Shape function space for trilinear hexahedron, obtained by a pushforward of the canonical linear (affine) functions. More...

#include <ElemUtil.hpp>

Inheritance diagram for moab::Element::QuadraticHex:

Collaboration diagram for moab::Element::QuadraticHex:

Public Member Functions
	QuadraticHex (const std::vector< CartVect > &vertices)

	QuadraticHex ()

virtual	~QuadraticHex ()

virtual CartVect	evaluate (const CartVect &xi) const
	Evaluate the map on $x_i$ (calculate $\vec x = F($\vec \xi)$ ) More...

virtual bool	inside_nat_space (const CartVect &xi, double &tol) const
	decide if within the natural param space, with a tolerance More...

virtual Matrix3	jacobian (const CartVect &xi) const
	Evaluate the map's Jacobi matrix. More...

virtual double	evaluate_scalar_field (const CartVect &xi, const double *field_vertex_values) const
	Evaluate a scalar field at a point given field values at the vertices. More...

virtual double	integrate_scalar_field (const double *field_vertex_values) const
	Integrate a scalar field over the element given field values at the vertices. More...

Public Member Functions inherited from moab::Element::Map
	Map (const std::vector< CartVect > &v)
	Construct a Map defined by the given std::vector of vertices. More...

	Map (const unsigned int n)
	Construct a Map defined by n vertices. More...

virtual	~Map ()

virtual CartVect	ievaluate (const CartVect &x, double tol=1e-6, const CartVect &x0=CartVect(0.0)) const
	Evaluate the inverse map (calculate $\vec \xi = F^-1($\vec x)$ to given tolerance) More...

virtual Matrix3	ijacobian (const CartVect &xi) const
	Evaluate the inverse of the Jacobi matrix. More...

virtual double	det_jacobian (const CartVect &xi) const
	Evaluate the determinate of the Jacobi matrix. More...

virtual double	det_ijacobian (const CartVect &xi) const
	Evaluate the determinate of the inverse Jacobi matrix. More...

unsigned int	size ()
	Size of the vertices vector. More...

const std::vector< CartVect > &	get_vertices ()
	Retrieve vertices. More...

virtual void	set_vertices (const std::vector< CartVect > &v)
	Set vertices. More...

virtual bool	inside_box (const CartVect &xi, double &tol) const

Static Protected Attributes
static const int	corner [27][3]

static const double	gauss [8][2]

static const unsigned int	corner_count = 27

static const unsigned int	gauss_count = 2

Additional Inherited Members
Protected Attributes inherited from moab::Element::Map
std::vector< CartVect >	vertex

Detailed Description

Shape function space for trilinear hexahedron, obtained by a pushforward of the canonical linear (affine) functions.

Definition at line 172 of file ElemUtil.hpp.

Constructor & Destructor Documentation

◆ QuadraticHex() [1/2]

moab::Element::QuadraticHex::QuadraticHex ( const std::vector< CartVect > & vertices )

inline

Definition at line 175 of file ElemUtil.hpp.

175 : Map( vertices ){};

◆ QuadraticHex() [2/2]

moab::Element::QuadraticHex::QuadraticHex ( )

Definition at line 804 of file ElemUtil.cpp.

804 : Map( 0 ) {}

◆ ~QuadraticHex()

moab::Element::QuadraticHex::~QuadraticHex ( )

virtual

Definition at line 806 of file ElemUtil.cpp.

806 {}

Member Function Documentation

◆ evaluate()

CartVect moab::Element::QuadraticHex::evaluate ( const CartVect & xi ) const

virtual

Evaluate the map on $x_i$ (calculate $\vec x = F($\vec \xi)$ )

Implements moab::Element::Map.

Definition at line 836 of file ElemUtil.cpp.

     {
  
         CartVect x( 0.0 );
         for( int i = 0; i < 27; i++ )
         {
             const double sh = SH( corner[i][0], xi[0] ) * SH( corner[i][1], xi[1] ) * SH( corner[i][2], xi[2] );
             x += sh * vertex[i];
         }
  
         return x;
     }

References corner, and moab::Element::SH().

◆ evaluate_scalar_field()

double moab::Element::QuadraticHex::evaluate_scalar_field	(	const CartVect &	xi,
		const double *	field_vertex_values
	)		const

virtual

Evaluate a scalar field at a point given field values at the vertices.

Implements moab::Element::Map.

Definition at line 874 of file ElemUtil.cpp.

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

References corner, and moab::Element::SH().

◆ inside_nat_space()

bool moab::Element::QuadraticHex::inside_nat_space	(	const CartVect &	xi,
		double &	tol
	)		const

virtual

decide if within the natural param space, with a tolerance

Implements moab::Element::Map.

Definition at line 849 of file ElemUtil.cpp.

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

Referenced by moab::Coupler::nat_param().

◆ integrate_scalar_field()

double moab::Element::QuadraticHex::integrate_scalar_field ( const double * field_vertex_values ) const

virtual

Integrate a scalar field over the element given field values at the vertices.

Implements moab::Element::Map.

Definition at line 885 of file ElemUtil.cpp.

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

◆ jacobian()

Matrix3 moab::Element::QuadraticHex::jacobian ( const CartVect & xi ) const

virtual

Evaluate the map's Jacobi matrix.

Implements moab::Element::Map.

Definition at line 855 of file ElemUtil.cpp.

     {
         Matrix3 J( 0.0 );
         for( int i = 0; i < 27; i++ )
         {
             const double sh[3]  = { SH( corner[i][0], xi[0] ), SH( corner[i][1], xi[1] ), SH( corner[i][2], xi[2] ) };
             const double dsh[3] = { DSH( corner[i][0], xi[0] ), DSH( corner[i][1], xi[1] ),
                                     DSH( corner[i][2], xi[2] ) };
  
             for( int j = 0; j < 3; j++ )
             {
                 J( j, 0 ) += dsh[0] * sh[1] * sh[2] * vertex[i][j];  // dxj/dr first column
                 J( j, 1 ) += sh[0] * dsh[1] * sh[2] * vertex[i][j];  // dxj/ds
                 J( j, 2 ) += sh[0] * sh[1] * dsh[2] * vertex[i][j];  // dxj/dt
             }
         }
  
         return J;
     }

References corner, moab::Element::DSH(), and moab::Element::SH().

Member Data Documentation

◆ corner

const int moab::Element::QuadraticHex::corner

staticprotected

Initial value:

= {
        { -1, -1, -1 }, { 1, -1, -1 }, { 1, 1, -1 },  
        { -1, 1, -1 },                                
        { -1, -1, 1 },                                
        { 1, -1, 1 },                                 
        { 1, 1, 1 },    { -1, 1, 1 },                 
        { 0, -1, -1 },                                
        { 1, 0, -1 },                                 
        { 0, 1, -1 },                                 
        { -1, 0, -1 },                                
        { -1, -1, 0 },                                
        { 1, -1, 0 },                                 
        { 1, 1, 0 },                                  
        { -1, 1, 0 },                                 
        { 0, -1, 1 },                                 
        { 1, 0, 1 },                                  
        { 0, 1, 1 },                                  
        { -1, 0, 1 },                                 
        { 0, -1, 0 },                                 
        { 1, 0, 0 },                                  
        { 0, 1, 0 },                                  
        { -1, 0, 0 },   { 0, 0, -1 },  { 0, 0, 1 },  { 0, 0, 0 } }

Definition at line 189 of file ElemUtil.hpp.

Referenced by evaluate(), evaluate_scalar_field(), and jacobian().

◆ corner_count

const unsigned int moab::Element::QuadraticHex::corner_count = 27

staticprotected

Definition at line 191 of file ElemUtil.hpp.

◆ gauss

const double moab::Element::QuadraticHex::gauss[8][2]

staticprotected

Definition at line 190 of file ElemUtil.hpp.

◆ gauss_count

const unsigned int moab::Element::QuadraticHex::gauss_count = 2

staticprotected

Definition at line 192 of file ElemUtil.hpp.

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

Public Member Functions

Static Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ QuadraticHex() [1/2]

◆ QuadraticHex() [2/2]

◆ ~QuadraticHex()

Member Function Documentation

◆ evaluate()

◆ evaluate_scalar_field()

◆ inside_nat_space()

◆ integrate_scalar_field()

◆ jacobian()

Member Data Documentation

◆ corner

◆ corner_count

◆ gauss

◆ gauss_count