Class representing a map (diffeomorphism) F parameterizing a 3D element by its canonical preimage. More...

#include <ElemUtil.hpp>

Inheritance diagram for moab::Element::Map:

Classes
class	ArgError
class	EvaluationError
Public Member Functions
	Map (const std::vector< CartVect > &v)
	Construct a Map defined by the given std::vector of vertices.
	Map (const unsigned int n)
	Construct a Map defined by n vertices.
virtual	~Map ()
virtual CartVect	evaluate (const CartVect &xi) const =0
	Evaluate the map on $x_i$ (calculate $\vec x = F($\vec \xi)$ )
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)
virtual bool	inside_nat_space (const CartVect &xi, double &tol) const =0
	decide if within the natural param space, with a tolerance
virtual Matrix3	jacobian (const CartVect &xi) const =0
	Evaluate the map's Jacobi matrix.
virtual Matrix3	ijacobian (const CartVect &xi) const
	Evaluate the inverse of the Jacobi matrix.
virtual double	det_jacobian (const CartVect &xi) const
	Evaluate the determinate of the Jacobi matrix.
virtual double	det_ijacobian (const CartVect &xi) const
	Evaluate the determinate of the inverse Jacobi matrix.
virtual double	evaluate_scalar_field (const CartVect &xi, const double *field_vertex_values) const =0
	Evaluate a scalar field at a point given field values at the vertices.
virtual double	integrate_scalar_field (const double *field_vertex_values) const =0
	Integrate a scalar field over the element given field values at the vertices.
unsigned int	size ()
	Size of the vertices vector.
const std::vector< CartVect > &	get_vertices ()
	Retrieve vertices.
virtual void	set_vertices (const std::vector< CartVect > &v)
	Set vertices.
virtual bool	inside_box (const CartVect &xi, double &tol) const
Protected Attributes
std::vector< CartVect >	vertex

Detailed Description

Class representing a map (diffeomorphism) F parameterizing a 3D element by its canonical preimage.

Definition at line 51 of file ElemUtil.hpp.

Constructor & Destructor Documentation

moab::Element::Map::Map ( const std::vector< CartVect > & v ) [inline]

Construct a Map defined by the given std::vector of vertices.

Definition at line 55 of file ElemUtil.hpp.

References set_vertices().

        {
            this->vertex.resize( v.size() );
            this->set_vertices( v );
        };

moab::Element::Map::Map ( const unsigned int n ) [inline]

Construct a Map defined by n vertices.

Definition at line 61 of file ElemUtil.hpp.

        {
            this->vertex = std::vector< CartVect >( n );
        };

moab::Element::Map::~Map ( ) [virtual]

Definition at line 396 of file ElemUtil.cpp.

{}

Member Function Documentation

virtual double moab::Element::Map::det_ijacobian ( const CartVect & xi ) const [inline, virtual]

Evaluate the determinate of the inverse Jacobi matrix.

Reimplemented in moab::Element::LinearTri, and moab::Element::LinearTet.

Definition at line 92 of file ElemUtil.hpp.

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

        {
            return this->jacobian( xi ).inverse().determinant();
        };

virtual double moab::Element::Map::det_jacobian ( const CartVect & xi ) const [inline, virtual]

Evaluate the determinate of the Jacobi matrix.

Reimplemented in moab::Element::LinearTri, and moab::Element::LinearTet.

Definition at line 85 of file ElemUtil.hpp.

References moab::Matrix3::determinant(), and jacobian().

Referenced by moab::Element::LinearHex::integrate_scalar_field(), moab::Element::LinearQuad::integrate_scalar_field(), and moab::Element::LinearEdge::integrate_scalar_field().

        {
            return this->jacobian( xi ).determinant();
        };

virtual CartVect moab::Element::Map::evaluate ( const CartVect & xi ) const [pure virtual]

Evaluate the map on $x_i$ (calculate $\vec x = F($\vec \xi)$ )

Implemented in moab::Element::SpectralQuad, moab::Element::LinearEdge, moab::Element::LinearTri, moab::Element::LinearQuad, moab::Element::SpectralHex, moab::Element::LinearTet, moab::Element::QuadraticHex, and moab::Element::LinearHex.

Referenced by ievaluate(), and time_forward_eval().

virtual double moab::Element::Map::evaluate_scalar_field	(	const CartVect &	xi,
		const double *	field_vertex_values
	)		const `[pure virtual]`

Evaluate a scalar field at a point given field values at the vertices.

Implemented in moab::Element::SpectralQuad, moab::Element::LinearEdge, moab::Element::LinearTri, moab::Element::LinearQuad, moab::Element::SpectralHex, moab::Element::LinearTet, moab::Element::QuadraticHex, and moab::Element::LinearHex.

Referenced by moab::Coupler::interp_field().

const std::vector< CartVect > & moab::Element::Map::get_vertices ( ) [inline]

Retrieve vertices.

Definition at line 398 of file ElemUtil.cpp.

References vertex.

    {
        return this->vertex;
    }

CartVect moab::Element::Map::ievaluate	(	const CartVect &	x,
		double	tol = `1e-6`,
		const CartVect &	x0 = `CartVect( 0.0 )`
	)		const `[virtual]`

Evaluate the inverse map (calculate $\vec \xi = F^-1($\vec x)$ to given tolerance)

Reimplemented in moab::Element::SpectralQuad, moab::Element::SphericalTri, moab::Element::LinearTri, moab::Element::SphericalQuad, moab::Element::SpectralHex, and moab::Element::LinearTet.

Definition at line 421 of file ElemUtil.cpp.

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

Referenced by moab::Coupler::nat_param(), test_hex(), test_hex_nat_coords(), and time_reverse_eval().

    {
        // TODO: should differentiate between epsilons used for
        // Newton Raphson iteration, and epsilons used for curved boundary geometry errors
        // right now, fix the tolerance used for NR
        tol                        = 1.0e-10;
        const double error_tol_sqr = tol * tol;
        double det;
        CartVect xi    = x0;
        CartVect delta = evaluate( xi ) - x;
        Matrix3 J;

        int iters = 0;
        while( delta % delta > error_tol_sqr )
        {
            if( ++iters > 10 ) throw Map::EvaluationError( x, vertex );

            J   = jacobian( xi );
            det = J.determinant();
            if( det < std::numeric_limits< double >::epsilon() ) throw Map::EvaluationError( x, vertex );
            xi -= J.inverse() * delta;
            delta = evaluate( xi ) - x;
        }
        return xi;
    }  // Map::ievaluate()

virtual Matrix3 moab::Element::Map::ijacobian ( const CartVect & xi ) const [inline, virtual]

Evaluate the inverse of the Jacobi matrix.

Reimplemented in moab::Element::LinearTri, and moab::Element::LinearTet.

Definition at line 79 of file ElemUtil.hpp.

References moab::Matrix3::inverse(), and jacobian().

        {
            return this->jacobian( xi ).inverse();
        };

bool moab::Element::Map::inside_box	(	const CartVect &	xi,
		double &	tol
	)		const `[virtual]`

Reimplemented in moab::Element::SphericalTri, and moab::Element::SphericalQuad.

Definition at line 412 of file ElemUtil.cpp.

References moab::CartVect::array(), box(), and moab::BoundBox::contains_point().

Referenced by moab::Coupler::nat_param(), test_hex(), and test_linear_tri().

    {
        // bail out early, before doing an expensive NR iteration
        // compute box
        BoundBox box( this->vertex );
        return box.contains_point( xi.array(), tol );
    }

virtual bool moab::Element::Map::inside_nat_space	(	const CartVect &	xi,
		double &	tol
	)		const `[pure virtual]`

decide if within the natural param space, with a tolerance

Implemented in moab::Element::SpectralQuad, moab::Element::LinearEdge, moab::Element::LinearTri, moab::Element::LinearQuad, moab::Element::SpectralHex, moab::Element::LinearTet, moab::Element::QuadraticHex, and moab::Element::LinearHex.

virtual double moab::Element::Map::integrate_scalar_field ( const double * field_vertex_values ) const [pure virtual]

Integrate a scalar field over the element given field values at the vertices.

Implemented in moab::Element::SpectralQuad, moab::Element::LinearEdge, moab::Element::LinearTri, moab::Element::LinearQuad, moab::Element::SpectralHex, moab::Element::LinearTet, moab::Element::QuadraticHex, and moab::Element::LinearHex.

Referenced by moab::Coupler::get_group_integ_vals(), and time_integrate().

virtual Matrix3 moab::Element::Map::jacobian ( const CartVect & xi ) const [pure virtual]

Evaluate the map's Jacobi matrix.

Implemented in moab::Element::SpectralQuad, moab::Element::LinearEdge, moab::Element::LinearTri, moab::Element::LinearQuad, moab::Element::SpectralHex, moab::Element::LinearTet, moab::Element::QuadraticHex, and moab::Element::LinearHex.

Referenced by det_ijacobian(), det_jacobian(), ievaluate(), ijacobian(), and time_jacobian().

void moab::Element::Map::set_vertices ( const std::vector< CartVect > & v ) [virtual]

Set vertices.

Reimplemented in moab::Element::LinearTri, and moab::Element::LinearTet.

Definition at line 403 of file ElemUtil.cpp.

Referenced by Map(), and test_spectral_quad().

    {
        if( v.size() != this->vertex.size() )
        {
            throw ArgError();
        }
        this->vertex = v;
    }

unsigned int moab::Element::Map::size ( ) [inline]

Size of the vertices vector.

Definition at line 103 of file ElemUtil.hpp.

        {
            return this->vertex.size();
        }

Member Data Documentation

std::vector< CartVect > moab::Element::Map::vertex [protected]

Definition at line 141 of file ElemUtil.hpp.

Referenced by get_vertices().

List of all members.

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

Classes

Public Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation