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::LinearHex:

Collaboration diagram for moab::Element::LinearHex:

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

	LinearHex ()

virtual	~LinearHex ()

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 double	corner [8][3]

static const double	gauss [2][2] = { { 1.0, -0.5773502691 }, { 1.0, 0.5773502691 } }

static const unsigned int	corner_count = 8

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 146 of file ElemUtil.hpp.

Constructor & Destructor Documentation

◆ LinearHex() [1/2]

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

inline

Definition at line 149 of file ElemUtil.hpp.

149 : Map( vertices ){};

◆ LinearHex() [2/2]

moab::Element::LinearHex::LinearHex ( )

Definition at line 685 of file ElemUtil.cpp.

685 : Map( 0 ) {} // LinearHex::LinearHex()

◆ ~LinearHex()

moab::Element::LinearHex::~LinearHex ( )

virtual

Definition at line 687 of file ElemUtil.cpp.

687 {}

Member Function Documentation

◆ evaluate()

CartVect moab::Element::LinearHex::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 699 of file ElemUtil.cpp.

     {
         CartVect x( 0.0 );
         for( unsigned i = 0; i < 8; ++i )
         {
             const double N_i =
                 ( 1 + xi[0] * corner[i][0] ) * ( 1 + xi[1] * corner[i][1] ) * ( 1 + xi[2] * corner[i][2] );
             x += N_i * this->vertex[i];
         }
         x *= 0.125;
         return x;
     }  // LinearHex::evaluate

References corner.

◆ evaluate_scalar_field()

double moab::Element::LinearHex::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 736 of file ElemUtil.cpp.

     {
         double f( 0.0 );
         for( unsigned i = 0; i < 8; ++i )
         {
             const double N_i =
                 ( 1 + xi[0] * corner[i][0] ) * ( 1 + xi[1] * corner[i][1] ) * ( 1 + xi[2] * corner[i][2] );
             f += N_i * field_vertex_value[i];
         }
         f *= 0.125;
         return f;
     }  // LinearHex::evaluate_scalar_field()

References corner.

Referenced by integrate_scalar_field().

◆ inside_nat_space()

bool moab::Element::LinearHex::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 772 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(), and test_hex_nat_coords().

◆ integrate_scalar_field()

double moab::Element::LinearHex::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 749 of file ElemUtil.cpp.

     {
         double I( 0.0 );
         for( unsigned int j1 = 0; j1 < this->gauss_count; ++j1 )
         {
             double x1 = this->gauss[j1][1];
             double w1 = this->gauss[j1][0];
             for( unsigned int j2 = 0; j2 < this->gauss_count; ++j2 )
             {
                 double x2 = this->gauss[j2][1];
                 double w2 = this->gauss[j2][0];
                 for( unsigned int j3 = 0; j3 < this->gauss_count; ++j3 )
                 {
                     double x3 = this->gauss[j3][1];
                     double w3 = this->gauss[j3][0];
                     CartVect x( x1, x2, x3 );
                     I += this->evaluate_scalar_field( x, field_vertex_values ) * w1 * w2 * w3 * this->det_jacobian( x );
                 }
             }
         }
         return I;
     }  // LinearHex::integrate_scalar_field()

References moab::Element::Map::det_jacobian(), evaluate_scalar_field(), gauss, and gauss_count.

Referenced by integrate_scalar_field_test().

◆ jacobian()

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

virtual

Evaluate the map's Jacobi matrix.

Implements moab::Element::Map.

Definition at line 712 of file ElemUtil.cpp.

     {
         Matrix3 J( 0.0 );
         for( unsigned i = 0; i < 8; ++i )
         {
             const double xi_p      = 1 + xi[0] * corner[i][0];
             const double eta_p     = 1 + xi[1] * corner[i][1];
             const double zeta_p    = 1 + xi[2] * corner[i][2];
             const double dNi_dxi   = corner[i][0] * eta_p * zeta_p;
             const double dNi_deta  = corner[i][1] * xi_p * zeta_p;
             const double dNi_dzeta = corner[i][2] * xi_p * eta_p;
             J( 0, 0 ) += dNi_dxi * vertex[i][0];
             J( 1, 0 ) += dNi_dxi * vertex[i][1];
             J( 2, 0 ) += dNi_dxi * vertex[i][2];
             J( 0, 1 ) += dNi_deta * vertex[i][0];
             J( 1, 1 ) += dNi_deta * vertex[i][1];
             J( 2, 1 ) += dNi_deta * vertex[i][2];
             J( 0, 2 ) += dNi_dzeta * vertex[i][0];
             J( 1, 2 ) += dNi_dzeta * vertex[i][1];
             J( 2, 2 ) += dNi_dzeta * vertex[i][2];
         }
         return J *= 0.125;
     }  // LinearHex::jacobian()

References corner.

Member Data Documentation

◆ corner

const double moab::Element::LinearHex::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 } }

Definition at line 163 of file ElemUtil.hpp.

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

◆ corner_count

const unsigned int moab::Element::LinearHex::corner_count = 8

staticprotected

Definition at line 165 of file ElemUtil.hpp.

◆ gauss

const double moab::Element::LinearHex::gauss = { { 1.0, -0.5773502691 }, { 1.0, 0.5773502691 } }

staticprotected

Definition at line 164 of file ElemUtil.hpp.

Referenced by integrate_scalar_field().

◆ gauss_count

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

staticprotected

Definition at line 166 of file ElemUtil.hpp.

Referenced by integrate_scalar_field().

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

◆ LinearHex() [1/2]

◆ LinearHex() [2/2]

◆ ~LinearHex()

Member Function Documentation

◆ evaluate()

◆ evaluate_scalar_field()

◆ inside_nat_space()

◆ integrate_scalar_field()

◆ jacobian()

Member Data Documentation

◆ corner

◆ corner_count

◆ gauss

◆ gauss_count