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.
virtual CartVect	evaluate (const CartVect &xi) const =0
	Evaluate mapping function (calculate \(\vec x = F($\vec \xi)\) )
virtual Matrix3	jacobian (const CartVect &xi) const =0
	Evaluate Jacobian of mapping function.
bool	solve_inverse (const CartVect &x, CartVect &xi, double tol) const
	Evaluate inverse of mapping function (calculate \(\vec \xi = F^-1($\vec x)\) )

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Detailed Description

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

Definition at line 16 of file ElemUtil.cpp.

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Member Function Documentation

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().

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().

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().

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.

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

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

    {
        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;
    }

List of all members.

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

• ElemUtil.cpp