The inverse transformation of a given ElementTransformation. More...

#include <eltrans.hpp>

Collaboration diagram for mfem::InverseElementTransformation:

Public Types
enum	InitGuessType { Center = 0 , ClosestPhysNode = 1 , ClosestRefNode = 2 , GivenPoint = 3 , EdgeScan }
	Algorithms for selecting an initial guess. More...

enum	SolverType { Newton = 0 , NewtonSegmentProject = 1 , NewtonElementProject = 2 }
	Solution strategy. More...

enum	TransformResult { Inside = 0 , Outside = 1 , Unknown = 2 }
	Values returned by Transform(). More...

Public Member Functions
	InverseElementTransformation (ElementTransformation *Trans=NULL)
	Construct the InverseElementTransformation with default parameters.

virtual	~InverseElementTransformation ()

void	SetTransformation (ElementTransformation &Trans)
	Set a new forward ElementTransformation, Trans.

void	SetInitialGuessType (InitGuessType itype)
	Choose how the initial guesses for subsequent calls to Transform() will be selected.

void	SetInitialGuess (const IntegrationPoint &init_ip)
	Set the initial guess for subsequent calls to Transform(), switching to the GivenPoint InitGuessType at the same time.

void	SetInitGuessPointsType (int q_type)

void	SetInitGuessRelOrder (int order)
	Set the relative order used for the `Closest*` initial guess types.

void	SetInitGuessOrder (int order)

void	SetSolverType (SolverType stype)
	Specify which algorithm to use for solving the transformation equation, i.e. when calling the Transform() method.

void	SetMaxIter (int max_it)
	Set the maximum number of iterations when solving for a reference point.

void	SetReferenceTol (real_t ref_sp_tol)
	Set the reference-space convergence tolerance.

void	SetPhysicalRelTol (real_t phys_rel_tol)
	Set the relative physical-space convergence tolerance.

void	SetElementTol (real_t el_tol)
	Set the tolerance used to determine if a point lies inside or outside of the reference element.

void	SetPrintLevel (int pr_level)
	Set the desired print level, useful for debugging.

int	FindClosestPhysPoint (const Vector &pt, const IntegrationRule &ir)
	Find the IntegrationPoint mapped closest to pt.

int	FindClosestRefPoint (const Vector &pt, const IntegrationRule &ir)
	Find the IntegrationPoint mapped closest to pt, using a norm that approximates the (unknown) distance in reference coordinates.

virtual int	Transform (const Vector &pt, IntegrationPoint &ip)
	Given a point, pt, in physical space, find its reference coordinates, ip.

Protected Member Functions
void	NewtonPrint (int mode, real_t val)

void	NewtonPrintPoint (const char prefix, const Vector &pt, const char suffix)

int	NewtonSolve (const Vector &pt, IntegrationPoint &ip)

Protected Attributes
ElementTransformation *	T

IntegrationPoint	ip0

int	init_guess_type

GeometryRefiner	refiner

int	qpts_order

int	rel_qpts_order

int	solver_type

int	max_iter

real_t	ref_tol

real_t	phys_rtol

real_t	ip_tol

int	print_level

Detailed Description

The inverse transformation of a given ElementTransformation.

Definition at line 199 of file eltrans.hpp.

Member Enumeration Documentation

◆ InitGuessType

enum mfem::InverseElementTransformation::InitGuessType

Algorithms for selecting an initial guess.

Enumerator
Center	Use the center of the reference element.
ClosestPhysNode	Use the point returned by FindClosestPhysPoint() from a reference-space grid of type and size controlled by SetInitGuessPointsType() and SetInitGuessRelOrder(), respectively.
ClosestRefNode	Use the point returned by FindClosestRefPoint() from a reference-space grid of type and size controlled by SetInitGuessPointsType() and SetInitGuessRelOrder(), respectively.
GivenPoint	Use a specific point, set with SetInitialGuess().
EdgeScan	Performs full solves on multiple points along the r/s/t=0 edges of the element. It is recommended that SetInitGuessRelOrder() is chosen such that max(trans_order+order,0)+1 <= 4 with SetInitGuessPointsType() as Quadrature1D::ClosedUniform. See also GeometryRefiner::EdgeScan

Definition at line 203 of file eltrans.hpp.

◆ SolverType

enum mfem::InverseElementTransformation::SolverType

Solution strategy.

Enumerator
Newton	Use Newton's algorithm, without restricting the reference-space points (iterates) to the reference element.
NewtonSegmentProject	Use Newton's algorithm, restricting the reference-space points to the reference element by scaling back the Newton increments, i.e. projecting new iterates, x_new, lying outside the element, to the intersection of the line segment [x_old, x_new] with the boundary.
NewtonElementProject	Use Newton's algorithm, restricting the reference-space points to the reference element by projecting new iterates, x_new, lying outside the element, to the point on the boundary closest (in reference-space) to x_new.

Definition at line 224 of file eltrans.hpp.

◆ TransformResult

enum mfem::InverseElementTransformation::TransformResult

Values returned by Transform().

Enumerator
Inside	The point is inside the element.
Outside	The point is probably outside the element.
Unknown	The algorithm failed to determine where the point is.

Definition at line 242 of file eltrans.hpp.

Constructor & Destructor Documentation

◆ InverseElementTransformation()

mfem::InverseElementTransformation::InverseElementTransformation ( ElementTransformation * Trans = NULL )

inline

Construct the InverseElementTransformation with default parameters.

Some practical considerations regarding the choice of initial guess type and solver type:

The combination of Center and NewtonSegmentProject provides the fastest way to estimate if a point lies inside an element, assuming that most queried elements are not very deformed, e.g. if most elements are convex.
[Default] The combination of Center and NewtonElementProject provides a somewhat slower alternative to 1 with the benefit of being more reliable in the case when the query point is inside the element but potentially slower in the case when the query point is outside the element.
The combination of ClosestPhysNode and NewtonElementProject is slower than 1 and 2 but much more reliable, especially in the case of highly distorted elements which do not have very high aspect ratios.
The combination of ClosestRefNode and NewtonElementProject should generally be the most reliable, coming at a bit higher computational cost than 3 while performing better on distorted meshes with elements having high aspect ratios.
Note
None of these choices provide a guarantee that if a query point is inside the element then it will be found. The only guarantee is that if the Transform() method returns Inside then the point lies inside the element up to one of the specified physical- or reference-space tolerances.

Definition at line 297 of file eltrans.hpp.

◆ ~InverseElementTransformation()

virtual mfem::InverseElementTransformation::~InverseElementTransformation ( )

inlinevirtual

Definition at line 317 of file eltrans.hpp.

Member Function Documentation

◆ FindClosestPhysPoint()

int mfem::InverseElementTransformation::FindClosestPhysPoint	(	const Vector &	pt,
		const IntegrationRule &	ir )

Find the IntegrationPoint mapped closest to pt.

This function uses the given IntegrationRule, ir, maps its points to physical space and finds the one that is closest to the point pt.

Parameters

pt	The query point.
ir	The IntegrationRule, i.e. the set of reference points to map to physical space and check.

Returns: The index of the IntegrationPoint in ir whose mapped point is closest to pt.

See also: FindClosestRefPoint().

Definition at line 71 of file eltrans.cpp.

◆ FindClosestRefPoint()

int mfem::InverseElementTransformation::FindClosestRefPoint	(	const Vector &	pt,
		const IntegrationRule &	ir )

Find the IntegrationPoint mapped closest to pt, using a norm that approximates the (unknown) distance in reference coordinates.

See also: FindClosestPhysPoint().

Definition at line 98 of file eltrans.cpp.

◆ NewtonPrint()

void mfem::InverseElementTransformation::NewtonPrint	(	int	mode,
		real_t	val )

protected

Definition at line 130 of file eltrans.cpp.

◆ NewtonPrintPoint()

void mfem::InverseElementTransformation::NewtonPrintPoint	(	const char *	prefix,
		const Vector &	pt,
		const char *	suffix )

protected

Definition at line 159 of file eltrans.cpp.

◆ NewtonSolve()

int mfem::InverseElementTransformation::NewtonSolve	(	const Vector &	pt,
		IntegrationPoint &	ip )

protected

Definition at line 173 of file eltrans.cpp.

◆ SetElementTol()

void mfem::InverseElementTransformation::SetElementTol ( real_t el_tol )

inline

Set the tolerance used to determine if a point lies inside or outside of the reference element.

This tolerance is used only with the pure Newton solver.

Definition at line 368 of file eltrans.hpp.

◆ SetInitGuessOrder()

void mfem::InverseElementTransformation::SetInitGuessOrder ( int order )

inline

The number of points in each spatial direction is given by the formula order+1.

Definition at line 347 of file eltrans.hpp.

◆ SetInitGuessPointsType()

void mfem::InverseElementTransformation::SetInitGuessPointsType ( int q_type )

inline

Set the Quadrature1D type used for the Closest* and EdgeScan initial guess types.

Definition at line 333 of file eltrans.hpp.

◆ SetInitGuessRelOrder()

void mfem::InverseElementTransformation::SetInitGuessRelOrder ( int order )

inline

Set the relative order used for the Closest* initial guess types.

The number of points in each spatial direction is given by the formula max(trans_order+order,0)+1, where trans_order is the order of the current ElementTransformation.

Definition at line 339 of file eltrans.hpp.

◆ SetInitialGuess()

void mfem::InverseElementTransformation::SetInitialGuess ( const IntegrationPoint & init_ip )

inline

Set the initial guess for subsequent calls to Transform(), switching to the GivenPoint InitGuessType at the same time.

Definition at line 328 of file eltrans.hpp.

◆ SetInitialGuessType()

void mfem::InverseElementTransformation::SetInitialGuessType ( InitGuessType itype )

inline

Choose how the initial guesses for subsequent calls to Transform() will be selected.

Definition at line 324 of file eltrans.hpp.

◆ SetMaxIter()

void mfem::InverseElementTransformation::SetMaxIter ( int max_it )

inline

Set the maximum number of iterations when solving for a reference point.

Definition at line 357 of file eltrans.hpp.

◆ SetPhysicalRelTol()

void mfem::InverseElementTransformation::SetPhysicalRelTol ( real_t phys_rel_tol )

inline

Set the relative physical-space convergence tolerance.

Definition at line 363 of file eltrans.hpp.

◆ SetPrintLevel()

void mfem::InverseElementTransformation::SetPrintLevel ( int pr_level )

inline

Set the desired print level, useful for debugging.

The valid options are: -1 - never print (default); 0 - print only errors; 1 - print the first and last iterations; 2 - print every iteration; and 3 - print every iteration including point coordinates.

Definition at line 374 of file eltrans.hpp.

◆ SetReferenceTol()

void mfem::InverseElementTransformation::SetReferenceTol ( real_t ref_sp_tol )

inline

Set the reference-space convergence tolerance.

Definition at line 360 of file eltrans.hpp.

◆ SetSolverType()

void mfem::InverseElementTransformation::SetSolverType ( SolverType stype )

inline

Specify which algorithm to use for solving the transformation equation, i.e. when calling the Transform() method.

Definition at line 354 of file eltrans.hpp.

◆ SetTransformation()

void mfem::InverseElementTransformation::SetTransformation ( ElementTransformation & Trans )

inline

Set a new forward ElementTransformation, Trans.

Definition at line 320 of file eltrans.hpp.

◆ Transform()

int mfem::InverseElementTransformation::Transform	(	const Vector &	pt,
		IntegrationPoint &	ip )

virtual

Given a point, pt, in physical space, find its reference coordinates, ip.

Returns: A value of type TransformResult.

Definition at line 338 of file eltrans.cpp.

Member Data Documentation

◆ init_guess_type

int mfem::InverseElementTransformation::init_guess_type

protected

Definition at line 255 of file eltrans.hpp.

◆ ip0

IntegrationPoint mfem::InverseElementTransformation::ip0

protected

Definition at line 254 of file eltrans.hpp.

◆ ip_tol

real_t mfem::InverseElementTransformation::ip_tol

protected

Definition at line 264 of file eltrans.hpp.

◆ max_iter

int mfem::InverseElementTransformation::max_iter

protected

Definition at line 261 of file eltrans.hpp.

◆ phys_rtol

real_t mfem::InverseElementTransformation::phys_rtol

protected

Definition at line 263 of file eltrans.hpp.

◆ print_level

int mfem::InverseElementTransformation::print_level

protected

Definition at line 265 of file eltrans.hpp.

◆ qpts_order

int mfem::InverseElementTransformation::qpts_order

protected

Definition at line 257 of file eltrans.hpp.

◆ ref_tol

real_t mfem::InverseElementTransformation::ref_tol

protected

Definition at line 262 of file eltrans.hpp.

◆ refiner

GeometryRefiner mfem::InverseElementTransformation::refiner

protected

Definition at line 256 of file eltrans.hpp.

◆ rel_qpts_order

int mfem::InverseElementTransformation::rel_qpts_order

protected

Definition at line 259 of file eltrans.hpp.

◆ solver_type

int mfem::InverseElementTransformation::solver_type

protected

Definition at line 260 of file eltrans.hpp.

◆ T

ElementTransformation* mfem::InverseElementTransformation::T

protected

Definition at line 251 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

Protected Member Functions

Protected Attributes

Detailed Description

Member Enumeration Documentation

◆ InitGuessType

◆ SolverType

◆ TransformResult

Constructor & Destructor Documentation

◆ InverseElementTransformation()

◆ ~InverseElementTransformation()

Member Function Documentation

◆ FindClosestPhysPoint()

◆ FindClosestRefPoint()

◆ NewtonPrint()

◆ NewtonPrintPoint()

◆ NewtonSolve()

◆ SetElementTol()

◆ SetInitGuessOrder()

◆ SetInitGuessPointsType()

◆ SetInitGuessRelOrder()

◆ SetInitialGuess()

◆ SetInitialGuessType()

◆ SetMaxIter()

◆ SetPhysicalRelTol()

◆ SetPrintLevel()

◆ SetReferenceTol()

◆ SetSolverType()

◆ SetTransformation()

◆ Transform()

Member Data Documentation

◆ init_guess_type

◆ ip0

◆ ip_tol

◆ max_iter

◆ phys_rtol

◆ print_level

◆ qpts_order

◆ ref_tol

◆ refiner

◆ rel_qpts_order

◆ solver_type

◆ T