Geometric multigrid associated with a hierarchy of finite element spaces. More...

#include <multigrid.hpp>

Inheritance diagram for mfem::GeometricMultigrid:

Collaboration diagram for mfem::GeometricMultigrid:

Public Member Functions
MFEM_DEPRECATED	GeometricMultigrid (const FiniteElementSpaceHierarchy &fespaces_)
	Deprecated.

	GeometricMultigrid (const FiniteElementSpaceHierarchy &fespaces_, const Array< int > &ess_bdr)
	Construct a geometric multigrid object for the given finite element space hierarchy fespaces_, where ess_bdr is a list of mesh boundary element attributes that define the essential DOFs.

virtual	~GeometricMultigrid ()
	Destructor.

void	FormFineLinearSystem (Vector &x, Vector &b, OperatorHandle &A, Vector &X, Vector &B)

void	RecoverFineFEMSolution (const Vector &X, const Vector &b, Vector &x)
	Recover the solution of a linear system formed with FormFineLinearSystem()

Public Member Functions inherited from mfem::Multigrid
	Multigrid ()=default
	Constructs an empty multigrid hierarchy.

	Multigrid (const Array< Operator * > &operators_, const Array< Solver * > &smoothers_, const Array< Operator * > &prolongations_, const Array< bool > &ownedOperators_, const Array< bool > &ownedSmoothers_, const Array< bool > &ownedProlongations_)
	Constructs a multigrid hierarchy from the given inputs.

virtual	~Multigrid ()
	Destructor.

Public Member Functions inherited from mfem::MultigridBase
	MultigridBase ()
	Constructs an empty multigrid hierarchy.

	MultigridBase (const Array< Operator * > &operators_, const Array< Solver * > &smoothers_, const Array< bool > &ownedOperators_, const Array< bool > &ownedSmoothers_)
	Constructs a multigrid hierarchy from the given inputs.

virtual	~MultigridBase ()
	Destructor.

void	AddLevel (Operator op, Solver smoother, bool ownOperator, bool ownSmoother)
	Adds a level to the multigrid operator hierarchy.

int	NumLevels () const
	Returns the number of levels.

int	GetFinestLevelIndex () const
	Returns the index of the finest level.

const Operator *	GetOperatorAtLevel (int level) const
	Returns operator at given level.

Operator *	GetOperatorAtLevel (int level)

const Operator *	GetOperatorAtFinestLevel () const
	Returns operator at finest level.

Operator *	GetOperatorAtFinestLevel ()

const Solver *	GetSmootherAtLevel (int level) const
	Returns smoother at given level.

Solver *	GetSmootherAtLevel (int level)

void	SetCycleType (CycleType cycleType_, int preSmoothingSteps_, int postSmoothingSteps_)
	Set cycle type and number of pre- and post-smoothing steps used by Mult.

virtual void	Mult (const Vector &x, Vector &y) const override
	Application of the multigrid as a preconditioner.

virtual void	ArrayMult (const Array< const Vector * > &X_, Array< Vector * > &Y_) const override
	Operator application on a matrix: `Y=A(X)`.

virtual void	SetOperator (const Operator &op) override
	Not supported for multigrid.

Public Member Functions inherited from mfem::Solver
	Solver (int s=0, bool iter_mode=false)
	Initialize a square Solver with size s.

	Solver (int h, int w, bool iter_mode=false)
	Initialize a Solver with height h and width w.

Public Member Functions inherited from mfem::Operator
void	InitTVectors (const Operator Po, const Operator Ri, const Operator *Pi, Vector &x, Vector &b, Vector &X, Vector &B) const
	Initializes memory for true vectors of linear system.

	Operator (int s=0)
	Construct a square Operator with given size s (default 0).

	Operator (int h, int w)
	Construct an Operator with the given height (output size) and width (input size).

int	Height () const
	Get the height (size of output) of the Operator. Synonym with NumRows().

int	NumRows () const
	Get the number of rows (size of output) of the Operator. Synonym with Height().

int	Width () const
	Get the width (size of input) of the Operator. Synonym with NumCols().

int	NumCols () const
	Get the number of columns (size of input) of the Operator. Synonym with Width().

virtual MemoryClass	GetMemoryClass () const
	Return the MemoryClass preferred by the Operator.

virtual void	MultTranspose (const Vector &x, Vector &y) const
	Action of the transpose operator: `y=A^t(x)`. The default behavior in class Operator is to generate an error.

virtual void	AddMult (const Vector &x, Vector &y, const real_t a=1.0) const
	Operator application: `y+=A(x)` (default) or `y+=a*A(x)`.

virtual void	AddMultTranspose (const Vector &x, Vector &y, const real_t a=1.0) const
	Operator transpose application: `y+=A^t(x)` (default) or `y+=a*A^t(x)`.

virtual void	ArrayMultTranspose (const Array< const Vector * > &X, Array< Vector * > &Y) const
	Action of the transpose operator on a matrix: `Y=A^t(X)`.

virtual void	ArrayAddMult (const Array< const Vector * > &X, Array< Vector * > &Y, const real_t a=1.0) const
	Operator application on a matrix: `Y+=A(X)` (default) or `Y+=a*A(X)`.

virtual void	ArrayAddMultTranspose (const Array< const Vector * > &X, Array< Vector * > &Y, const real_t a=1.0) const
	Operator transpose application on a matrix: `Y+=A^t(X)` (default) or `Y+=a*A^t(X)`.

virtual Operator &	GetGradient (const Vector &x) const
	Evaluate the gradient operator at the point x. The default behavior in class Operator is to generate an error.

virtual void	AssembleDiagonal (Vector &diag) const
	Computes the diagonal entries into diag. Typically, this operation only makes sense for linear Operators. In some cases, only an approximation of the diagonal is computed.

virtual const Operator *	GetProlongation () const
	Prolongation operator from linear algebra (linear system) vectors, to input vectors for the operator. `NULL` means identity.

virtual const Operator *	GetRestriction () const
	Restriction operator from input vectors for the operator to linear algebra (linear system) vectors. `NULL` means identity.

virtual const Operator *	GetOutputProlongation () const
	Prolongation operator from linear algebra (linear system) vectors, to output vectors for the operator. `NULL` means identity.

virtual const Operator *	GetOutputRestrictionTranspose () const
	Transpose of GetOutputRestriction, directly available in this form to facilitate matrix-free RAP-type operators.

virtual const Operator *	GetOutputRestriction () const
	Restriction operator from output vectors for the operator to linear algebra (linear system) vectors. `NULL` means identity.

void	FormLinearSystem (const Array< int > &ess_tdof_list, Vector &x, Vector &b, Operator *&A, Vector &X, Vector &B, int copy_interior=0)
	Form a constrained linear system using a matrix-free approach.

void	FormRectangularLinearSystem (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, Vector &x, Vector &b, Operator *&A, Vector &X, Vector &B)
	Form a column-constrained linear system using a matrix-free approach.

virtual void	RecoverFEMSolution (const Vector &X, const Vector &b, Vector &x)
	Reconstruct a solution vector x (e.g. a GridFunction) from the solution X of a constrained linear system obtained from Operator::FormLinearSystem() or Operator::FormRectangularLinearSystem().

void	FormSystemOperator (const Array< int > &ess_tdof_list, Operator *&A)
	Return in A a parallel (on truedofs) version of this square operator.

void	FormRectangularSystemOperator (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, Operator *&A)
	Return in A a parallel (on truedofs) version of this rectangular operator (including constraints).

void	FormDiscreteOperator (Operator *&A)
	Return in A a parallel (on truedofs) version of this rectangular operator.

void	PrintMatlab (std::ostream &out, int n, int m=0) const
	Prints operator with input size n and output size m in Matlab format.

virtual void	PrintMatlab (std::ostream &out) const
	Prints operator in Matlab format.

virtual	~Operator ()
	Virtual destructor.

Type	GetType () const
	Return the type ID of the Operator class.

Protected Attributes
const FiniteElementSpaceHierarchy &	fespaces

Array< Array< int > * >	essentialTrueDofs

Array< BilinearForm * >	bfs

Protected Attributes inherited from mfem::Multigrid
Array< Operator * >	prolongations

Array< bool >	ownedProlongations

Protected Attributes inherited from mfem::MultigridBase
Array< Operator * >	operators

Array< Solver * >	smoothers

Array< bool >	ownedOperators

Array< bool >	ownedSmoothers

CycleType	cycleType

int	preSmoothingSteps

int	postSmoothingSteps

Array2D< Vector * >	X

Array2D< Vector * >	Y

Array2D< Vector * >	R

Array2D< Vector * >	Z

int	nrhs

Protected Attributes inherited from mfem::Operator
int	height
	Dimension of the output / number of rows in the matrix.

int	width
	Dimension of the input / number of columns in the matrix.

Additional Inherited Members
Public Types inherited from mfem::MultigridBase
enum class	CycleType { VCYCLE , WCYCLE }

Public Types inherited from mfem::Operator
enum	DiagonalPolicy { DIAG_ZERO , DIAG_ONE , DIAG_KEEP }
	Defines operator diagonal policy upon elimination of rows and/or columns. More...

enum	Type { ANY_TYPE , MFEM_SPARSEMAT , Hypre_ParCSR , PETSC_MATAIJ , PETSC_MATIS , PETSC_MATSHELL , PETSC_MATNEST , PETSC_MATHYPRE , PETSC_MATGENERIC , Complex_Operator , MFEM_ComplexSparseMat , Complex_Hypre_ParCSR , Complex_DenseMat , MFEM_Block_Matrix , MFEM_Block_Operator }
	Enumeration defining IDs for some classes derived from Operator. More...

Public Attributes inherited from mfem::Solver
bool	iterative_mode
	If true, use the second argument of Mult() as an initial guess.

Protected Member Functions inherited from mfem::Operator
void	FormConstrainedSystemOperator (const Array< int > &ess_tdof_list, ConstrainedOperator *&Aout)
	see FormSystemOperator()

void	FormRectangularConstrainedSystemOperator (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, RectangularConstrainedOperator *&Aout)
	see FormRectangularSystemOperator()

Operator *	SetupRAP (const Operator Pi, const Operator Po)
	Returns RAP Operator of this, using input/output Prolongation matrices Pi corresponds to "P", Po corresponds to "Rt".

Detailed Description

Geometric multigrid associated with a hierarchy of finite element spaces.

Definition at line 165 of file multigrid.hpp.

Constructor & Destructor Documentation

◆ GeometricMultigrid() [1/2]

mfem::GeometricMultigrid::GeometricMultigrid ( const FiniteElementSpaceHierarchy & fespaces_ )

Deprecated.

Construct an empty geometric multigrid object for the given finite element space hierarchy fespaces_.

Deprecated: Use GeometricMultigrid::GeometricMultigrid(const FiniteElementSpaceHierarchy&, const Array<int>&) instead. This version constructs prolongation and restriction operators without eliminated essential boundary conditions.

Definition at line 257 of file multigrid.cpp.

◆ GeometricMultigrid() [2/2]

mfem::GeometricMultigrid::GeometricMultigrid	(	const FiniteElementSpaceHierarchy &	fespaces_,
		const Array< int > &	ess_bdr )

Construct a geometric multigrid object for the given finite element space hierarchy fespaces_, where ess_bdr is a list of mesh boundary element attributes that define the essential DOFs.

If ess_bdr is empty, or all its entries are 0, then no essential boundary conditions are imposed and the protected array essentialTrueDofs remains empty.

Definition at line 272 of file multigrid.cpp.

◆ ~GeometricMultigrid()

mfem::GeometricMultigrid::~GeometricMultigrid ( )

virtual

Destructor.

Definition at line 316 of file multigrid.cpp.

Member Function Documentation

◆ FormFineLinearSystem()

void mfem::GeometricMultigrid::FormFineLinearSystem	(	Vector &	x,
		Vector &	b,
		OperatorHandle &	A,
		Vector &	X,
		Vector &	B )

Form the linear system A X = B, corresponding to the operator on the finest level of the geometric multigrid hierarchy

Definition at line 328 of file multigrid.cpp.

◆ RecoverFineFEMSolution()

void mfem::GeometricMultigrid::RecoverFineFEMSolution	(	const Vector &	X,
		const Vector &	b,
		Vector &	x )

Recover the solution of a linear system formed with FormFineLinearSystem()

Definition at line 335 of file multigrid.cpp.

Member Data Documentation

◆ bfs

Array<BilinearForm*> mfem::GeometricMultigrid::bfs

protected

Definition at line 170 of file multigrid.hpp.

◆ essentialTrueDofs

Array<Array<int>*> mfem::GeometricMultigrid::essentialTrueDofs

protected

Definition at line 169 of file multigrid.hpp.

◆ fespaces

const FiniteElementSpaceHierarchy& mfem::GeometricMultigrid::fespaces

protected

Definition at line 168 of file multigrid.hpp.

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

fem/multigrid.hpp
fem/multigrid.cpp

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ GeometricMultigrid() [1/2]

◆ GeometricMultigrid() [2/2]

◆ ~GeometricMultigrid()

Member Function Documentation

◆ FormFineLinearSystem()

◆ RecoverFineFEMSolution()

Member Data Documentation

◆ bfs

◆ essentialTrueDofs

◆ fespaces