ug::ReferenceMapping< TRefElem, TWorldDim > Class Template Reference

#include <reference_mapping.h>

Public Member Functions
void	global_to_local (MathVector< dim > &locPos, const MathVector< worldDim > &globPos, const size_t maxIter=1000, const number tol=1e-10) const
	map global coordinate to local coordinate More...
void	global_to_local (MathVector< dim > *vLocPos, const MathVector< worldDim > *vGlobPos, size_t n, const size_t maxIter=1000, const number tol=1e-10) const
	map global coordinate to local coordinate for n local positions More...
void	global_to_local (std::vector< MathVector< dim > > &vLocPos, const std::vector< MathVector< worldDim > > &vGlobPos, const size_t maxIter=1000, const number tol=1e-10) const
	map global coordinate to local coordinate for a vector of local positions More...
bool	is_linear () const
	returns if mapping is affine More...
void	jacobian (MathMatrix< worldDim, dim > &J, const MathVector< dim > &locPos) const
	returns jacobian More...
void	jacobian (MathMatrix< worldDim, dim > *vJ, const MathVector< dim > *vLocPos, size_t n) const
	returns jacobian for n local positions More...
void	jacobian (std::vector< MathMatrix< worldDim, dim > > &J, const std::vector< MathVector< dim > > &vLocPos) const
	returns jacobian for a vector of local positions More...
void	jacobian_transposed (MathMatrix< dim, worldDim > &JT, const MathVector< dim > &locPos) const
	returns transposed of jacobian More...
void	jacobian_transposed (MathMatrix< dim, worldDim > *vJT, const MathVector< dim > *vLocPos, size_t n) const
	returns transposed of jacobian for n local positions More...
void	jacobian_transposed (std::vector< MathMatrix< dim, worldDim > > &vJT, const std::vector< MathVector< dim > > &vLocPos) const
	returns transposed of jacobian for a vector of positions More...
number	jacobian_transposed_inverse (MathMatrix< worldDim, dim > &JTInv, const MathVector< dim > &locPos) const
	returns transposed of the inverse of the jacobian and sqrt of gram determinante More...
void	jacobian_transposed_inverse (MathMatrix< worldDim, dim > *vJTInv, const MathVector< dim > *vLocPos, size_t n) const
	returns transposed of the inverse of the jacobian for n local positions More...
void	jacobian_transposed_inverse (MathMatrix< worldDim, dim > *vJTInv, number *vDet, const MathVector< dim > *vLocPos, size_t n) const
	returns transposed of the inverse of the jacobian for n local positions More...
void	jacobian_transposed_inverse (std::vector< MathMatrix< worldDim, dim > > &vJTInv, const std::vector< MathVector< dim > > &vLocPos) const
	returns transposed of the inverse of the jacobian for a vector of positions More...
void	jacobian_transposed_inverse (std::vector< MathMatrix< worldDim, dim > > &vJTInv, std::vector< number > &vDet, const std::vector< MathVector< dim > > &vLocPos) const
	returns transposed of the inverse of the jacobian for a vector of positions More...
void	local_to_global (MathVector< worldDim > &globPos, const MathVector< dim > &locPos) const
	map local coordinate to global coordinate More...
void	local_to_global (MathVector< worldDim > *vGlobPos, const MathVector< dim > *vLocPos, size_t n) const
	map local coordinate to global coordinate for n local positions More...
void	local_to_global (std::vector< MathVector< worldDim > > &vGlobPos, const std::vector< MathVector< dim > > &vLocPos) const
	map local coordinate to global coordinate for a vector of local positions More...
	ReferenceMapping ()
	Default Constructor. More...
	ReferenceMapping (const MathVector< worldDim > *vCornerCoord)
	Constructor setting the corners of the element. More...
	ReferenceMapping (const std::vector< MathVector< worldDim > > &vCornerCoord)
	Constructor setting the corners of the element. More...
number	sqrt_gram_det (const MathVector< dim > &locPos) const
	returns the determinate of the jacobian More...
void	sqrt_gram_det (number *vDet, const MathVector< dim > *vLocPos, size_t n) const
	returns the determinate of the jacobian for n local positions More...
void	sqrt_gram_det (std::vector< number > vDet, const std::vector< MathVector< dim > > &vLocPos) const
	returns the determinate of the jacobian for a vector of local positions More...
void	update (const MathVector< worldDim > *vCornerCoord)
	refresh mapping for new set of corners More...
void	update (const std::vector< MathVector< worldDim > > &vCornerCoord)
	refresh mapping for new set of corners More...

Static Public Attributes
static const int	dim = TRefElem::dim
	reference dimension (domain space dimension) More...
static const bool	isLinear = false
	flag if mapping is linear (i.e. Jacobian does not depend on x) More...
static const int	worldDim = TWorldDim
	world dimension (range space dimension) More...

Detailed Description

template<typename TRefElem, int TWorldDim>
class ug::ReferenceMapping< TRefElem, TWorldDim >

This class describes the mapping from a reference element into the real (physical) world. The mapping is initialized by the physical positions of the vertices of the real world element. The order of those points must be given as indicated by the corresponding reference element.

Let \(R\) be the reference element and \(T\) be the element. Then, the reference mapping is a mapping:

\[ \phi: R \mapsto T \]

Template Parameters

TRefElem	reference element
TWorldDim	world dimension

Constructor & Destructor Documentation

ReferenceMapping() [1/3]

template<typename TRefElem , int TWorldDim>

ug::ReferenceMapping< TRefElem, TWorldDim >::ReferenceMapping

(

)

Default Constructor.

ReferenceMapping() [2/3]

template<typename TRefElem , int TWorldDim>

ug::ReferenceMapping< TRefElem, TWorldDim >::ReferenceMapping

(

const MathVector< worldDim > *

vCornerCoord

)

Constructor setting the corners of the element.

ReferenceMapping() [3/3]

template<typename TRefElem , int TWorldDim>

ug::ReferenceMapping< TRefElem, TWorldDim >::ReferenceMapping

(

const std::vector< MathVector< worldDim > > &

vCornerCoord

)

Constructor setting the corners of the element.

Member Function Documentation

global_to_local() [1/3]

template<typename TRefElem , int TWorldDim>

void ug::ReferenceMapping< TRefElem, TWorldDim >::global_to_local	(	MathVector< dim > &	locPos,
		const MathVector< worldDim > &	globPos,
		const size_t	maxIter = 1000,
		const number	tol = 1e-10
	)		const

map global coordinate to local coordinate

global_to_local() [2/3]

template<typename TRefElem , int TWorldDim>

void ug::ReferenceMapping< TRefElem, TWorldDim >::global_to_local	(	MathVector< dim > *	vLocPos,
		const MathVector< worldDim > *	vGlobPos,
		size_t	n,
		const size_t	maxIter = 1000,
		const number	tol = 1e-10
	)		const

map global coordinate to local coordinate for n local positions

global_to_local() [3/3]

template<typename TRefElem , int TWorldDim>

void ug::ReferenceMapping< TRefElem, TWorldDim >::global_to_local	(	std::vector< MathVector< dim > > &	vLocPos,
		const std::vector< MathVector< worldDim > > &	vGlobPos,
		const size_t	maxIter = 1000,
		const number	tol = 1e-10
	)		const

map global coordinate to local coordinate for a vector of local positions

is_linear()

template<typename TRefElem , int TWorldDim>

bool ug::ReferenceMapping< TRefElem, TWorldDim >::is_linear

(

)

const

returns if mapping is affine

jacobian() [1/3]

template<typename TRefElem , int TWorldDim>

void ug::ReferenceMapping< TRefElem, TWorldDim >::jacobian	(	MathMatrix< worldDim, dim > &	J,
		const MathVector< dim > &	locPos
	)		const

returns jacobian

jacobian() [2/3]

template<typename TRefElem , int TWorldDim>

void ug::ReferenceMapping< TRefElem, TWorldDim >::jacobian	(	MathMatrix< worldDim, dim > *	vJ,
		const MathVector< dim > *	vLocPos,
		size_t	n
	)		const

returns jacobian for n local positions

jacobian() [3/3]

template<typename TRefElem , int TWorldDim>

void ug::ReferenceMapping< TRefElem, TWorldDim >::jacobian	(	std::vector< MathMatrix< worldDim, dim > > &	J,
		const std::vector< MathVector< dim > > &	vLocPos
	)		const

returns jacobian for a vector of local positions

jacobian_transposed() [1/3]

template<typename TRefElem , int TWorldDim>

void ug::ReferenceMapping< TRefElem, TWorldDim >::jacobian_transposed	(	MathMatrix< dim, worldDim > &	JT,
		const MathVector< dim > &	locPos
	)		const

returns transposed of jacobian

Referenced by ug::StdLinConsistentGravity< refDim >::prepare_edge(), ug::StdLinConsistentGravity< refDim >::prepare_hexahedron(), ug::StdLinConsistentGravity< refDim >::prepare_prism(), ug::StdLinConsistentGravity< refDim >::prepare_pyramid(), ug::StdLinConsistentGravity< refDim >::prepare_quadrilateral(), ug::StdLinConsistentGravity< refDim >::prepare_tetrahedron(), and ug::StdLinConsistentGravity< refDim >::prepare_triangle().

jacobian_transposed() [2/3]

template<typename TRefElem , int TWorldDim>

void ug::ReferenceMapping< TRefElem, TWorldDim >::jacobian_transposed	(	MathMatrix< dim, worldDim > *	vJT,
		const MathVector< dim > *	vLocPos,
		size_t	n
	)		const

returns transposed of jacobian for n local positions

jacobian_transposed() [3/3]

template<typename TRefElem , int TWorldDim>

void ug::ReferenceMapping< TRefElem, TWorldDim >::jacobian_transposed	(	std::vector< MathMatrix< dim, worldDim > > &	vJT,
		const std::vector< MathVector< dim > > &	vLocPos
	)		const

returns transposed of jacobian for a vector of positions

jacobian_transposed_inverse() [1/5]

template<typename TRefElem , int TWorldDim>

number ug::ReferenceMapping< TRefElem, TWorldDim >::jacobian_transposed_inverse	(	MathMatrix< worldDim, dim > &	JTInv,
		const MathVector< dim > &	locPos
	)		const

returns transposed of the inverse of the jacobian and sqrt of gram determinante

Referenced by ug::StdLinConsistentGravityX< refDim >::prepare_simplex().

jacobian_transposed_inverse() [2/5]

template<typename TRefElem , int TWorldDim>

void ug::ReferenceMapping< TRefElem, TWorldDim >::jacobian_transposed_inverse	(	MathMatrix< worldDim, dim > *	vJTInv,
		const MathVector< dim > *	vLocPos,
		size_t	n
	)		const

returns transposed of the inverse of the jacobian for n local positions

jacobian_transposed_inverse() [3/5]

template<typename TRefElem , int TWorldDim>

void ug::ReferenceMapping< TRefElem, TWorldDim >::jacobian_transposed_inverse	(	MathMatrix< worldDim, dim > *	vJTInv,
		number *	vDet,
		const MathVector< dim > *	vLocPos,
		size_t	n
	)		const

returns transposed of the inverse of the jacobian for n local positions

jacobian_transposed_inverse() [4/5]

template<typename TRefElem , int TWorldDim>

void ug::ReferenceMapping< TRefElem, TWorldDim >::jacobian_transposed_inverse	(	std::vector< MathMatrix< worldDim, dim > > &	vJTInv,
		const std::vector< MathVector< dim > > &	vLocPos
	)		const

returns transposed of the inverse of the jacobian for a vector of positions

jacobian_transposed_inverse() [5/5]

template<typename TRefElem , int TWorldDim>

void ug::ReferenceMapping< TRefElem, TWorldDim >::jacobian_transposed_inverse	(	std::vector< MathMatrix< worldDim, dim > > &	vJTInv,
		std::vector< number > &	vDet,
		const std::vector< MathVector< dim > > &	vLocPos
	)		const

returns transposed of the inverse of the jacobian for a vector of positions

local_to_global() [1/3]

template<typename TRefElem , int TWorldDim>

void ug::ReferenceMapping< TRefElem, TWorldDim >::local_to_global	(	MathVector< worldDim > &	globPos,
		const MathVector< dim > &	locPos
	)		const

map local coordinate to global coordinate

Referenced by ug::InterpolateOnDiffElements(), ug::MaxErrorOnElements(), ug::DimFVGeometry< TWorldDim, TDim >::update(), ug::FVGeometry< TOrder, TElem, TWorldDim, TQuadOrder >::update_boundary_faces(), ug::DimFVGeometry< TWorldDim, TDim >::update_boundary_faces(), ug::DimFVGeometry< TWorldDim, TDim >::update_local(), and ug::FVGeometry< TOrder, TElem, TWorldDim, TQuadOrder >::update_local_data().

local_to_global() [2/3]

template<typename TRefElem , int TWorldDim>

void ug::ReferenceMapping< TRefElem, TWorldDim >::local_to_global	(	MathVector< worldDim > *	vGlobPos,
		const MathVector< dim > *	vLocPos,
		size_t	n
	)		const

map local coordinate to global coordinate for n local positions

local_to_global() [3/3]

template<typename TRefElem , int TWorldDim>

void ug::ReferenceMapping< TRefElem, TWorldDim >::local_to_global	(	std::vector< MathVector< worldDim > > &	vGlobPos,
		const std::vector< MathVector< dim > > &	vLocPos
	)		const

map local coordinate to global coordinate for a vector of local positions

sqrt_gram_det() [1/3]

template<typename TRefElem , int TWorldDim>

number ug::ReferenceMapping< TRefElem, TWorldDim >::sqrt_gram_det

(

const MathVector< dim > &

locPos

)

const

returns the determinate of the jacobian

Referenced by ug::FVGeometry< TOrder, TElem, TWorldDim, TQuadOrder >::update(), and ug::DimFVGeometry< TWorldDim, TDim >::update().

sqrt_gram_det() [2/3]

template<typename TRefElem , int TWorldDim>

void ug::ReferenceMapping< TRefElem, TWorldDim >::sqrt_gram_det	(	number *	vDet,
		const MathVector< dim > *	vLocPos,
		size_t	n
	)		const

returns the determinate of the jacobian for n local positions

sqrt_gram_det() [3/3]

template<typename TRefElem , int TWorldDim>

void ug::ReferenceMapping< TRefElem, TWorldDim >::sqrt_gram_det	(	std::vector< number >	vDet,
		const std::vector< MathVector< dim > > &	vLocPos
	)		const

returns the determinate of the jacobian for a vector of local positions

update() [1/2]

template<typename TRefElem , int TWorldDim>

void ug::ReferenceMapping< TRefElem, TWorldDim >::update

(

const MathVector< worldDim > *

vCornerCoord

)

refresh mapping for new set of corners

Referenced by ug::InterpolateOnDiffElements(), ug::MaxErrorOnElements(), ug::StdLinConsistentGravity< refDim >::prepare_edge(), ug::StdLinConsistentGravity< refDim >::prepare_hexahedron(), ug::StdLinConsistentGravity< refDim >::prepare_prism(), ug::StdLinConsistentGravity< refDim >::prepare_pyramid(), ug::StdLinConsistentGravity< refDim >::prepare_quadrilateral(), ug::StdLinConsistentGravityX< refDim >::prepare_simplex(), ug::StdLinConsistentGravity< refDim >::prepare_tetrahedron(), ug::StdLinConsistentGravity< refDim >::prepare_triangle(), ug::ReferenceMapping< ReferenceVertex, TWorldDim >::ReferenceMapping(), ug::ReferenceMapping< ReferenceEdge, TWorldDim >::ReferenceMapping(), ug::ReferenceMapping< ReferenceTriangle, TWorldDim >::ReferenceMapping(), ug::ReferenceMapping< ReferenceQuadrilateral, TWorldDim >::ReferenceMapping(), ug::ReferenceMapping< ReferenceTetrahedron, TWorldDim >::ReferenceMapping(), ug::ReferenceMapping< ReferencePyramid, TWorldDim >::ReferenceMapping(), ug::ReferenceMapping< ReferencePrism, TWorldDim >::ReferenceMapping(), ug::ReferenceMapping< ReferenceHexahedron, TWorldDim >::ReferenceMapping(), ug::ReferenceMapping< ReferenceOctahedron, TWorldDim >::ReferenceMapping(), ug::ReferenceMapping< ReferenceVertex, TWorldDim >::update(), ug::ReferenceMapping< ReferenceEdge, TWorldDim >::update(), ug::ReferenceMapping< ReferenceTriangle, TWorldDim >::update(), ug::ReferenceMapping< ReferenceQuadrilateral, TWorldDim >::update(), ug::ReferenceMapping< ReferenceTetrahedron, TWorldDim >::update(), ug::ReferenceMapping< ReferencePyramid, TWorldDim >::update(), ug::ReferenceMapping< ReferencePrism, TWorldDim >::update(), ug::ReferenceMapping< ReferenceHexahedron, TWorldDim >::update(), and ug::ReferenceMapping< ReferenceOctahedron, TWorldDim >::update().

update() [2/2]

template<typename TRefElem , int TWorldDim>

void ug::ReferenceMapping< TRefElem, TWorldDim >::update

(

const std::vector< MathVector< worldDim > > &

vCornerCoord

)

refresh mapping for new set of corners

Member Data Documentation

dim

template<typename TRefElem , int TWorldDim>

const int ug::ReferenceMapping< TRefElem, TWorldDim >::dim = TRefElem::dim

static

reference dimension (domain space dimension)

isLinear

template<typename TRefElem , int TWorldDim>

const bool ug::ReferenceMapping< TRefElem, TWorldDim >::isLinear = false

static

flag if mapping is linear (i.e. Jacobian does not depend on x)

worldDim

template<typename TRefElem , int TWorldDim>

const int ug::ReferenceMapping< TRefElem, TWorldDim >::worldDim = TWorldDim

static

world dimension (range space dimension)

Referenced by ug::ReferenceMapping< ReferenceEdge, TWorldDim >::jacobian_transposed(), ug::ReferenceMapping< ReferenceTriangle, TWorldDim >::jacobian_transposed(), ug::ReferenceMapping< ReferenceQuadrilateral, TWorldDim >::jacobian_transposed(), ug::ReferenceMapping< ReferenceTetrahedron, TWorldDim >::jacobian_transposed(), ug::ReferenceMapping< ReferencePyramid, TWorldDim >::jacobian_transposed(), ug::ReferenceMapping< ReferencePrism, TWorldDim >::jacobian_transposed(), ug::ReferenceMapping< ReferenceHexahedron, TWorldDim >::jacobian_transposed(), ug::ReferenceMapping< ReferenceOctahedron, TWorldDim >::jacobian_transposed(), ug::ReferenceMapping< ReferencePyramid, TWorldDim >::local_to_global(), ug::ReferenceMapping< ReferencePrism, TWorldDim >::local_to_global(), ug::ReferenceMapping< ReferenceHexahedron, TWorldDim >::local_to_global(), and ug::ReferenceMapping< ReferenceOctahedron, TWorldDim >::local_to_global().

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

• ugbase/lib_disc/reference_element/reference_mapping.h