moab::ElemUtil::LinearHexMap Class Reference

Shape function for trilinear hexahedron. More...

Inheritance diagram for moab::ElemUtil::LinearHexMap:

Collaboration diagram for moab::ElemUtil::LinearHexMap:

Public Member Functions
	LinearHexMap (const CartVect *corner_coords)
virtual CartVect	center_xi () const
	Return \(\vec \xi\) corresponding to logical center of element. More...
virtual CartVect	evaluate (const CartVect &xi) const
	Evaluate mapping function (calculate \(\vec x = F($\vec \xi)\) ) More...
virtual double	evaluate_scalar_field (const CartVect &xi, const double *f_vals) const
virtual Matrix3	jacobian (const CartVect &xi) const
	Evaluate Jacobian of mapping function. More...
Public Member Functions inherited from moab::ElemUtil::VolMap
bool	solve_inverse (const CartVect &x, CartVect &xi, double tol) const
	Evaluate inverse of mapping function (calculate \(\vec \xi = F^-1($\vec x)\) ) More...

Private Attributes
const CartVect *	corners

Static Private Attributes
static const double	corner_xi [8][3]

Detailed Description

Shape function for trilinear hexahedron.

Definition at line 48 of file ElemUtil.cpp.

Constructor & Destructor Documentation

LinearHexMap()

moab::ElemUtil::LinearHexMap::LinearHexMap ( const CartVect *  corner_coords )

inline

Definition at line 51 of file ElemUtil.cpp.

: corners( corner_coords ) {}

Member Function Documentation

center_xi()

CartVect moab::ElemUtil::LinearHexMap::center_xi ( ) const

virtual

Return \(\vec \xi\) corresponding to logical center of element.

Implements moab::ElemUtil::VolMap.

Definition at line 64 of file ElemUtil.cpp.

 {
 return CartVect( 0.0 );
 }

evaluate()

CartVect moab::ElemUtil::LinearHexMap::evaluate ( const CartVect &  xi ) const

virtual

Evaluate mapping function (calculate \(\vec x = F($\vec \xi)\) )

Implements moab::ElemUtil::VolMap.

Definition at line 69 of file ElemUtil.cpp.

 {
 CartVect x( 0.0 );
 for( unsigned i = 0; i < 8; ++i )
 {
 const double N_i =
 ( 1 + xi[0] * corner_xi[i][0] ) * ( 1 + xi[1] * corner_xi[i][1] ) * ( 1 + xi[2] * corner_xi[i][2] );
 x += N_i * corners[i];
 }
 x *= 0.125;
 return x;
 }

References corner_xi, and corners.

evaluate_scalar_field()

double moab::ElemUtil::LinearHexMap::evaluate_scalar_field ( const CartVect &  xi, const double *  f_vals  ) const

virtual

Definition at line 82 of file ElemUtil.cpp.

 {
 double f( 0.0 );
 for( unsigned i = 0; i < 8; ++i )
 {
 const double N_i =
 ( 1 + xi[0] * corner_xi[i][0] ) * ( 1 + xi[1] * corner_xi[i][1] ) * ( 1 + xi[2] * corner_xi[i][2] );
 f += N_i * f_vals[i];
 }
 f *= 0.125;
 return f;
 }

References corner_xi.

Referenced by moab::ElemUtil::integrate_trilinear_hex().

jacobian()

Matrix3 moab::ElemUtil::LinearHexMap::jacobian ( const CartVect &  xi ) const

virtual

Evaluate Jacobian of mapping function.

Implements moab::ElemUtil::VolMap.

Definition at line 95 of file ElemUtil.cpp.

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

References corner_xi, and corners.

Referenced by moab::ElemUtil::integrate_trilinear_hex().

Member Data Documentation

corner_xi

const double moab::ElemUtil::LinearHexMap::corner_xi

staticprivate

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 59 of file ElemUtil.cpp.

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

corners

const CartVect* moab::ElemUtil::LinearHexMap::corners

private

Definition at line 58 of file ElemUtil.cpp.

Referenced by evaluate(), and jacobian().

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

• ElemUtil.cpp