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.

  700     {
  701         CartVect x( 0.0 );
  702         for( unsigned i = 0; i < 8; ++i )
  703         {
  704             const double N_i =
  705                 ( 1 + xi[0] * corner[i][0] ) * ( 1 + xi[1] * corner[i][1] ) * ( 1 + xi[2] * corner[i][2] );
  706             x += N_i * this->vertex[i];
  707         }
  708         x *= 0.125;
  709         return x;
  710     }  // 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.

  737     {
  738         double f( 0.0 );
  739         for( unsigned i = 0; i < 8; ++i )
  740         {
  741             const double N_i =
  742                 ( 1 + xi[0] * corner[i][0] ) * ( 1 + xi[1] * corner[i][1] ) * ( 1 + xi[2] * corner[i][2] );
  743             f += N_i * field_vertex_value[i];
  744         }
  745         f *= 0.125;
  746         return f;
  747     }  // 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.

  773     {
  774         // just look at the box+tol here
  775         return ( xi[0] >= -1. - tol ) && ( xi[0] <= 1. + tol ) && ( xi[1] >= -1. - tol ) && ( xi[1] <= 1. + tol ) &&
  776                ( xi[2] >= -1. - tol ) && ( xi[2] <= 1. + tol );
  777     }

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.

  750     {
  751         double I( 0.0 );
  752         for( unsigned int j1 = 0; j1 < this->gauss_count; ++j1 )
  753         {
  754             double x1 = this->gauss[j1][1];
  755             double w1 = this->gauss[j1][0];
  756             for( unsigned int j2 = 0; j2 < this->gauss_count; ++j2 )
  757             {
  758                 double x2 = this->gauss[j2][1];
  759                 double w2 = this->gauss[j2][0];
  760                 for( unsigned int j3 = 0; j3 < this->gauss_count; ++j3 )
  761                 {
  762                     double x3 = this->gauss[j3][1];
  763                     double w3 = this->gauss[j3][0];
  764                     CartVect x( x1, x2, x3 );
  765                     I += this->evaluate_scalar_field( x, field_vertex_values ) * w1 * w2 * w3 * this->det_jacobian( x );
  766                 }
  767             }
  768         }
  769         return I;
  770     }  // 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.

  713     {
  714         Matrix3 J( 0.0 );
  715         for( unsigned i = 0; i < 8; ++i )
  716         {
  717             const double xi_p      = 1 + xi[0] * corner[i][0];
  718             const double eta_p     = 1 + xi[1] * corner[i][1];
  719             const double zeta_p    = 1 + xi[2] * corner[i][2];
  720             const double dNi_dxi   = corner[i][0] * eta_p * zeta_p;
  721             const double dNi_deta  = corner[i][1] * xi_p * zeta_p;
  722             const double dNi_dzeta = corner[i][2] * xi_p * eta_p;
  723             J( 0, 0 ) += dNi_dxi * vertex[i][0];
  724             J( 1, 0 ) += dNi_dxi * vertex[i][1];
  725             J( 2, 0 ) += dNi_dxi * vertex[i][2];
  726             J( 0, 1 ) += dNi_deta * vertex[i][0];
  727             J( 1, 1 ) += dNi_deta * vertex[i][1];
  728             J( 2, 1 ) += dNi_deta * vertex[i][2];
  729             J( 0, 2 ) += dNi_dzeta * vertex[i][0];
  730             J( 1, 2 ) += dNi_dzeta * vertex[i][1];
  731             J( 2, 2 ) += dNi_dzeta * vertex[i][2];
  732         }
  733         return J *= 0.125;
  734     }  // 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