Mesh Oriented datABase  (version 5.4.1)
Array-based unstructured mesh datastructure
Public Member Functions | Static Public Member Functions | Private Types | Private Member Functions
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 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

Static Public Member Functions

typedef _Matrix Matrix

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

template<typename _Matrix>
typedef _Matrix moab::element_utility::Quadratic_hex_map< _Matrix >::Matrix [static]

Definition at line 54 of file quadratic_hex_map.hpp.

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

template<typename _Matrix>
moab::element_utility::Quadratic_hex_map< _Matrix >::Quadratic_hex_map ( ) [inline]

Definition at line 61 of file quadratic_hex_map.hpp.

{}
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

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 [inline, private]

Definition at line 169 of file quadratic_hex_map.hpp.

Referenced by moab::element_utility::Quadratic_hex_map< moab::Matrix3 >::solve_inverse().

        {
            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;
        }
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 [inline, private]

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;
        }
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 [inline, private]

Definition at line 202 of file quadratic_hex_map.hpp.

        {
            // TODO: gaussian integration , probably 2x2x2
            return 0.;
        }
template<typename _Matrix>
template<typename Point >
bool moab::element_utility::Quadratic_hex_map< _Matrix >::is_contained ( const Point &  p,
const double  tol 
) const [inline, private]

Definition at line 110 of file quadratic_hex_map.hpp.

Referenced by moab::element_utility::Quadratic_hex_map< moab::Matrix3 >::operator()().

        {
            // 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 );
        }
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 [inline, private]

Definition at line 209 of file quadratic_hex_map.hpp.

Referenced by moab::element_utility::Quadratic_hex_map< moab::Matrix3 >::solve_inverse().

        {
            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;
        }
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 );
        }
template<typename _Matrix>
double moab::element_utility::Quadratic_hex_map< _Matrix >::reference_points ( const std::size_t &  i,
const std::size_t &  j 
) const [inline, private]

Definition at line 83 of file quadratic_hex_map.hpp.

Referenced by moab::element_utility::Quadratic_hex_map< moab::Matrix3 >::evaluate(), moab::element_utility::Quadratic_hex_map< moab::Matrix3 >::evaluate_scalar_field(), and moab::element_utility::Quadratic_hex_map< moab::Matrix3 >::jacobian().

        {
            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];
        }
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 [inline, private]

Definition at line 118 of file quadratic_hex_map.hpp.

Referenced by moab::element_utility::Quadratic_hex_map< moab::Matrix3 >::operator()().

        {
            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;
        }

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