moab::element_utility::Quadratic_hex_map< _Matrix > Class Template Reference

#include <quadratic_hex_map.hpp>

Inheritance diagram for moab::element_utility::Quadratic_hex_map< _Matrix >:

Public Types
typedef _Matrix	Matrix

Public Member Functions
	Quadratic_hex_map ()
	Quadratic_hex_map (const Self &f)
template<typename Moab , typename Entity_handle , typename Points , typename Point >
std::pair< bool, Point >	operator() (const Moab &, const Entity_handle &, const Points &v, const Point &p, const double tol=1.e-6) const

Private Types
typedef Quadratic_hex_map< Matrix >	Self

Private Member Functions
double	reference_points (const std::size_t &i, const std::size_t &j) const
template<typename Point >
bool	is_contained (const Point &p, const double tol) const
template<typename Point , typename Points >
bool	solve_inverse (const Point &x, Point &xi, const Points &points, const double tol=1.e-6) const
template<typename Point , typename Points >
Point &	evaluate (const Point &p, const Points &points, Point &f) const
template<typename Point , typename Field >
double	evaluate_scalar_field (const Point &p, const Field &field) const
template<typename Field , typename Points >
double	integrate_scalar_field (const Points &p, const Field &field_values) const
template<typename Point , typename Points >
Matrix &	jacobian (const Point &p, const Points &, Matrix &J) const

Detailed Description

template<typename _Matrix>
class moab::element_utility::Quadratic_hex_map< _Matrix >

Definition at line 51 of file quadratic_hex_map.hpp.

Member Typedef Documentation

Matrix

template<typename _Matrix >

typedef _Matrix moab::element_utility::Quadratic_hex_map< _Matrix >::Matrix

Definition at line 54 of file quadratic_hex_map.hpp.

Self

template<typename _Matrix >

typedef Quadratic_hex_map< Matrix > moab::element_utility::Quadratic_hex_map< _Matrix >::Self

private

Definition at line 57 of file quadratic_hex_map.hpp.

Constructor & Destructor Documentation

Quadratic_hex_map() [1/2]

template<typename _Matrix >

moab::element_utility::Quadratic_hex_map< _Matrix >::Quadratic_hex_map ( )

inline

Definition at line 61 of file quadratic_hex_map.hpp.

{}

Quadratic_hex_map() [2/2]

template<typename _Matrix >

moab::element_utility::Quadratic_hex_map< _Matrix >::Quadratic_hex_map ( const Self &  f )

inline

Definition at line 63 of file quadratic_hex_map.hpp.

{}

Member Function Documentation

evaluate()

template<typename _Matrix >

template<typename Point , typename Points >

Point& moab::element_utility::Quadratic_hex_map< _Matrix >::evaluate ( const Point &  p, const Points &  points, Point &  f  ) const

inlineprivate

Definition at line 169 of file quadratic_hex_map.hpp.

 {
 typedef typename Points::value_type Vector;
 Vector result;
 for( int i = 0; i < 3; ++i )
 {
 result[i] = 0;
 }
 for( unsigned i = 0; i < 27; ++i )
 {
 const double sh = SH( reference_points( i, 0 ), p[0] ) * SH( reference_points( i, 1 ), p[1] ) *
 SH( reference_points( i, 2 ), p[2] );
 result += sh * points[i];
 }
 for( int i = 0; i < 3; ++i )
 {
 f[i] = result[i];
 }
 return f;
 }

References moab::element_utility::Quadratic_hex_map< _Matrix >::reference_points(), and moab::Element::SH().

Referenced by moab::element_utility::Quadratic_hex_map< _Matrix >::solve_inverse().

evaluate_scalar_field()

template<typename _Matrix >

template<typename Point , typename Field >

double moab::element_utility::Quadratic_hex_map< _Matrix >::evaluate_scalar_field ( const Point &  p, const Field &  field  ) const

inlineprivate

Definition at line 190 of file quadratic_hex_map.hpp.

 {
 double x = 0.0;
 for( int i = 0; i < 27; i++ )
 {
 const double sh = SH( reference_points( i, 0 ), p[0] ) * SH( reference_points( i, 1 ), p[1] ) *
 SH( reference_points( i, 2 ), p[2] );
 x += sh * field[i];
 }
 return x;
 }

References moab::element_utility::Quadratic_hex_map< _Matrix >::reference_points(), and moab::Element::SH().

integrate_scalar_field()

template<typename _Matrix >

template<typename Field , typename Points >

double moab::element_utility::Quadratic_hex_map< _Matrix >::integrate_scalar_field ( const Points &  p, const Field &  field_values  ) const

inlineprivate

Definition at line 202 of file quadratic_hex_map.hpp.

 {
 // TODO: gaussian integration , probably 2x2x2
 return 0.;
 }

is_contained()

template<typename _Matrix >

template<typename Point >

bool moab::element_utility::Quadratic_hex_map< _Matrix >::is_contained ( const Point &  p, const double  tol  ) const

inlineprivate

Definition at line 110 of file quadratic_hex_map.hpp.

 {
 // just look at the box+tol here
 return ( p[0] >= -1. - tol ) && ( p[0] <= 1. + tol ) && ( p[1] >= -1. - tol ) && ( p[1] <= 1. + tol ) &&
 ( p[2] >= -1. - tol ) && ( p[2] <= 1. + tol );
 }

Referenced by moab::element_utility::Quadratic_hex_map< _Matrix >::operator()().

jacobian()

template<typename _Matrix >

template<typename Point , typename Points >

Matrix& moab::element_utility::Quadratic_hex_map< _Matrix >::jacobian ( const Point &  p, const Points &  , Matrix &  J  ) const

inlineprivate

Definition at line 209 of file quadratic_hex_map.hpp.

 {
 J = Matrix( 0.0 );
 for( int i = 0; i < 27; i++ )
 {
 const double sh[3] = { SH( reference_points( i, 0 ), p[0] ), SH( reference_points( i, 1 ), p[1] ),
 SH( reference_points( i, 2 ), p[2] ) };
 const double dsh[3] = { DSH( reference_points( i, 0 ), p[0] ), DSH( reference_points( i, 1 ), p[1] ),
 DSH( reference_points( i, 2 ), p[2] ) };
 for( int j = 0; j < 3; j++ )
 {
 // dxj/dr first column
 J( j, 0 ) += dsh[0] * sh[1] * sh[2] * reference_points( i, j );
 J( j, 1 ) += sh[0] * dsh[1] * sh[2] * reference_points( i, j ); // dxj/ds
 J( j, 2 ) += sh[0] * sh[1] * dsh[2] * reference_points( i, j ); // dxj/dt
 }
 }
 return J;
 }

References moab::Element::DSH(), moab::element_utility::Quadratic_hex_map< _Matrix >::reference_points(), and moab::Element::SH().

Referenced by moab::element_utility::Quadratic_hex_map< _Matrix >::solve_inverse().

operator()()

template<typename _Matrix >

template<typename Moab , typename Entity_handle , typename Points , typename Point >

std::pair< bool, Point > moab::element_utility::Quadratic_hex_map< _Matrix >::operator() ( const Moab &  , const Entity_handle &  , const Points &  v, const Point &  p, const double  tol = 1.e-6  ) const

inline

Definition at line 68 of file quadratic_hex_map.hpp.

 {
 Point result( 3, 0.0 );
 bool point_found = solve_inverse( p, result, v, tol ) && is_contained( result, tol );
 return std::make_pair( point_found, result );
 }

References moab::element_utility::Quadratic_hex_map< _Matrix >::is_contained(), and moab::element_utility::Quadratic_hex_map< _Matrix >::solve_inverse().

reference_points()

template<typename _Matrix >

double moab::element_utility::Quadratic_hex_map< _Matrix >::reference_points ( const std::size_t &  i, const std::size_t &  j  ) const

inlineprivate

Definition at line 83 of file quadratic_hex_map.hpp.

 {
 const double rpts[27][3] = { { -1, -1, -1 }, { 1, -1, -1 }, { 1, 1, -1 }, // reference_points nodes: 0-7
 { -1, 1, -1 }, // mid-edge nodes: 8-19
 { -1, -1, 1 }, // center-face nodes 20-25 center node 26
 { 1, -1, 1 }, //
 { 1, 1, 1 }, { -1, 1, 1 }, // 4 ----- 19 ----- 7
 { 0, -1, -1 }, // . | . |
 { 1, 0, -1 }, // 16 25 18 |
 { 0, 1, -1 }, // . | . |
 { -1, 0, -1 }, // 5 ----- 17 ----- 6 |
 { -1, -1, 0 }, // | 12 | 23 15
 { 1, -1, 0 }, // | | |
 { 1, 1, 0 }, // | 20 | 26 | 22 |
 { -1, 1, 0 }, // | | |
 { 0, -1, 1 }, // 13 21 | 14 |
 { 1, 0, 1 }, // | 0 ----- 11 ----- 3
 { 0, 1, 1 }, // | . | .
 { -1, 0, 1 }, // | 8 24 | 10
 { 0, -1, 0 }, // | . | .
 { 1, 0, 0 }, // 1 ----- 9 ----- 2
 { 0, 1, 0 }, //
 { -1, 0, 0 }, { 0, 0, -1 }, { 0, 0, 1 }, { 0, 0, 0 } };
 return rpts[i][j];
 }

Referenced by moab::element_utility::Quadratic_hex_map< _Matrix >::evaluate(), moab::element_utility::Quadratic_hex_map< _Matrix >::evaluate_scalar_field(), and moab::element_utility::Quadratic_hex_map< _Matrix >::jacobian().

solve_inverse()

template<typename _Matrix >

template<typename Point , typename Points >

bool moab::element_utility::Quadratic_hex_map< _Matrix >::solve_inverse ( const Point &  x, Point &  xi, const Points &  points, const double  tol = 1.e-6  ) const

inlineprivate

Definition at line 118 of file quadratic_hex_map.hpp.

 {
 const double error_tol_sqr = tol * tol;
 Point delta( 3, 0.0 );
 xi = delta;
 evaluate( xi, points, delta );
 vec_subtract( delta, x );
 std::size_t num_iterations = 0;
#ifdef QUADRATIC_HEX_DEBUG
 std::stringstream ss;
 ss << "Point: ";
 ss << x[0] << ", " << x[1] << ", " << x[2] << std::endl;
 ss << "Hex: ";
 for( int i = 0; i < 8; ++i )
 {
 ss << points[i][0] << ", " << points[i][1] << ", " << points[i][2] << std::endl;
 }
 ss << std::endl;
#endif
 while( normsq( delta ) > error_tol_sqr )
 {
#ifdef QUADRATIC_HEX_DEBUG
 ss << "Iter #: " << num_iterations << " Err: " << sqrt( normsq( delta ) ) << " Iterate: ";
 ss << xi[0] << ", " << xi[1] << ", " << xi[2] << std::endl;
#endif
 if( ++num_iterations >= 5 )
 {
 return false;
 }
 Matrix J;
 jacobian( xi, points, J );
 double det = moab::Matrix::determinant3( J );
 if( fabs( det ) < 1.e-10 )
 {
#ifdef QUADRATIC_HEX_DEBUG
 std::cerr << ss.str();
#endif
#ifndef QUADRATIC_HEX_DEBUG
 std::cerr << x[0] << ", " << x[1] << ", " << x[2] << std::endl;
#endif
 std::cerr << "inverse solve failure: det: " << det << std::endl;
 exit( -1 );
 }
 vec_subtract( xi, moab::Matrix::inverse( J, 1.0 / det ) * delta );
 evaluate( xi, points, delta );
 vec_subtract( delta, x );
 }
 return true;
 }

References moab::element_utility::Quadratic_hex_map< _Matrix >::evaluate(), moab::Matrix::inverse(), and moab::element_utility::Quadratic_hex_map< _Matrix >::jacobian().

Referenced by moab::element_utility::Quadratic_hex_map< _Matrix >::operator()().

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The documentation for this class was generated from the following file:

• quadratic_hex_map.hpp