#include <eltrans.hpp>

Inheritance diagram for mfem::ElementTransformation:

Collaboration diagram for mfem::ElementTransformation:

Public Types
enum	{ ELEMENT = 1 , BDR_ELEMENT = 2 , EDGE = 3 , FACE = 4 , BDR_FACE = 5 }

Public Member Functions
	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.

virtual void	Transform (const IntegrationPoint &, Vector &)=0
	Transform integration point from reference coordinates to physical coordinates and store them in the vector.

virtual void	Transform (const IntegrationRule &, DenseMatrix &)=0
	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)=0
	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.

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.

virtual int	Order () const =0
	Return the order of the current element we are using for the transformation.

virtual int	OrderJ () const =0
	Return the order of the elements of the Jacobian of the transformation.

virtual int	OrderW () const =0
	Return the order of the determinant of the Jacobian (weight) of the transformation.

virtual int	OrderGrad (const FiniteElement *fe) const =0
	Return the order of \( adj(J)^T \nabla fi \).

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

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

virtual int	GetSpaceDim () const =0
	Get the dimension of the target (physical) space.

virtual int	TransformBack (const Vector &pt, IntegrationPoint &ip, const real_t phys_tol=tol_0)=0
	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	~ElementTransformation ()

Public Attributes
int	Attribute

int	ElementNo

int	ElementType

const Mesh *	mesh
	The Mesh object containing the element.

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

Protected Member Functions
virtual const DenseMatrix &	EvalJacobian ()=0
	Evaluate the Jacobian of the transformation at the IntPoint and store it in dFdx.

virtual const DenseMatrix &	EvalHessian ()=0
	Evaluate the Hessian of the transformation at the IntPoint and store it in d2Fdx2.

real_t	EvalWeight ()

const DenseMatrix &	EvalAdjugateJ ()

const DenseMatrix &	EvalTransAdjugateJ ()

const DenseMatrix &	EvalInverseJ ()

Protected Attributes
const IntegrationPoint *	IntPoint

DenseMatrix	dFdx

DenseMatrix	adjJ

DenseMatrix	invJ

DenseMatrix	d2Fdx2

DenseMatrix	adjJT

real_t	Wght

int	EvalState

Geometry::Type	geom

Static Protected Attributes
Tolerance used for point comparisons
static constexpr real_t	tol_0 = 1e-15

Detailed Description

Definition at line 27 of file eltrans.hpp.

Member Enumeration Documentation

◆ anonymous enum

anonymous enum

This enumeration declares the values stored in ElementTransformation::ElementType and indicates which group of objects the index stored in ElementTransformation::ElementNo refers:

Enumerator
ELEMENT
BDR_ELEMENT
EDGE
FACE
BDR_FACE

Definition at line 82 of file eltrans.hpp.

◆ StateMasks

enum mfem::ElementTransformation::StateMasks

protected

Enumerator
JACOBIAN_MASK
WEIGHT_MASK
ADJUGATE_MASK
INVERSE_MASK
HESSIAN_MASK
TRANS_ADJUGATE_MASK

Definition at line 35 of file eltrans.hpp.

Constructor & Destructor Documentation

◆ ElementTransformation()

mfem::ElementTransformation::ElementTransformation ( )

Definition at line 21 of file eltrans.cpp.

◆ ~ElementTransformation()

virtual mfem::ElementTransformation::~ElementTransformation ( )

inlinevirtual

Definition at line 194 of file eltrans.hpp.

Member Function Documentation

◆ AdjugateJacobian()

const DenseMatrix & mfem::ElementTransformation::AdjugateJacobian ( )

inline

Return the adjugate of the Jacobian matrix of the transformation at the currently set IntegrationPoint.

Definition at line 148 of file eltrans.hpp.

◆ EvalAdjugateJ()

const DenseMatrix & mfem::ElementTransformation::EvalAdjugateJ ( )

protected

Definition at line 38 of file eltrans.cpp.

◆ EvalHessian()

virtual const DenseMatrix & mfem::ElementTransformation::EvalHessian ( )

protectedpure virtual

Evaluate the Hessian of the transformation at the IntPoint and store it in d2Fdx2.

◆ EvalInverseJ()

const DenseMatrix & mfem::ElementTransformation::EvalInverseJ ( )

protected

Definition at line 59 of file eltrans.cpp.

◆ EvalJacobian()

virtual const DenseMatrix & mfem::ElementTransformation::EvalJacobian ( )

protectedpure virtual

Evaluate the Jacobian of the transformation at the IntPoint and store it in dFdx.

◆ EvalTransAdjugateJ()

const DenseMatrix & mfem::ElementTransformation::EvalTransAdjugateJ ( )

protected

Definition at line 48 of file eltrans.cpp.

◆ EvalWeight()

real_t mfem::ElementTransformation::EvalWeight ( )

protected

Definition at line 30 of file eltrans.cpp.

◆ GetDimension()

int mfem::ElementTransformation::GetDimension ( ) const

inline

Return the topological dimension of the reference element.

Definition at line 178 of file eltrans.hpp.

◆ GetGeometryType()

Geometry::Type mfem::ElementTransformation::GetGeometryType ( ) const

inline

Return the Geometry::Type of the reference element.

Definition at line 175 of file eltrans.hpp.

◆ GetIntPoint()

const IntegrationPoint & mfem::ElementTransformation::GetIntPoint ( )

inline

Get a const reference to the currently set integration point. This will return NULL if no integration point is set.

Definition at line 111 of file eltrans.hpp.

◆ GetSpaceDim()

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

pure virtual

Get the dimension of the target (physical) space.

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

Implemented in mfem::IsoparametricTransformation.

◆ Hessian()

const DenseMatrix & mfem::ElementTransformation::Hessian ( )

inline

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

Definition at line 138 of file eltrans.hpp.

◆ InverseJacobian()

const DenseMatrix & mfem::ElementTransformation::InverseJacobian ( )

inline

Return the inverse of the Jacobian matrix of the transformation at the currently set IntegrationPoint.

Definition at line 158 of file eltrans.hpp.

◆ Jacobian()

const DenseMatrix & mfem::ElementTransformation::Jacobian ( )

inline

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

The dimensions of the Jacobian matrix are physical-space-dim by reference-space-dim. The first column contains the x derivatives of the transformation, the second – the y derivatives, etc.

Definition at line 132 of file eltrans.hpp.

◆ Order()

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

pure virtual

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

Implemented in mfem::IsoparametricTransformation.

◆ OrderGrad()

virtual int mfem::ElementTransformation::OrderGrad ( const FiniteElement * fe ) const

pure virtual

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

Implemented in mfem::IsoparametricTransformation.

◆ OrderJ()

virtual int mfem::ElementTransformation::OrderJ ( ) const

pure virtual

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

Implemented in mfem::IsoparametricTransformation.

◆ OrderW()

virtual int mfem::ElementTransformation::OrderW ( ) const

pure virtual

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

Implemented in mfem::IsoparametricTransformation.

◆ Reset()

void mfem::ElementTransformation::Reset ( )

inline

Force the reevaluation of the Jacobian in the next call.

Definition at line 102 of file eltrans.hpp.

◆ SetIntPoint()

void mfem::ElementTransformation::SetIntPoint ( const IntegrationPoint * ip )

inline

Set the integration point ip that weights and Jacobians will be evaluated at.

Definition at line 106 of file eltrans.hpp.

◆ Transform() [1/3]

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

pure 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.

Implemented in mfem::FaceElementTransformations, and mfem::IsoparametricTransformation.

◆ Transform() [2/3]

virtual void mfem::ElementTransformation::Transform	(	const IntegrationPoint &	,
		Vector &	)

pure virtual

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

Implemented in mfem::FaceElementTransformations, and mfem::IsoparametricTransformation.

◆ Transform() [3/3]

virtual void mfem::ElementTransformation::Transform	(	const IntegrationRule &	,
		DenseMatrix &	)

pure 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.

Implemented in mfem::FaceElementTransformations, and mfem::IsoparametricTransformation.

◆ TransformBack()

virtual int mfem::ElementTransformation::TransformBack	(	const Vector &	pt,
		IntegrationPoint &	ip,
		const real_t	phys_tol = tol_0 )

pure virtual

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.

Implemented in mfem::IsoparametricTransformation.

◆ TransposeAdjugateJacobian()

const DenseMatrix & mfem::ElementTransformation::TransposeAdjugateJacobian ( )

inline

Return the transpose of the adjugate of the Jacobian matrix of the transformation at the currently set IntegrationPoint.

Definition at line 153 of file eltrans.hpp.

◆ Weight()

real_t mfem::ElementTransformation::Weight ( )

inline

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

Definition at line 144 of file eltrans.hpp.

Member Data Documentation

◆ adjJ

DenseMatrix mfem::ElementTransformation::adjJ

protected

Definition at line 31 of file eltrans.hpp.

◆ adjJT

DenseMatrix mfem::ElementTransformation::adjJT

protected

Definition at line 32 of file eltrans.hpp.

◆ Attribute

int mfem::ElementTransformation::Attribute

Definition at line 91 of file eltrans.hpp.

◆ d2Fdx2

DenseMatrix mfem::ElementTransformation::d2Fdx2

protected

Definition at line 32 of file eltrans.hpp.

◆ dFdx

DenseMatrix mfem::ElementTransformation::dFdx

protected

Definition at line 31 of file eltrans.hpp.

◆ ElementNo

int mfem::ElementTransformation::ElementNo

Definition at line 91 of file eltrans.hpp.

◆ ElementType

int mfem::ElementTransformation::ElementType

Definition at line 91 of file eltrans.hpp.

◆ EvalState

int mfem::ElementTransformation::EvalState

protected

Definition at line 34 of file eltrans.hpp.

◆ geom

Geometry::Type mfem::ElementTransformation::geom

protected

Definition at line 44 of file eltrans.hpp.

◆ IntPoint

const IntegrationPoint* mfem::ElementTransformation::IntPoint

protected

Definition at line 30 of file eltrans.hpp.

◆ invJ

DenseMatrix mfem::ElementTransformation::invJ

protected

Definition at line 31 of file eltrans.hpp.

◆ mesh

const Mesh* mfem::ElementTransformation::mesh

The Mesh object containing the element.

If the element transformation belongs to a mesh, this will point to the containing Mesh object. ElementNo will be the number of the element in this Mesh. This will be NULL if the element does not belong to a mesh.

Definition at line 97 of file eltrans.hpp.

◆ tol_0

static constexpr real_t mfem::ElementTransformation::tol_0 = 1e-15

staticconstexprprotected

Definition at line 62 of file eltrans.hpp.

◆ Wght

real_t mfem::ElementTransformation::Wght

protected

Definition at line 33 of file eltrans.hpp.

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

fem/eltrans.hpp
fem/eltrans.cpp

Public Types

Public Member Functions

Public Attributes

Protected Types

Protected Member Functions

Protected Attributes

Static Protected Attributes

Detailed Description

Member Enumeration Documentation

◆ anonymous enum

◆ StateMasks

Constructor & Destructor Documentation

◆ ElementTransformation()

◆ ~ElementTransformation()

Member Function Documentation

◆ AdjugateJacobian()

◆ EvalAdjugateJ()

◆ EvalHessian()

◆ EvalInverseJ()

◆ EvalJacobian()

◆ EvalTransAdjugateJ()

◆ EvalWeight()

◆ GetDimension()

◆ GetGeometryType()

◆ GetIntPoint()

◆ GetSpaceDim()

◆ Hessian()

◆ InverseJacobian()

◆ Jacobian()

◆ Order()

◆ OrderGrad()

◆ OrderJ()

◆ OrderW()

◆ Reset()

◆ SetIntPoint()

◆ Transform() [1/3]

◆ Transform() [2/3]

◆ Transform() [3/3]

◆ TransformBack()

◆ TransposeAdjugateJacobian()

◆ Weight()

Member Data Documentation

◆ adjJ

◆ adjJT

◆ Attribute

◆ d2Fdx2

◆ dFdx

◆ ElementNo

◆ ElementType

◆ EvalState

◆ geom

◆ IntPoint

◆ invJ

◆ mesh

◆ tol_0

◆ Wght