moab::ElemUtil::VolMap Class Reference

Class representing a 3-D mapping function (e.g. shape function for volume element) More...

Inheritance diagram for moab::ElemUtil::VolMap:

Public Member Functions
virtual CartVect	center_xi () const =0
	Return $\vec \xi$ corresponding to logical center of element. More...
virtual CartVect	evaluate (const CartVect &xi) const =0
	Evaluate mapping function (calculate $\vec x = F($\vec \xi)$ ) More...
virtual Matrix3	jacobian (const CartVect &xi) const =0
	Evaluate Jacobian of mapping function. More...
bool	solve_inverse (const CartVect &x, CartVect &xi, double tol) const
	Evaluate inverse of mapping function (calculate $\vec \xi = F^-1($\vec x)$ ) More...

Detailed Description

Class representing a 3-D mapping function (e.g. shape function for volume element)

Definition at line 16 of file ElemUtil.cpp.

Member Function Documentation

center_xi()

virtual CartVect moab::ElemUtil::VolMap::center_xi ( ) const

pure virtual

Return $\vec \xi$ corresponding to logical center of element.

Implemented in moab::ElemUtil::LinearHexMap.

Referenced by solve_inverse().

evaluate()

virtual CartVect moab::ElemUtil::VolMap::evaluate ( const CartVect &  xi ) const

pure virtual

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

Implemented in moab::ElemUtil::LinearHexMap.

Referenced by solve_inverse().

jacobian()

virtual Matrix3 moab::ElemUtil::VolMap::jacobian ( const CartVect &  xi ) const

pure virtual

Evaluate Jacobian of mapping function.

Implemented in moab::ElemUtil::LinearHexMap.

Referenced by solve_inverse().

solve_inverse()

bool moab::ElemUtil::VolMap::solve_inverse	(	const CartVect &	x,
		CartVect &	xi,
		double	tol
	)		const

Evaluate inverse of mapping function (calculate $\vec \xi = F^-1($\vec x)$ )

Definition at line 29 of file ElemUtil.cpp.

   30     {
   31         const double error_tol_sqr = tol * tol;
   32         double det;
   33         xi             = center_xi();
   34         CartVect delta = evaluate( xi ) - x;
   35         Matrix3 J;
   36         while( delta % delta > error_tol_sqr )
   37         {
   38             J   = jacobian( xi );
   39             det = J.determinant();
   40             if( det < std::numeric_limits< double >::epsilon() ) return false;
   41             xi -= J.inverse() * delta;
   42             delta = evaluate( xi ) - x;
   43         }
   44         return true;
   45     }

References center_xi(), moab::Matrix3::determinant(), evaluate(), moab::Matrix3::inverse(), and jacobian().

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

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

• ElemUtil.cpp