Jacobi smoothing for a given bilinear form (no matrix necessary). More...

#include <solvers.hpp>

Inheritance diagram for mfem::OperatorJacobiSmoother:

Collaboration diagram for mfem::OperatorJacobiSmoother:

Public Member Functions
	OperatorJacobiSmoother (const real_t damping=1.0)
	Default constructor: the diagonal will be computed by subsequent calls to SetOperator() using the Operator method AssembleDiagonal.

	OperatorJacobiSmoother (const BilinearForm &a, const Array< int > &ess_tdof_list, const real_t damping=1.0)

	OperatorJacobiSmoother (const Vector &d, const Array< int > &ess_tdof_list, const real_t damping=1.0)

	~OperatorJacobiSmoother ()

void	SetPositiveDiagonal (bool pos_diag=true)
	Replace diagonal entries with their absolute values.

void	Mult (const Vector &x, Vector &y) const
	Approach the solution of the linear system by applying Jacobi smoothing.

void	MultTranspose (const Vector &x, Vector &y) const
	Approach the solution of the transposed linear system by applying Jacobi smoothing.

void	SetOperator (const Operator &op)
	Recompute the diagonal using the method AssembleDiagonal of the given new Operator, op.

void	Setup (const Vector &diag)

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

Additional Inherited Members
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".

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.

Detailed Description

Jacobi smoothing for a given bilinear form (no matrix necessary).

Useful with tensorized, partially assembled operators. Can also be defined by given diagonal vector. This is basic Jacobi iteration; for tolerances, iteration control, etc. wrap with SLISolver.

Definition at line 312 of file solvers.hpp.

Constructor & Destructor Documentation

◆ OperatorJacobiSmoother() [1/3]

mfem::OperatorJacobiSmoother::OperatorJacobiSmoother ( const real_t damping = 1.0 )

Default constructor: the diagonal will be computed by subsequent calls to SetOperator() using the Operator method AssembleDiagonal.

In this case the array of essential tdofs will be empty.

Definition at line 200 of file solvers.cpp.

◆ OperatorJacobiSmoother() [2/3]

mfem::OperatorJacobiSmoother::OperatorJacobiSmoother	(	const BilinearForm &	a,
		const Array< int > &	ess_tdof_list,
		const real_t	damping = 1.0 )

Setup a Jacobi smoother with the diagonal of a obtained by calling a.AssembleDiagonal(). It is assumed that the underlying operator acts as the identity on entries in ess_tdof_list, corresponding to (assembled) DIAG_ONE policy or ConstrainedOperator in the matrix-free setting.

Note: For objects created with this constructor, calling SetOperator() will only set the internal Operator pointer to the given new Operator without any other changes to the object. This is done to preserve the original behavior of this class.

Definition at line 207 of file solvers.cpp.

◆ OperatorJacobiSmoother() [3/3]

mfem::OperatorJacobiSmoother::OperatorJacobiSmoother	(	const Vector &	d,
		const Array< int > &	ess_tdof_list,
		const real_t	damping = 1.0 )

Application is by the inverse of the given vector. It is assumed that the underlying operator acts as the identity on entries in ess_tdof_list, corresponding to (assembled) DIAG_ONE policy or ConstrainedOperator in the matrix-free setting.

Note: For objects created with this constructor, calling SetOperator() will only set the internal Operator pointer to the given new Operator without any other changes to the object. This is done to preserve the original behavior of this class.

Definition at line 226 of file solvers.cpp.

◆ ~OperatorJacobiSmoother()

mfem::OperatorJacobiSmoother::~OperatorJacobiSmoother ( )

inline

Definition at line 346 of file solvers.hpp.

Member Function Documentation

◆ Mult()

void mfem::OperatorJacobiSmoother::Mult	(	const Vector &	x,
		Vector &	y ) const

virtual

Approach the solution of the linear system by applying Jacobi smoothing.

Implements mfem::Operator.

Definition at line 303 of file solvers.cpp.

◆ MultTranspose()

void mfem::OperatorJacobiSmoother::MultTranspose	(	const Vector &	x,
		Vector &	y ) const

inlinevirtual

Approach the solution of the transposed linear system by applying Jacobi smoothing.

Reimplemented from mfem::Operator.

Definition at line 356 of file solvers.hpp.

◆ SetOperator()

void mfem::OperatorJacobiSmoother::SetOperator ( const Operator & op )

virtual

Recompute the diagonal using the method AssembleDiagonal of the given new Operator, op.

Note that (Par)BilinearForm operators are treated similar to the way they are treated in the constructor that takes a BilinearForm parameter. Specifically, this means that the OperatorJacobiSmoother will work with true-dof vectors even though the size of the BilinearForm may be different.

When the new Operator, op, is not a (Par)BilinearForm, any previously set array of essential true-dofs will be thrown away because in this case any essential b.c. will be handled by the AssembleDiagonal method.

Implements mfem::Solver.

Definition at line 241 of file solvers.cpp.

◆ SetPositiveDiagonal()

void mfem::OperatorJacobiSmoother::SetPositiveDiagonal ( bool pos_diag = true )

inline

Replace diagonal entries with their absolute values.

Definition at line 349 of file solvers.hpp.

◆ Setup()

void mfem::OperatorJacobiSmoother::Setup ( const Vector & diag )

Definition at line 277 of file solvers.cpp.

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

linalg/solvers.hpp
linalg/solvers.cpp

Public Member Functions

Additional Inherited Members