mfem::InverseElementTransformation Class Reference

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 }
	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. More...
virtual	~InverseElementTransformation ()
void	SetTransformation (ElementTransformation &Trans)
	Set a new forward ElementTransformation, Trans. More...
void	SetInitialGuessType (InitGuessType itype)
	Choose how the initial guesses for subsequent calls to Transform() will be selected. More...
void	SetInitialGuess (const IntegrationPoint &init_ip)
	Set the initial guess for subsequent calls to Transform(), switching to the GivenPoint InitGuessType at the same time. More...
void	SetInitGuessPointsType (int q_type)
	Set the Quadrature1D type used for the Closest* initial guess types. More...
void	SetInitGuessRelOrder (int order)
	Set the relative order used for the Closest* initial guess types. More...
void	SetSolverType (SolverType stype)
	Specify which algorithm to use for solving the transformation equation, i.e. when calling the Transform() method. More...
void	SetMaxIter (int max_it)
	Set the maximum number of iterations when solving for a reference point. More...
void	SetReferenceTol (double ref_sp_tol)
	Set the reference-space convergence tolerance. More...
void	SetPhysicalRelTol (double phys_rel_tol)
	Set the relative physical-space convergence tolerance. More...
void	SetElementTol (double el_tol)
	Set the tolerance used to determine if a point lies inside or outside of the reference element. More...
void	SetPrintLevel (int pr_level)
	Set the desired print level, useful for debugging. More...
int	FindClosestPhysPoint (const Vector &pt, const IntegrationRule &ir)
	Find the IntegrationPoint mapped closest to pt. More...
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. More...
virtual int	Transform (const Vector &pt, IntegrationPoint &ip)
	Given a point, pt, in physical space, find its reference coordinates, ip. More...

Protected Member Functions
void	NewtonPrint (int mode, double val)
void	NewtonPrintPoint (const char *prefix, const Vector &pt, const char *suffix)
int	NewtonSolve (const Vector &pt, IntegrationPoint &ip)

Protected Attributes
ElementTransformation *	T
const IntegrationPoint *	ip0
int	init_guess_type
int	qpts_type
int	rel_qpts_order
int	solver_type
int	max_iter
double	ref_tol
double	phys_rtol
double	ip_tol
int	print_level

Detailed Description

The inverse transformation of a given ElementTransformation.

Definition at line 108 of file eltrans.hpp.

Member Enumeration Documentation

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().

Definition at line 112 of file eltrans.hpp.

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 127 of file eltrans.hpp.

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 145 of file eltrans.hpp.

Constructor & Destructor Documentation

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:

1. 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.
2. [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.
3. 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.
4. 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 198 of file eltrans.hpp.

virtual mfem::InverseElementTransformation::~InverseElementTransformation ( )

inlinevirtual

Definition at line 212 of file eltrans.hpp.

Member Function Documentation

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 57 of file eltrans.cpp.

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 84 of file eltrans.cpp.

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

protected

Definition at line 116 of file eltrans.cpp.

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

protected

Definition at line 145 of file eltrans.cpp.

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

protected

Definition at line 159 of file eltrans.cpp.

void mfem::InverseElementTransformation::SetElementTol ( double  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 251 of file eltrans.hpp.

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

inline

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

Definition at line 227 of file eltrans.hpp.

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 233 of file eltrans.hpp.

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 223 of file eltrans.hpp.

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

inline

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

Definition at line 219 of file eltrans.hpp.

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

inline

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

Definition at line 240 of file eltrans.hpp.

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

inline

Set the relative physical-space convergence tolerance.

Definition at line 246 of file eltrans.hpp.

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 last iterations; 2 - print every iteration; and 3 - print every iteration including point coordinates.

Definition at line 257 of file eltrans.hpp.

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

inline

Set the reference-space convergence tolerance.

Definition at line 243 of file eltrans.hpp.

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 237 of file eltrans.hpp.

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

inline

Set a new forward ElementTransformation, Trans.

Definition at line 215 of file eltrans.hpp.

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 323 of file eltrans.cpp.

Member Data Documentation

int mfem::InverseElementTransformation::init_guess_type

protected

Definition at line 158 of file eltrans.hpp.

const IntegrationPoint* mfem::InverseElementTransformation::ip0

protected

Definition at line 157 of file eltrans.hpp.

double mfem::InverseElementTransformation::ip_tol

protected

Definition at line 165 of file eltrans.hpp.

int mfem::InverseElementTransformation::max_iter

protected

Definition at line 162 of file eltrans.hpp.

double mfem::InverseElementTransformation::phys_rtol

protected

Definition at line 164 of file eltrans.hpp.

int mfem::InverseElementTransformation::print_level

protected

Definition at line 166 of file eltrans.hpp.

int mfem::InverseElementTransformation::qpts_type

protected

Definition at line 159 of file eltrans.hpp.

double mfem::InverseElementTransformation::ref_tol

protected

Definition at line 163 of file eltrans.hpp.

int mfem::InverseElementTransformation::rel_qpts_order

protected

Definition at line 160 of file eltrans.hpp.

int mfem::InverseElementTransformation::solver_type

protected

Definition at line 161 of file eltrans.hpp.

ElementTransformation* mfem::InverseElementTransformation::T

protected

Definition at line 154 of file eltrans.hpp.

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

• fem/eltrans.hpp
• fem/eltrans.cpp