.
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
// Compute basisvalues.
basisvalues[0] = 1.0;
basisvalues[1] = tmp0;
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
basisvalues[0] *= std::sqrt(0.75);
basisvalues[3] *= std::sqrt(1.25);
basisvalues[2] *= std::sqrt(2.5);
basisvalues[1] *= std::sqrt(7.5);
// Table(s) of coefficients.
static const double coefficients0[4] = \
{0.288675134594813, -0.182574185835055, -0.105409255338946, -0.074535599249993};
// Compute value(s).
for (unsigned int r = 0; r < 4; r++)
{
*values += coefficients0[r]*basisvalues[r];
}// end loop over 'r'
break;
}
case 1:
{
// Array of basisvalues.
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
// Declare helper variables.
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
// Compute basisvalues.
basisvalues[0] = 1.0;
basisvalues[1] = tmp0;
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
basisvalues[0] *= std::sqrt(0.75);
basisvalues[3] *= std::sqrt(1.25);
basisvalues[2] *= std::sqrt(2.5);
basisvalues[1] *= std::sqrt(7.5);
// Table(s) of coefficients.
static const double coefficients0[4] = \
{0.288675134594813, 0.182574185835055, -0.105409255338946, -0.074535599249993};
// Compute value(s).
for (unsigned int r = 0; r < 4; r++)
{
*values += coefficients0[r]*basisvalues[r];
}// end loop over 'r'
break;
}
case 2:
{
// Array of basisvalues.
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
// Declare helper variables.
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
// Compute basisvalues.
basisvalues[0] = 1.0;
basisvalues[1] = tmp0;
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
basisvalues[0] *= std::sqrt(0.75);
basisvalues[3] *= std::sqrt(1.25);
basisvalues[2] *= std::sqrt(2.5);
basisvalues[1] *= std::sqrt(7.5);
// Table(s) of coefficients.
static const double coefficients0[4] = \
{0.288675134594813, 0.0, 0.210818510677892, -0.074535599249993};
// Compute value(s).
for (unsigned int r = 0; r < 4; r++)
{
*values += coefficients0[r]*basisvalues[r];
}// end loop over 'r'
break;
}
case 3:
{
// Array of basisvalues.
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
// Declare helper variables.
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
// Compute basisvalues.
basisvalues[0] = 1.0;
basisvalues[1] = tmp0;
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
basisvalues[0] *= std::sqrt(0.75);
basisvalues[3] *= std::sqrt(1.25);
basisvalues[2] *= std::sqrt(2.5);
basisvalues[1] *= std::sqrt(7.5);
// Table(s) of coefficients.
static const double coefficients0[4] = \
{0.288675134594813, 0.0, 0.0, 0.223606797749979};
// Compute value(s).
for (unsigned int r = 0; r < 4; r++)
{
*values += coefficients0[r]*basisvalues[r];
}// end loop over 'r'
break;
}
}
}
/// Evaluate all basis functions at given point in cell
virtual void evaluate_basis_all(double* values,
const double* coordinates,
const ufc::cell& c) const
{
// Helper variable to hold values of a single dof.
double dof_values = 0.0;
// Loop dofs and call evaluate_basis.
for (unsigned int r = 0; r < 4; r++)
{
evaluate_basis(r, &dof_values, coordinates, c);
values[r] = dof_values;
}// end loop over 'r'
}
/// 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 * 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_02 = x[3][0] - x[0][0];
const double J_10 = x[1][1] - x[0][1];
const double J_11 = x[2][1] - x[0][1];
const double J_12 = x[3][1] - x[0][1];
const double J_20 = x[1][2] - x[0][2];
const double J_21 = x[2][2] - x[0][2];
const double J_22 = x[3][2] - x[0][2];
// Compute sub determinants
const double d_00 = J_11*J_22 - J_12*J_21;
const double d_01 = J_12*J_20 - J_10*J_22;
const double d_02 = J_10*J_21 - J_11*J_20;
const double d_10 = J_02*J_21 - J_01*J_22;
const double d_11 = J_00*J_22 - J_02*J_20;
const double d_12 = J_01*J_20 - J_00*J_21;
const double d_20 = J_01*J_12 - J_02*J_11;
const double d_21 = J_02*J_10 - J_00*J_12;
const double d_22 = J_00*J_11 - J_01*J_10;
// Compute determinant of Jacobian
double detJ = J_00*d_00 + J_10*d_10 + J_20*d_20;
// Compute inverse of Jacobian
const double K_00 = d_00 / detJ;
const double K_01 = d_10 / detJ;
const double K_02 = d_20 / detJ;
const double K_10 = d_01 / detJ;
const double K_11 = d_11 / detJ;
const double K_12 = d_21 / detJ;
const double K_20 = d_02 / detJ;
const double K_21 = d_12 / detJ;
const double K_22 = d_22 / detJ;
// Compute constants
const double C0 = x[3][0] + x[2][0] + x[1][0] - x[0][0];
const double C1 = x[3][1] + x[2][1] + x[1][1] - x[0][1];
const double C2 = x[3][2] + x[2][2] + x[1][2] - x[0][2];
// Get coordinates and map to the reference (FIAT) element
double X = (d_00*(2.0*coordinates[0] - C0) + d_10*(2.0*coordinates[1] - C1) + d_20*(2.0*coordinates[2] - C2)) / detJ;
double Y = (d_01*(2.0*coordinates[0] - C0) + d_11*(2.0*coordinates[1] - C1) + d_21*(2.0*coordinates[2] - C2)) / detJ;
double Z = (d_02*(2.0*coordinates[0] - C0) + d_12*(2.0*coordinates[1] - C1) + d_22*(2.0*coordinates[2] - C2)) / detJ;
// Compute number of derivatives.
unsigned int num_derivatives = 1;
for (unsigned int r = 0; r < n; r++)
{
num_derivatives *= 3;
}// end loop over 'r'
// Declare pointer to two dimensional array that holds combinations of derivatives and initialise
unsigned int **combinations = new unsigned int *[num_derivatives];
for (unsigned int row = 0; row < num_derivatives; row++)
{
combinations[row] = new unsigned int [n];
for (unsigned int col = 0; col < n; col++)
combinations[row][col] = 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] = {{K_00, K_01, K_02}, {K_10, K_11, K_12}, {K_20, K_21, K_22}};
// 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. Assuming that values is always an array.
for (unsigned int r = 0; r < num_derivatives; r++)
{
values[r] = 0.0;
}// end loop over 'r'
switch (i)
{
case 0:
{
// Array of basisvalues.
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
// Declare helper variables.
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
// Compute basisvalues.
basisvalues[0] = 1.0;
basisvalues[1] = tmp0;
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
basisvalues[0] *= std::sqrt(0.75);
basisvalues[3] *= std::sqrt(1.25);
basisvalues[2] *= std::sqrt(2.5);
basisvalues[1] *= std::sqrt(7.5);
// Table(s) of coefficients.
static const double coefficients0[4] = \
{0.288675134594813, -0.182574185835055, -0.105409255338946, -0.074535599249993};
// Tables of derivatives of the polynomial base (transpose).
static const double dmats0[4][4] = \
{{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}};
static const double dmats1[4][4] = \
{{0.0, 0.0, 0.0, 0.0},
{3.16227766016838, 0.0, 0.0, 0.0},
{5.47722557505166, 0.0, 0.0, 0.0},
{0.0, 0.0, 0.0, 0.0}};
static const double dmats2[4][4] = \
{{0.0, 0.0, 0.0, 0.0},
{3.16227766016838, 0.0, 0.0, 0.0},
{1.82574185835055, 0.0, 0.0, 0.0},
{5.16397779494322, 0.0, 0.0, 0.0}};
// Compute reference derivatives.
// Declare pointer to array of derivatives on FIAT element.
double *derivatives = new double[num_derivatives];
for (unsigned int r = 0; r < num_derivatives; r++)
{
derivatives[r] = 0.0;
}// end loop over 'r'
// Declare derivative matrix (of polynomial basis).
double dmats[4][4] = \
{{1.0, 0.0, 0.0, 0.0},
{0.0, 1.0, 0.0, 0.0},
{0.0, 0.0, 1.0, 0.0},
{0.0, 0.0, 0.0, 1.0}};
// Declare (auxiliary) derivative matrix (of polynomial basis).
double dmats_old[4][4] = \
{{1.0, 0.0, 0.0, 0.0},
{0.0, 1.0, 0.0, 0.0},
{0.0, 0.0, 1.0, 0.0},
{0.0, 0.0, 0.0, 1.0}};
// Loop possible derivatives.
for (unsigned int r = 0; r < num_derivatives; r++)
{
// Resetting dmats values to compute next derivative.
for (unsigned int t = 0; t < 4; t++)
{
for (unsigned int u = 0; u < 4; u++)
{
dmats[t][u] = 0.0;
if (t == u)
{
dmats[t][u] = 1.0;
}
}// end loop over 'u'
}// end loop over 't'
// Looping derivative order to generate dmats.
for (unsigned int s = 0; s < n; s++)
{
// Updating dmats_old with new values and resetting dmats.
for (unsigned int t = 0; t < 4; t++)
{
for (unsigned int u = 0; u < 4; u++)
{
dmats_old[t][u] = dmats[t][u];
dmats[t][u] = 0.0;
}// end loop over 'u'
}// end loop over 't'
// Update dmats using an inner product.
if (combinations[r][s] == 0)
{
for (unsigned int t = 0; t < 4; t++)
{
for (unsigned int u = 0; u < 4; u++)
{
for (unsigned int tu = 0; tu < 4; tu++)
{
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
}// end loop over 'tu'
}// end loop over 'u'
}// end loop over 't'
}
if (combinations[r][s] == 1)
{
for (unsigned int t = 0; t < 4; t++)
{
for (unsigned int u = 0; u < 4; u++)
{
for (unsigned int tu = 0; tu < 4; tu++)
{
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
}// end loop over 'tu'
}// end loop over 'u'
}// end loop over 't'
}
if (combinations[r][s] == 2)
{
for (unsigned int t = 0; t < 4; t++)
{
for (unsigned int u = 0; u < 4; u++)
{
for (unsigned int tu = 0; tu < 4; tu++)
{
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
}// end loop over 'tu'
}// end loop over 'u'
}// end loop over 't'
}
}// end loop over 's'
for (unsigned int s = 0; s < 4; s++)
{
for (unsigned int t = 0; t < 4; t++)
{
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
}// end loop over 't'
}// end loop over 's'
}// end loop over 'r'
// Transform derivatives back to physical element
for (unsigned int r = 0; r < num_derivatives; r++)
{
for (unsigned int s = 0; s < num_derivatives; s++)
{
values[r] += transform[r][s]*derivatives[s];
}// end loop over 's'
}// end loop over 'r'
// Delete pointer to array of derivatives on FIAT element
delete [] derivatives;
// Delete pointer to array of combinations of derivatives and transform
for (unsigned int r = 0; r < num_derivatives; r++)
{
delete [] combinations[r];
}// end loop over 'r'
delete [] combinations;
for (unsigned int r = 0; r < num_derivatives; r++)
{
delete [] transform[r];
}// end loop over 'r'
delete [] transform;
break;
}
case 1:
{
// Array of basisvalues.
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
// Declare helper variables.
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
// Compute basisvalues.
basisvalues[0] = 1.0;
basisvalues[1] = tmp0;
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
basisvalues[0] *= std::sqrt(0.75);
basisvalues[3] *= std::sqrt(1.25);
basisvalues[2] *= std::sqrt(2.5);
basisvalues[1] *= std::sqrt(7.5);
// Table(s) of coefficients.
static const double coefficients0[4] = \
{0.288675134594813, 0.182574185835055, -0.105409255338946, -0.074535599249993};
// Tables of derivatives of the polynomial base (transpose).
static const double dmats0[4][4] = \
{{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}};
static const double dmats1[4][4] = \
{{0.0, 0.0, 0.0, 0.0},
{3.16227766016838, 0.0, 0.0, 0.0},
{5.47722557505166, 0.0, 0.0, 0.0},
{0.0, 0.0, 0.0, 0.0}};
static const double dmats2[4][4] = \
{{0.0, 0.0, 0.0, 0.0},
{3.16227766016838, 0.0, 0.0, 0.0},
{1.82574185835055, 0.0, 0.0, 0.0},
{5.16397779494322, 0.0, 0.0, 0.0}};
// Compute reference derivatives.
// Declare pointer to array of derivatives on FIAT element.
double *derivatives = new double[num_derivatives];
for (unsigned int r = 0; r < num_derivatives; r++)
{
derivatives[r] = 0.0;
}// end loop over 'r'
// Declare derivative matrix (of polynomial basis).
double dmats[4][4] = \
{{1.0, 0.0, 0.0, 0.0},
{0.0, 1.0, 0.0, 0.0},
{0.0, 0.0, 1.0, 0.0},
{0.0, 0.0, 0.0, 1.0}};
// Declare (auxiliary) derivative matrix (of polynomial basis).
double dmats_old[4][4] = \
{{1.0, 0.0, 0.0, 0.0},
{0.0, 1.0, 0.0, 0.0},
{0.0, 0.0, 1.0, 0.0},
{0.0, 0.0, 0.0, 1.0}};
// Loop possible derivatives.
for (unsigned int r = 0; r < num_derivatives; r++)
{
// Resetting dmats values to compute next derivative.
for (unsigned int t = 0; t < 4; t++)
{
for (unsigned int u = 0; u < 4; u++)
{
dmats[t][u] = 0.0;
if (t == u)
{
dmats[t][u] = 1.0;
}
}// end loop over 'u'
}// end loop over 't'
// Looping derivative order to generate dmats.
for (unsigned int s = 0; s < n; s++)
{
// Updating dmats_old with new values and resetting dmats.
for (unsigned int t = 0; t < 4; t++)
{
for (unsigned int u = 0; u < 4; u++)
{
dmats_old[t][u] = dmats[t][u];
dmats[t][u] = 0.0;
}// end loop over 'u'
}// end loop over 't'
// Update dmats using an inner product.
if (combinations[r][s] == 0)
{
for (unsigned int t = 0; t < 4; t++)
{
for (unsigned int u = 0; u < 4; u++)
{
for (unsigned int tu = 0; tu < 4; tu++)
{
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
}// end loop over 'tu'
}// end loop over 'u'
}// end loop over 't'
}
if (combinations[r][s] == 1)
{
for (unsigned int t = 0; t < 4; t++)
{
for (unsigned int u = 0; u < 4; u++)
{
for (unsigned int tu = 0; tu < 4; tu++)
{
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
}// end loop over 'tu'
}// end loop over 'u'
}// end loop over 't'
}
if (combinations[r][s] == 2)
{
for (unsigned int t = 0; t < 4; t++)
{
for (unsigned int u = 0; u < 4; u++)
{
for (unsigned int tu = 0; tu < 4; tu++)
{
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
}// end loop over 'tu'
}// end loop over 'u'
}// end loop over 't'
}
}// end loop over 's'
for (unsigned int s = 0; s < 4; s++)
{
for (unsigned int t = 0; t < 4; t++)
{
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
}// end loop over 't'
}// end loop over 's'
}// end loop over 'r'
// Transform derivatives back to physical element
for (unsigned int r = 0; r < num_derivatives; r++)
{
for (unsigned int s = 0; s < num_derivatives; s++)
{
values[r] += transform[r][s]*derivatives[s];
}// end loop over 's'
}// end loop over 'r'
// Delete pointer to array of derivatives on FIAT element
delete [] derivatives;
// Delete pointer to array of combinations of derivatives and transform
for (unsigned int r = 0; r < num_derivatives; r++)
{
delete [] combinations[r];
}// end loop over 'r'
delete [] combinations;
for (unsigned int r = 0; r < num_derivatives; r++)
{
delete [] transform[r];
}// end loop over 'r'
delete [] transform;
break;
}
case 2:
{
// Array of basisvalues.
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
// Declare helper variables.
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
// Compute basisvalues.
basisvalues[0] = 1.0;
basisvalues[1] = tmp0;
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
basisvalues[0] *= std::sqrt(0.75);
basisvalues[3] *= std::sqrt(1.25);
basisvalues[2] *= std::sqrt(2.5);
basisvalues[1] *= std::sqrt(7.5);
// Table(s) of coefficients.
static const double coefficients0[4] = \
{0.288675134594813, 0.0, 0.210818510677892, -0.074535599249993};
// Tables of derivatives of the polynomial base (transpose).
static const double dmats0[4][4] = \
{{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}};
static const double dmats1[4][4] = \
{{0.0, 0.0, 0.0, 0.0},
{3.16227766016838, 0.0, 0.0, 0.0},
{5.47722557505166, 0.0, 0.0, 0.0},
{0.0, 0.0, 0.0, 0.0}};
static const double dmats2[4][4] = \
{{0.0, 0.0, 0.0, 0.0},
{3.16227766016838, 0.0, 0.0, 0.0},
{1.82574185835055, 0.0, 0.0, 0.0},
{5.16397779494322, 0.0, 0.0, 0.0}};
// Compute reference derivatives.
// Declare pointer to array of derivatives on FIAT element.
double *derivatives = new double[num_derivatives];
for (unsigned int r = 0; r < num_derivatives; r++)
{
derivatives[r] = 0.0;
}// end loop over 'r'
// Declare derivative matrix (of polynomial basis).
double dmats[4][4] = \
{{1.0, 0.0, 0.0, 0.0},
{0.0, 1.0, 0.0, 0.0},
{0.0, 0.0, 1.0, 0.0},
{0.0, 0.0, 0.0, 1.0}};
// Declare (auxiliary) derivative matrix (of polynomial basis).
double dmats_old[4][4] = \
{{1.0, 0.0, 0.0, 0.0},
{0.0, 1.0, 0.0, 0.0},
{0.0, 0.0, 1.0, 0.0},
{0.0, 0.0, 0.0, 1.0}};
// Loop possible derivatives.
for (unsigned int r = 0; r < num_derivatives; r++)
{
// Resetting dmats values to compute next derivative.
for (unsigned int t = 0; t < 4; t++)
{
for (unsigned int u = 0; u < 4; u++)
{
dmats[t][u] = 0.0;
if (t == u)
{
dmats[t][u] = 1.0;
}
}// end loop over 'u'
}// end loop over 't'
// Looping derivative order to generate dmats.
for (unsigned int s = 0; s < n; s++)
{
// Updating dmats_old with new values and resetting dmats.
for (unsigned int t = 0; t < 4; t++)
{
for (unsigned int u = 0; u < 4; u++)
{
dmats_old[t][u] = dmats[t][u];
dmats[t][u] = 0.0;
}// end loop over 'u'
}// end loop over 't'
// Update dmats using an inner product.
if (combinations[r][s] == 0)
{
for (unsigned int t = 0; t < 4; t++)
{
for (unsigned int u = 0; u < 4; u++)
{
for (unsigned int tu = 0; tu < 4; tu++)
{
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
}// end loop over 'tu'
}// end loop over 'u'
}// end loop over 't'
}
if (combinations[r][s] == 1)
{
for (unsigned int t = 0; t < 4; t++)
{
for (unsigned int u = 0; u < 4; u++)
{
for (unsigned int tu = 0; tu < 4; tu++)
{
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
}// end loop over 'tu'
}// end loop over 'u'
}// end loop over 't'
}
if (combinations[r][s] == 2)
{
for (unsigned int t = 0; t < 4; t++)
{
for (unsigned int u = 0; u < 4; u++)
{
for (unsigned int tu = 0; tu < 4; tu++)
{
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
}// end loop over 'tu'
}// end loop over 'u'
}// end loop over 't'
}
}// end loop over 's'
for (unsigned int s = 0; s < 4; s++)
{
for (unsigned int t = 0; t < 4; t++)
{
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
}// end loop over 't'
}// end loop over 's'
}// end loop over 'r'
// Transform derivatives back to physical element
for (unsigned int r = 0; r < num_derivatives; r++)
{
for (unsigned int s = 0; s < num_derivatives; s++)
{
values[r] += transform[r][s]*derivatives[s];
}// end loop over 's'
}// end loop over 'r'
// Delete pointer to array of derivatives on FIAT element
delete [] derivatives;
// Delete pointer to array of combinations of derivatives and transform
for (unsigned int r = 0; r < num_derivatives; r++)
{
delete [] combinations[r];
}// end loop over 'r'
delete [] combinations;
for (unsigned int r = 0; r < num_derivatives; r++)
{
delete [] transform[r];
}// end loop over 'r'
delete [] transform;
break;
}
case 3:
{
// Array of basisvalues.
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
// Declare helper variables.
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
// Compute basisvalues.
basisvalues[0] = 1.0;
basisvalues[1] = tmp0;
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
basisvalues[0] *= std::sqrt(0.75);
basisvalues[3] *= std::sqrt(1.25);
basisvalues[2] *= std::sqrt(2.5);
basisvalues[1] *= std::sqrt(7.5);
// Table(s) of coefficients.
static const double coefficients0[4] = \
{0.288675134594813, 0.0, 0.0, 0.223606797749979};
// Tables of derivatives of the polynomial base (transpose).
static const double dmats0[4][4] = \
{{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}};
static const double dmats1[4][4] = \
{{0.0, 0.0, 0.0, 0.0},
{3.16227766016838, 0.0, 0.0, 0.0},
{5.47722557505166, 0.0, 0.0, 0.0},
{0.0, 0.0, 0.0, 0.0}};
static const double dmats2[4][4] = \
{{0.0, 0.0, 0.0, 0.0},
{3.16227766016838, 0.0, 0.0, 0.0},
{1.82574185835055, 0.0, 0.0, 0.0},
{5.16397779494322, 0.0, 0.0, 0.0}};
// Compute reference derivatives.
// Declare pointer to array of derivatives on FIAT element.
double *derivatives = new double[num_derivatives];
for (unsigned int r = 0; r < num_derivatives; r++)
{
derivatives[r] = 0.0;
}// end loop over 'r'
// Declare derivative matrix (of polynomial basis).
double dmats[4][4] = \
{{1.0, 0.0, 0.0, 0.0},
{0.0, 1.0, 0.0, 0.0},
{0.0, 0.0, 1.0, 0.0},
{0.0, 0.0, 0.0, 1.0}};
// Declare (auxiliary) derivative matrix (of polynomial basis).
double dmats_old[4][4] = \
{{1.0, 0.0, 0.0, 0.0},
{0.0, 1.0, 0.0, 0.0},
{0.0, 0.0, 1.0, 0.0},
{0.0, 0.0, 0.0, 1.0}};
// Loop possible derivatives.
for (unsigned int r = 0; r < num_derivatives; r++)
{
// Resetting dmats values to compute next derivative.
for (unsigned int t = 0; t < 4; t++)
{
for (unsigned int u = 0; u < 4; u++)
{
dmats[t][u] = 0.0;
if (t == u)
{
dmats[t][u] = 1.0;
}
}// end loop over 'u'
}// end loop over 't'
// Looping derivative order to generate dmats.
for (unsigned int s = 0; s < n; s++)
{
// Updating dmats_old with new values and resetting dmats.
for (unsigned int t = 0; t < 4; t++)
{
for (unsigned int u = 0; u < 4; u++)
{
dmats_old[t][u] = dmats[t][u];
dmats[t][u] = 0.0;
}// end loop over 'u'
}// end loop over 't'
// Update dmats using an inner product.
if (combinations[r][s] == 0)
{
for (unsigned int t = 0; t < 4; t++)
{
for (unsigned int u = 0; u < 4; u++)
{
for (unsigned int tu = 0; tu < 4; tu++)
{
dmats[t][u] += dmats0[t][tu]*dmats_old[tu][u];
}// end loop over 'tu'
}// end loop over 'u'
}// end loop over 't'
}
if (combinations[r][s] == 1)
{
for (unsigned int t = 0; t < 4; t++)
{
for (unsigned int u = 0; u < 4; u++)
{
for (unsigned int tu = 0; tu < 4; tu++)
{
dmats[t][u] += dmats1[t][tu]*dmats_old[tu][u];
}// end loop over 'tu'
}// end loop over 'u'
}// end loop over 't'
}
if (combinations[r][s] == 2)
{
for (unsigned int t = 0; t < 4; t++)
{
for (unsigned int u = 0; u < 4; u++)
{
for (unsigned int tu = 0; tu < 4; tu++)
{
dmats[t][u] += dmats2[t][tu]*dmats_old[tu][u];
}// end loop over 'tu'
}// end loop over 'u'
}// end loop over 't'
}
}// end loop over 's'
for (unsigned int s = 0; s < 4; s++)
{
for (unsigned int t = 0; t < 4; t++)
{
derivatives[r] += coefficients0[s]*dmats[s][t]*basisvalues[t];
}// end loop over 't'
}// end loop over 's'
}// end loop over 'r'
// Transform derivatives back to physical element
for (unsigned int r = 0; r < num_derivatives; r++)
{
for (unsigned int s = 0; s < num_derivatives; s++)
{
values[r] += transform[r][s]*derivatives[s];
}// end loop over 's'
}// end loop over 'r'
// Delete pointer to array of derivatives on FIAT element
delete [] derivatives;
// Delete pointer to array of combinations of derivatives and transform
for (unsigned int r = 0; r < num_derivatives; r++)
{
delete [] combinations[r];
}// end loop over 'r'
delete [] combinations;
for (unsigned int r = 0; r < num_derivatives; r++)
{
delete [] transform[r];
}// end loop over 'r'
delete [] transform;
break;
}
}
}
/// 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
{
// Compute number of derivatives.
unsigned int num_derivatives = 1;
for (unsigned int r = 0; r < n; r++)
{
num_derivatives *= 3;
}// end loop over 'r'
// Helper variable to hold values of a single dof.
double *dof_values = new double[num_derivatives];
for (unsigned int r = 0; r < num_derivatives; r++)
{
dof_values[r] = 0.0;
}// end loop over 'r'
// Loop dofs and call evaluate_basis_derivatives.
for (unsigned int r = 0; r < 4; r++)
{
evaluate_basis_derivatives(r, n, dof_values, coordinates, c);
for (unsigned int s = 0; s < num_derivatives; s++)
{
values[r*num_derivatives + s] = dof_values[s];
}// end loop over 's'
}// end loop over 'r'
// Delete pointer.
delete [] dof_values;
}
/// 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
{
// Declare variables for result of evaluation.
double vals[1];
// Declare variable for physical coordinates.
double y[3];
const double * const * x = c.coordinates;
switch (i)
{
case 0:
{
y[0] = x[0][0];
y[1] = x[0][1];
y[2] = x[0][2];
f.evaluate(vals, y, c);
return vals[0];
break;
}
case 1:
{
y[0] = x[1][0];
y[1] = x[1][1];
y[2] = x[1][2];
f.evaluate(vals, y, c);
return vals[0];
break;
}
case 2:
{
y[0] = x[2][0];
y[1] = x[2][1];
y[2] = x[2][2];
f.evaluate(vals, y, c);
return vals[0];
break;
}
case 3:
{
y[0] = x[3][0];
y[1] = x[3][1];
y[2] = x[3][2];
f.evaluate(vals, y, c);
return vals[0];
break;
}
}
return 0.0;
}
/// 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
{
// Declare variables for result of evaluation.
double vals[1];
// Declare variable for physical coordinates.
double y[3];
const double * const * x = c.coordinates;
y[0] = x[0][0];
y[1] = x[0][1];
y[2] = x[0][2];
f.evaluate(vals, y, c);
values[0] = vals[0];
y[0] = x[1][0];
y[1] = x[1][1];
y[2] = x[1][2];
f.evaluate(vals, y, c);
values[1] = vals[0];
y[0] = x[2][0];
y[1] = x[2][1];
y[2] = x[2][2];
f.evaluate(vals, y, c);
values[2] = vals[0];
y[0] = x[3][0];
y[1] = x[3][1];
y[2] = x[3][2];
f.evaluate(vals, y, c);
values[3] = vals[0];
}
/// Interpolate vertex values from dof values
virtual void interpolate_vertex_values(double* vertex_values,
const double* dof_values,
const ufc::cell& c) const
{
// Evaluate function and change variables
vertex_values[0] = dof_values[0];
vertex_values[1] = dof_values[1];
vertex_values[2] = dof_values[2];
vertex_values[3] = dof_values[3];
}
/// Map coordinate xhat from reference cell to coordinate x in cell
virtual void map_from_reference_cell(double* x,
const double* xhat,
const ufc::cell& c) const
{
throw std::runtime_error("map_from_reference_cell not yet implemented (introduced in UFC 2.0).");
}
/// Map from coordinate x in cell to coordinate xhat in reference cell
virtual void map_to_reference_cell(double* xhat,
const double* x,
const ufc::cell& c) const
{
throw std::runtime_error("map_to_reference_cell not yet implemented (introduced in UFC 2.0).");
}
/// Return the number of sub elements (for a mixed element)
virtual unsigned int num_sub_elements() const
{
return 0;
}
/// 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 0;
}
/// Create a new class instance
virtual ufc::finite_element* create() const
{
return new poisson3d_finite_element_0();
}
};
/// This class defines the interface for a local-to-global mapping of
/// degrees of freedom (dofs).
class poisson3d_dofmap_0: public ufc::dofmap
{
private:
unsigned int _global_dimension;
public:
/// Constructor
poisson3d_dofmap_0() : ufc::dofmap()
{
_global_dimension = 0;
}
/// Destructor
virtual ~poisson3d_dofmap_0()
{
// Do nothing
}
/// Return a string identifying the dofmap
virtual const char* signature() const
{
return "FFC dofmap for FiniteElement('Lagrange', Cell('tetrahedron', Space(3)), 1, None)";
}
/// Return true iff mesh entities of topological dimension d are needed
virtual bool needs_mesh_entities(unsigned int d) const
{
switch (d)
{
case 0:
{
return true;
break;
}
case 1:
{
return false;
break;
}
case 2:
{
return false;
break;
}
case 3:
{
return false;
break;
}
}
return false;
}
/// Initialize dofmap for mesh (return true iff init_cell() is needed)
virtual bool init_mesh(const ufc::mesh& m)
{
_global_dimension = m.num_entities[0];
return false;
}
/// Initialize dofmap for given cell
virtual void init_cell(const ufc::mesh& m,
const ufc::cell& c)
{
// Do nothing
}
/// Finish initialization of dofmap for cells
virtual void init_cell_finalize()
{
// Do nothing
}
/// Return the topological dimension of the associated cell shape
virtual unsigned int topological_dimension() const
{
return 3;
}
/// Return the geometric dimension of the associated cell shape
virtual unsigned int geometric_dimension() const
{
return 3;
}
/// Return the dimension of the global finite element function space
virtual unsigned int global_dimension() const
{
return _global_dimension;
}
/// Return the dimension of the local finite element function space for a cell
virtual unsigned int local_dimension(const ufc::cell& c) const
{
return 4;
}
/// Return the maximum dimension of the local finite element function space
virtual unsigned int max_local_dimension() const
{
return 4;
}
/// Return the number of dofs on each cell facet
virtual unsigned int num_facet_dofs() const
{
return 3;
}
/// Return the number of dofs associated with each cell entity of dimension d
virtual unsigned int num_entity_dofs(unsigned int d) const
{
switch (d)
{
case 0:
{
return 1;
break;
}
case 1:
{
return 0;
break;
}
case 2:
{
return 0;
break;
}
case 3:
{
return 0;
break;
}
}
return 0;
}
/// Tabulate the local-to-global mapping of dofs on a cell
virtual void tabulate_dofs(unsigned int* dofs,
const ufc::mesh& m,
const ufc::cell& c) const
{
dofs[0] = c.entity_indices[0][0];
dofs[1] = c.entity_indices[0][1];
dofs[2] = c.entity_indices[0][2];
dofs[3] = c.entity_indices[0][3];
}
/// Tabulate the local-to-local mapping from facet dofs to cell dofs
virtual void tabulate_facet_dofs(unsigned int* dofs,
unsigned int facet) const
{
switch (facet)
{
case 0:
{
dofs[0] = 1;
dofs[1] = 2;
dofs[2] = 3;
break;
}
case 1:
{
dofs[0] = 0;
dofs[1] = 2;
dofs[2] = 3;
break;
}
case 2:
{
dofs[0] = 0;
dofs[1] = 1;
dofs[2] = 3;
break;
}
case 3:
{
dofs[0] = 0;
dofs[1] = 1;
dofs[2] = 2;
break;
}
}
}
/// Tabulate the local-to-local mapping of dofs on entity (d, i)
virtual void tabulate_entity_dofs(unsigned int* dofs,
unsigned int d, unsigned int i) const
{
if (d > 3)
{
throw std::runtime_error("d is larger than dimension (3)");
}
switch (d)
{
case 0:
{
if (i > 3)
{
throw std::runtime_error("i is larger than number of entities (3)");
}
switch (i)
{
case 0:
{
dofs[0] = 0;
break;
}
case 1:
{
dofs[0] = 1;
break;
}
case 2:
{
dofs[0] = 2;
break;
}
case 3:
{
dofs[0] = 3;
break;
}
}
break;
}
case 1:
{
break;
}
case 2:
{
break;
}
case 3:
{
break;
}
}
}
/// Tabulate the coordinates of all dofs on a cell
virtual void tabulate_coordinates(double** coordinates,
const ufc::cell& c) const
{
const double * const * x = c.coordinates;
coordinates[0][0] = x[0][0];
coordinates[0][1] = x[0][1];
coordinates[0][2] = x[0][2];
coordinates[1][0] = x[1][0];
coordinates[1][1] = x[1][1];
coordinates[1][2] = x[1][2];
coordinates[2][0] = x[2][0];
coordinates[2][1] = x[2][1];
coordinates[2][2] = x[2][2];
coordinates[3][0] = x[3][0];
coordinates[3][1] = x[3][1];
coordinates[3][2] = x[3][2];
}
/// Return the number of sub dofmaps (for a mixed element)
virtual unsigned int num_sub_dofmaps() const
{
return 0;
}
/// Create a new dofmap for sub dofmap i (for a mixed element)
virtual ufc::dofmap* create_sub_dofmap(unsigned int i) const
{
return 0;
}
/// Create a new class instance
virtual ufc::dofmap* create() const
{
return new poisson3d_dofmap_0();
}
};
/// This class defines the interface for the tabulation of the cell
/// tensor corresponding to the local contribution to a form from
/// the integral over a cell.
class poisson3d_cell_integral_0_0: public ufc::cell_integral
{
public:
/// Constructor
poisson3d_cell_integral_0_0() : ufc::cell_integral()
{
// Do nothing
}
/// Destructor
virtual ~poisson3d_cell_integral_0_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
{
// Number of operations (multiply-add pairs) for Jacobian data: 32
// Number of operations (multiply-add pairs) for geometry tensor: 27
// Number of operations (multiply-add pairs) for tensor contraction: 28
// Total number of operations (multiply-add pairs): 87
// 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_02 = x[3][0] - x[0][0];
const double J_10 = x[1][1] - x[0][1];
const double J_11 = x[2][1] - x[0][1];
const double J_12 = x[3][1] - x[0][1];
const double J_20 = x[1][2] - x[0][2];
const double J_21 = x[2][2] - x[0][2];
const double J_22 = x[3][2] - x[0][2];
// Compute sub determinants
const double d_00 = J_11*J_22 - J_12*J_21;
const double d_01 = J_12*J_20 - J_10*J_22;
const double d_02 = J_10*J_21 - J_11*J_20;
const double d_10 = J_02*J_21 - J_01*J_22;
const double d_11 = J_00*J_22 - J_02*J_20;
const double d_12 = J_01*J_20 - J_00*J_21;
const double d_20 = J_01*J_12 - J_02*J_11;
const double d_21 = J_02*J_10 - J_00*J_12;
const double d_22 = J_00*J_11 - J_01*J_10;
// Compute determinant of Jacobian
double detJ = J_00*d_00 + J_10*d_10 + J_20*d_20;
// Compute inverse of Jacobian
const double K_00 = d_00 / detJ;
const double K_01 = d_10 / detJ;
const double K_02 = d_20 / detJ;
const double K_10 = d_01 / detJ;
const double K_11 = d_11 / detJ;
const double K_12 = d_21 / detJ;
const double K_20 = d_02 / detJ;
const double K_21 = d_12 / detJ;
const double K_22 = d_22 / detJ;
// Set scale factor
const double det = std::abs(detJ);
// Compute geometry tensor
const double G0_0_0 = det*(K_00*K_00 + K_01*K_01 + K_02*K_02);
const double G0_0_1 = det*(K_00*K_10 + K_01*K_11 + K_02*K_12);
const double G0_0_2 = det*(K_00*K_20 + K_01*K_21 + K_02*K_22);
const double G0_1_0 = det*(K_10*K_00 + K_11*K_01 + K_12*K_02);
const double G0_1_1 = det*(K_10*K_10 + K_11*K_11 + K_12*K_12);
const double G0_1_2 = det*(K_10*K_20 + K_11*K_21 + K_12*K_22);
const double G0_2_0 = det*(K_20*K_00 + K_21*K_01 + K_22*K_02);
const double G0_2_1 = det*(K_20*K_10 + K_21*K_11 + K_22*K_12);
const double G0_2_2 = det*(K_20*K_20 + K_21*K_21 + K_22*K_22);
// Compute element tensor
A[0] = 0.166666666666667*G0_0_0 + 0.166666666666667*G0_0_1 + 0.166666666666667*G0_0_2 + 0.166666666666667*G0_1_0 + 0.166666666666667*G0_1_1 + 0.166666666666667*G0_1_2 + 0.166666666666667*G0_2_0 + 0.166666666666667*G0_2_1 + 0.166666666666667*G0_2_2;
A[1] = -0.166666666666667*G0_0_0 - 0.166666666666667*G0_1_0 - 0.166666666666667*G0_2_0;
A[2] = -0.166666666666667*G0_0_1 - 0.166666666666667*G0_1_1 - 0.166666666666667*G0_2_1;
A[3] = -0.166666666666667*G0_0_2 - 0.166666666666667*G0_1_2 - 0.166666666666667*G0_2_2;
A[4] = -0.166666666666667*G0_0_0 - 0.166666666666667*G0_0_1 - 0.166666666666667*G0_0_2;
A[5] = 0.166666666666667*G0_0_0;
A[6] = 0.166666666666667*G0_0_1;
A[7] = 0.166666666666667*G0_0_2;
A[8] = -0.166666666666667*G0_1_0 - 0.166666666666667*G0_1_1 - 0.166666666666667*G0_1_2;
A[9] = 0.166666666666667*G0_1_0;
A[10] = 0.166666666666667*G0_1_1;
A[11] = 0.166666666666667*G0_1_2;
A[12] = -0.166666666666667*G0_2_0 - 0.166666666666667*G0_2_1 - 0.166666666666667*G0_2_2;
A[13] = 0.166666666666667*G0_2_0;
A[14] = 0.166666666666667*G0_2_1;
A[15] = 0.166666666666667*G0_2_2;
}
/// Tabulate the tensor for the contribution from a local cell
/// using the specified reference cell quadrature points/weights
virtual void tabulate_tensor(double* A,
const double * const * w,
const ufc::cell& c,
unsigned int num_quadrature_points,
const double * const * quadrature_points,
const double* quadrature_weights) const
{
throw std::runtime_error("Quadrature version of tabulate_tensor not available when using the FFC tensor representation.");
}
};
/// 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 poisson3d_form_0: public ufc::form
{
public:
/// Constructor
poisson3d_form_0() : ufc::form()
{
// Do nothing
}
/// Destructor
virtual ~poisson3d_form_0()
{
// Do nothing
}
/// Return a string identifying the form
virtual const char* signature() const
{
return "Form([Integral(IndexSum(Product(Indexed(ComponentTensor(SpatialDerivative(Argument(FiniteElement('Lagrange', Cell('tetrahedron', Space(3)), 1, None), 0), MultiIndex((Index(0),), {Index(0): 3})), MultiIndex((Index(0),), {Index(0): 3})), MultiIndex((Index(1),), {Index(1): 3})), Indexed(ComponentTensor(SpatialDerivative(Argument(FiniteElement('Lagrange', Cell('tetrahedron', Space(3)), 1, None), 1), MultiIndex((Index(2),), {Index(2): 3})), MultiIndex((Index(2),), {Index(2): 3})), MultiIndex((Index(1),), {Index(1): 3}))), MultiIndex((Index(1),), {Index(1): 3})), Measure('cell', 0, None))])";
}
/// Return the rank of the global tensor (r)
virtual unsigned int rank() const
{
return 2;
}
/// Return the number of coefficients (n)
virtual unsigned int num_coefficients() const
{
return 0;
}
/// Return the number of cell domains
virtual unsigned int num_cell_domains() const
{
return 1;
}
/// Return the number of exterior facet domains
virtual unsigned int num_exterior_facet_domains() const
{
return 0;
}
/// Return the number of interior facet domains
virtual unsigned int num_interior_facet_domains() const
{
return 0;
}
/// Create a new finite element for argument function i
virtual ufc::finite_element* create_finite_element(unsigned int i) const
{
switch (i)
{
case 0:
{
return new poisson3d_finite_element_0();
break;
}
case 1:
{
return new poisson3d_finite_element_0();
break;
}
}
return 0;
}
/// Create a new dofmap for argument function i
virtual ufc::dofmap* create_dofmap(unsigned int i) const
{
switch (i)
{
case 0:
{
return new poisson3d_dofmap_0();
break;
}
case 1:
{
return new poisson3d_dofmap_0();
break;
}
}
return 0;
}
/// Create a new cell integral on sub domain i
virtual ufc::cell_integral* create_cell_integral(unsigned int i) const
{
switch (i)
{
case 0:
{
return new poisson3d_cell_integral_0_0();
break;
}
}
return 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
// Standard library includes
#include <string>
// DOLFIN includes
#include <dolfin/common/NoDeleter.h>
#include <dolfin/fem/FiniteElement.h>
#include <dolfin/fem/DofMap.h>
#include <dolfin/fem/Form.h>
#include <dolfin/function/FunctionSpace.h>
#include <dolfin/function/GenericFunction.h>
#include <dolfin/function/CoefficientAssigner.h>
#include <dolfin/adaptivity/ErrorControl.h>
#include <dolfin/adaptivity/GoalFunctional.h>
namespace Poisson3D
{
class Form_0_FunctionSpace_0: public dolfin::FunctionSpace
{
public:
Form_0_FunctionSpace_0(const dolfin::Mesh& mesh):
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson3d_finite_element_0()))),
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new poisson3d_dofmap_0()), mesh)))
{
// Do nothing
}
Form_0_FunctionSpace_0(dolfin::Mesh& mesh):
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson3d_finite_element_0()))),
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new poisson3d_dofmap_0()), mesh)))
{
// Do nothing
}
Form_0_FunctionSpace_0(boost::shared_ptr<dolfin::Mesh> mesh):
dolfin::FunctionSpace(mesh,
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson3d_finite_element_0()))),
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new poisson3d_dofmap_0()), *mesh)))
{
// Do nothing
}
Form_0_FunctionSpace_0(boost::shared_ptr<const dolfin::Mesh> mesh):
dolfin::FunctionSpace(mesh,
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson3d_finite_element_0()))),
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new poisson3d_dofmap_0()), *mesh)))
{
// Do nothing
}
~Form_0_FunctionSpace_0()
{
}
};
class Form_0_FunctionSpace_1: public dolfin::FunctionSpace
{
public:
Form_0_FunctionSpace_1(const dolfin::Mesh& mesh):
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson3d_finite_element_0()))),
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new poisson3d_dofmap_0()), mesh)))
{
// Do nothing
}
Form_0_FunctionSpace_1(dolfin::Mesh& mesh):
dolfin::FunctionSpace(dolfin::reference_to_no_delete_pointer(mesh),
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson3d_finite_element_0()))),
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new poisson3d_dofmap_0()), mesh)))
{
// Do nothing
}
Form_0_FunctionSpace_1(boost::shared_ptr<dolfin::Mesh> mesh):
dolfin::FunctionSpace(mesh,
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson3d_finite_element_0()))),
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new poisson3d_dofmap_0()), *mesh)))
{
// Do nothing
}
Form_0_FunctionSpace_1(boost::shared_ptr<const dolfin::Mesh> mesh):
dolfin::FunctionSpace(mesh,
boost::shared_ptr<const dolfin::FiniteElement>(new dolfin::FiniteElement(boost::shared_ptr<ufc::finite_element>(new poisson3d_finite_element_0()))),
boost::shared_ptr<const dolfin::DofMap>(new dolfin::DofMap(boost::shared_ptr<ufc::dofmap>(new poisson3d_dofmap_0()), *mesh)))
{
// Do nothing
}
~Form_0_FunctionSpace_1()
{
}
};
class Form_0: public dolfin::Form
{
public:
// Constructor
Form_0(const dolfin::FunctionSpace& V1, const dolfin::FunctionSpace& V0):
dolfin::Form(2, 0)
{
_function_spaces[0] = reference_to_no_delete_pointer(V0);
_function_spaces[1] = reference_to_no_delete_pointer(V1);
_ufc_form = boost::shared_ptr<const ufc::form>(new poisson3d_form_0());
}
// Constructor
Form_0(boost::shared_ptr<const dolfin::FunctionSpace> V1, boost::shared_ptr<const dolfin::FunctionSpace> V0):
dolfin::Form(2, 0)
{
_function_spaces[0] = V0;
_function_spaces[1] = V1;
_ufc_form = boost::shared_ptr<const ufc::form>(new poisson3d_form_0());
}
// Destructor
~Form_0()
{}
/// Return the number of the coefficient with this name
virtual dolfin::uint coefficient_number(const std::string& name) const
{
dolfin::dolfin_error("generated code for class Form",
"access coeficient data",
"There are no coefficients");
return 0;
}
/// Return the name of the coefficient with this number
virtual std::string coefficient_name(dolfin::uint i) const
{
dolfin::dolfin_error("generated code for class Form",
"access coeficient data",
"There are no coefficients");
return "unnamed";
}
// Typedefs
typedef Form_0_FunctionSpace_0 TestSpace;
typedef Form_0_FunctionSpace_1 TrialSpace;
// Coefficients
};
// Class typedefs
typedef Form_0 BilinearForm;
typedef Form_0 JacobianForm;
typedef Form_0::TestSpace FunctionSpace;
}
#endif
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