A standard isoparametric element transformation. More...

#include <eltrans.hpp>

Inheritance diagram for mfem::IsoparametricTransformation:

Collaboration diagram for mfem::IsoparametricTransformation:

Public Member Functions
	IsoparametricTransformation ()

void	SetFE (const FiniteElement *FE)
	Set the element that will be used to compute the transformations.

const FiniteElement *	GetFE () const
	Get the current element used to compute the transformations.

void	SetPointMat (const DenseMatrix &pm)
	Set the underlying point matrix describing the transformation.

const DenseMatrix &	GetPointMat () const
	Return the stored point matrix.

DenseMatrix &	GetPointMat ()
	Write access to the stored point matrix. Use with caution.

void	SetIdentityTransformation (Geometry::Type GeomType)
	Set the FiniteElement Geometry for the reference elements being used.

virtual void	Transform (const IntegrationPoint &, Vector &)
	Transform integration point from reference coordinates to physical coordinates and store them in the vector.

virtual void	Transform (const IntegrationRule &, DenseMatrix &)
	Transform all the integration points from the integration rule from reference coordinates to physical coordinates and store them as column vectors in the matrix.

virtual void	Transform (const DenseMatrix &matrix, DenseMatrix &result)
	Transform all the integration points from the column vectors of matrix from reference coordinates to physical coordinates and store them as column vectors in result.

virtual int	Order () const
	Return the order of the current element we are using for the transformation.

virtual int	OrderJ () const
	Return the order of the elements of the Jacobian of the transformation.

virtual int	OrderW () const
	Return the order of the determinant of the Jacobian (weight) of the transformation.

virtual int	OrderGrad (const FiniteElement *fe) const
	Return the order of \( adj(J)^T \nabla fi \).

virtual int	GetSpaceDim () const
	Get the dimension of the target (physical) space.

virtual int	TransformBack (const Vector &v, IntegrationPoint &ip, const real_t phys_rel_tol=1e-15)
	Transform a point pt from physical space to a point ip in reference space and optionally can set a solver tolerance using phys_tol.

virtual	~IsoparametricTransformation ()

MFEM_DEPRECATED void	FinalizeTransformation ()

Public Member Functions inherited from mfem::ElementTransformation
	ElementTransformation ()

void	Reset ()
	Force the reevaluation of the Jacobian in the next call.

void	SetIntPoint (const IntegrationPoint *ip)
	Set the integration point ip that weights and Jacobians will be evaluated at.

const IntegrationPoint &	GetIntPoint ()
	Get a const reference to the currently set integration point. This will return NULL if no integration point is set.

const DenseMatrix &	Jacobian ()
	Return the Jacobian matrix of the transformation at the currently set IntegrationPoint, using the method SetIntPoint().

const DenseMatrix &	Hessian ()
	Return the Hessian matrix of the transformation at the currently set IntegrationPoint, using the method SetIntPoint().

real_t	Weight ()
	Return the weight of the Jacobian matrix of the transformation at the currently set IntegrationPoint. The Weight evaluates to \( \sqrt{\lvert J^T J \rvert} \).

const DenseMatrix &	AdjugateJacobian ()
	Return the adjugate of the Jacobian matrix of the transformation at the currently set IntegrationPoint.

const DenseMatrix &	TransposeAdjugateJacobian ()
	Return the transpose of the adjugate of the Jacobian matrix of the transformation at the currently set IntegrationPoint.

const DenseMatrix &	InverseJacobian ()
	Return the inverse of the Jacobian matrix of the transformation at the currently set IntegrationPoint.

Geometry::Type	GetGeometryType () const
	Return the Geometry::Type of the reference element.

int	GetDimension () const
	Return the topological dimension of the reference element.

virtual	~ElementTransformation ()

Additional Inherited Members
Public Types inherited from mfem::ElementTransformation
enum	{ ELEMENT = 1 , BDR_ELEMENT = 2 , EDGE = 3 , FACE = 4 , BDR_FACE = 5 }

Public Attributes inherited from mfem::ElementTransformation
int	Attribute

int	ElementNo

int	ElementType

const Mesh *	mesh
	The Mesh object containing the element.

Protected Types inherited from mfem::ElementTransformation
enum	StateMasks { JACOBIAN_MASK = 1 , WEIGHT_MASK = 2 , ADJUGATE_MASK = 4 , INVERSE_MASK = 8 , HESSIAN_MASK = 16 , TRANS_ADJUGATE_MASK = 32 }

Protected Member Functions inherited from mfem::ElementTransformation
real_t	EvalWeight ()

const DenseMatrix &	EvalAdjugateJ ()

const DenseMatrix &	EvalTransAdjugateJ ()

const DenseMatrix &	EvalInverseJ ()

Protected Attributes inherited from mfem::ElementTransformation
const IntegrationPoint *	IntPoint

DenseMatrix	dFdx

DenseMatrix	adjJ

DenseMatrix	invJ

DenseMatrix	d2Fdx2

DenseMatrix	adjJT

real_t	Wght

int	EvalState

Geometry::Type	geom

Detailed Description

A standard isoparametric element transformation.

Definition at line 362 of file eltrans.hpp.

Constructor & Destructor Documentation

◆ IsoparametricTransformation()

mfem::IsoparametricTransformation::IsoparametricTransformation ( )

inline

Definition at line 379 of file eltrans.hpp.

◆ ~IsoparametricTransformation()

virtual mfem::IsoparametricTransformation::~IsoparametricTransformation ( )

inlinevirtual

Definition at line 459 of file eltrans.hpp.

Member Function Documentation

◆ FinalizeTransformation()

MFEM_DEPRECATED void mfem::IsoparametricTransformation::FinalizeTransformation ( )

inline

Definition at line 461 of file eltrans.hpp.

◆ GetFE()

const FiniteElement * mfem::IsoparametricTransformation::GetFE ( ) const

inline

Get the current element used to compute the transformations.

Definition at line 390 of file eltrans.hpp.

◆ GetPointMat() [1/2]

DenseMatrix & mfem::IsoparametricTransformation::GetPointMat ( )

inline

Write access to the stored point matrix. Use with caution.

If the point matrix is altered using this member function the Reset function should also be called to force the reevaluation of the Jacobian, etc..

Definition at line 411 of file eltrans.hpp.

◆ GetPointMat() [2/2]

const DenseMatrix & mfem::IsoparametricTransformation::GetPointMat ( ) const

inline

Return the stored point matrix.

Definition at line 405 of file eltrans.hpp.

◆ GetSpaceDim()

virtual int mfem::IsoparametricTransformation::GetSpaceDim ( ) const

inlinevirtual

Get the dimension of the target (physical) space.

We support 2D meshes embedded in 3D; in this case the function will return "3".

Implements mfem::ElementTransformation.

Definition at line 443 of file eltrans.hpp.

◆ Order()

virtual int mfem::IsoparametricTransformation::Order ( ) const

inlinevirtual

Return the order of the current element we are using for the transformation.

Implements mfem::ElementTransformation.

Definition at line 431 of file eltrans.hpp.

◆ OrderGrad()

int mfem::IsoparametricTransformation::OrderGrad ( const FiniteElement * fe ) const

virtual

Return the order of \( adj(J)^T \nabla fi \).

Implements mfem::ElementTransformation.

Definition at line 467 of file eltrans.cpp.

◆ OrderJ()

int mfem::IsoparametricTransformation::OrderJ ( ) const

virtual

Return the order of the elements of the Jacobian of the transformation.

Implements mfem::ElementTransformation.

Definition at line 439 of file eltrans.cpp.

◆ OrderW()

int mfem::IsoparametricTransformation::OrderW ( ) const

virtual

Return the order of the determinant of the Jacobian (weight) of the transformation.

Implements mfem::ElementTransformation.

Definition at line 453 of file eltrans.cpp.

◆ SetFE()

void mfem::IsoparametricTransformation::SetFE ( const FiniteElement * FE )

inline

Set the element that will be used to compute the transformations.

Definition at line 382 of file eltrans.hpp.

◆ SetIdentityTransformation()

void mfem::IsoparametricTransformation::SetIdentityTransformation ( Geometry::Type GeomType )

Set the FiniteElement Geometry for the reference elements being used.

Definition at line 379 of file eltrans.cpp.

◆ SetPointMat()

void mfem::IsoparametricTransformation::SetPointMat ( const DenseMatrix & pm )

inline

Set the underlying point matrix describing the transformation.

The dimensions of the matrix are space-dim x dof. The transformation is defined as \( x = F( \hat x ) = P \phi( \hat x ) \)

where \( \hat x \) is the reference point, x is the corresponding physical point, P is the point matrix, and \( \phi( \hat x ) \) is the column-vector of all basis functions evaluated at \( \hat x \) . The columns of P represent the control points in physical space defining the transformation.

Definition at line 402 of file eltrans.hpp.

◆ Transform() [1/3]

void mfem::IsoparametricTransformation::Transform	(	const DenseMatrix &	matrix,
		DenseMatrix &	result )

virtual

Transform all the integration points from the column vectors of matrix from reference coordinates to physical coordinates and store them as column vectors in result.

Implements mfem::ElementTransformation.

Reimplemented in mfem::FaceElementTransformations.

Definition at line 525 of file eltrans.cpp.

◆ Transform() [2/3]

void mfem::IsoparametricTransformation::Transform	(	const IntegrationPoint &	ip,
		Vector &	trans )

virtual

Transform integration point from reference coordinates to physical coordinates and store them in the vector.

Implements mfem::ElementTransformation.

Reimplemented in mfem::FaceElementTransformations.

Definition at line 488 of file eltrans.cpp.

◆ Transform() [3/3]

void mfem::IsoparametricTransformation::Transform	(	const IntegrationRule &	ir,
		DenseMatrix &	tr )

virtual

Transform all the integration points from the integration rule from reference coordinates to physical coordinates and store them as column vectors in the matrix.

Implements mfem::ElementTransformation.

Reimplemented in mfem::FaceElementTransformations.

Definition at line 499 of file eltrans.cpp.

◆ TransformBack()

virtual int mfem::IsoparametricTransformation::TransformBack	(	const Vector &	v,
		IntegrationPoint &	ip,
		const real_t	phys_rel_tol = 1e-15 )

inlinevirtual

Transform a point pt from physical space to a point ip in reference space and optionally can set a solver tolerance using phys_tol.

Attempt to find the IntegrationPoint that is transformed into the given point in physical space. If the inversion fails a non-zero value is returned. This method is not 100 percent reliable for non-linear transformations.

Implements mfem::ElementTransformation.

Definition at line 451 of file eltrans.hpp.

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

fem/eltrans.hpp
fem/eltrans.cpp

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ IsoparametricTransformation()

◆ ~IsoparametricTransformation()

Member Function Documentation

◆ FinalizeTransformation()

◆ GetFE()

◆ GetPointMat() [1/2]

◆ GetPointMat() [2/2]

◆ GetSpaceDim()

◆ Order()

◆ OrderGrad()

◆ OrderJ()

◆ OrderW()

◆ SetFE()

◆ SetIdentityTransformation()

◆ SetPointMat()

◆ Transform() [1/3]

◆ Transform() [2/3]

◆ Transform() [3/3]

◆ TransformBack()