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.

    {
        const double error_tol_sqr = tol * tol;
        double det;
        xi             = center_xi();
        CartVect delta = evaluate( xi ) - x;
        Matrix3 J;
        while( delta % delta > error_tol_sqr )
        {
            J   = jacobian( xi );
            det = J.determinant();
            if( det < std::numeric_limits< double >::epsilon() ) return false;
            xi -= J.inverse() * delta;
            delta = evaluate( xi ) - x;
        }
        return true;
    }

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