Square Operator for imposing essential boundary conditions using only the action, Mult(), of a given unconstrained Operator. More...

#include <operator.hpp>

Inheritance diagram for mfem::ConstrainedOperator:

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Collaboration diagram for mfem::ConstrainedOperator:

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Public Member Functions
	ConstrainedOperator (Operator *A, const Array< int > &list, bool own_A=false, DiagonalPolicy diag_policy=DIAG_ONE)
	Constructor from a general Operator and a list of essential indices/dofs.

MemoryClass	GetMemoryClass () const override
	Returns the type of memory in which the solution and temporaries are stored.

void	SetDiagonalPolicy (const DiagonalPolicy diag_policy_)
	Set the diagonal policy for the constrained operator.

void	AssembleDiagonal (Vector &diag) const override
	Diagonal of A, modified according to the used DiagonalPolicy.

void	EliminateRHS (const Vector &x, Vector &b) const
	Eliminate "essential boundary condition" values specified in x from the given right-hand side b.

void	Mult (const Vector &x, Vector &y) const override
	Constrained operator action.

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

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

void	ConstrainedMult (const Vector &x, Vector &y, const bool transpose) const
	Implementation of Mult or MultTranspose. TODO - Generalize to allow constraining rows and columns differently.

	~ConstrainedOperator () override
	Destructor: destroys the unconstrained Operator, if owned.

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 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 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
Array< int >	constraint_list
	List of constrained indices/dofs.

Operator *	A
	The unconstrained Operator.

bool	own_A
	Ownership flag for A.

Vector	z

Vector	w
	Auxiliary vectors.

MemoryClass	mem_class

DiagonalPolicy	diag_policy
	Diagonal policy for constrained dofs.

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::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...

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

Square Operator for imposing essential boundary conditions using only the action, Mult(), of a given unconstrained Operator.

Square operator constrained by fixing certain entries in the solution to given "essential boundary condition" values. This class is used by the general, matrix-free system formulation of Operator::FormLinearSystem.

Do not confuse with ConstrainedSolver, which despite the name has very different functionality.

Definition at line 894 of file operator.hpp.

Constructor & Destructor Documentation

◆ ConstrainedOperator()

mfem::ConstrainedOperator::ConstrainedOperator	(	Operator *	A,
		const Array< int > &	list,
		bool	own_A = false,
		DiagonalPolicy	diag_policy = DIAG_ONE )

Constructor from a general Operator and a list of essential indices/dofs.

Specify the unconstrained operator *A and a list of indices to constrain, i.e. each entry list[i] represents an essential dof. If the ownership flag own_A is true, the operator *A will be destroyed when this object is destroyed. The diag_policy determines how the operator sets entries corresponding to essential dofs.

Definition at line 511 of file operator.cpp.

◆ ~ConstrainedOperator()

mfem::ConstrainedOperator::~ConstrainedOperator ( )

inlineoverride

Destructor: destroys the unconstrained Operator, if owned.

Definition at line 959 of file operator.hpp.

Member Function Documentation

◆ AddMult()

void mfem::ConstrainedOperator::AddMult	(	const Vector &	x,
		Vector &	y,
		const real_t	a = 1.0 ) const

overridevirtual

Operator application: y+=A(x) (default) or y+=a*A(x).

Reimplemented from mfem::Operator.

Definition at line 660 of file operator.cpp.

◆ AssembleDiagonal()

void mfem::ConstrainedOperator::AssembleDiagonal ( Vector & diag ) const

overridevirtual

Diagonal of A, modified according to the used DiagonalPolicy.

Reimplemented from mfem::Operator.

Definition at line 528 of file operator.cpp.

◆ ConstrainedMult()

void mfem::ConstrainedOperator::ConstrainedMult	(	const Vector &	x,
		Vector &	y,
		const bool	transpose ) const

Implementation of Mult or MultTranspose. TODO - Generalize to allow constraining rows and columns differently.

Definition at line 586 of file operator.cpp.

◆ EliminateRHS()

void mfem::ConstrainedOperator::EliminateRHS	(	const Vector &	x,
		Vector &	b ) const

Eliminate "essential boundary condition" values specified in x from the given right-hand side b.

Performs the following steps:

z = A((0,x_b));  b_i -= z_i;  b_b = x_b;

where the "_b" subscripts denote the essential (boundary) indices/dofs of the vectors, and "_i" – the rest of the entries.

Note: This method is consistent with DiagonalPolicy::DIAG_ONE.

Definition at line 559 of file operator.cpp.

◆ GetMemoryClass()

MemoryClass mfem::ConstrainedOperator::GetMemoryClass ( ) const

inlineoverridevirtual

Returns the type of memory in which the solution and temporaries are stored.

Reimplemented from mfem::Operator.

Definition at line 917 of file operator.hpp.

◆ Mult()

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

overridevirtual

Constrained operator action.

Performs the following steps:

z = A((x_i,0));  y_i = z_i;  y_b = x_b;

where the "_b" subscripts denote the essential (boundary) indices/dofs of the vectors, and "_i" – the rest of the entries.

Implements mfem::Operator.

Definition at line 648 of file operator.cpp.

◆ MultTranspose()

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

overridevirtual

Action of the transpose operator: y=A^t(x). The default behavior in class Operator is to generate an error.

Reimplemented from mfem::Operator.

Definition at line 654 of file operator.cpp.

◆ SetDiagonalPolicy()

void mfem::ConstrainedOperator::SetDiagonalPolicy ( const DiagonalPolicy diag_policy_ )

inline

Set the diagonal policy for the constrained operator.

Definition at line 920 of file operator.hpp.

Member Data Documentation

◆ A

Operator* mfem::ConstrainedOperator::A

protected

The unconstrained Operator.

Definition at line 898 of file operator.hpp.

◆ constraint_list

Array<int> mfem::ConstrainedOperator::constraint_list

protected

List of constrained indices/dofs.

Definition at line 897 of file operator.hpp.

◆ diag_policy

DiagonalPolicy mfem::ConstrainedOperator::diag_policy

protected

Diagonal policy for constrained dofs.

Definition at line 902 of file operator.hpp.

◆ mem_class

MemoryClass mfem::ConstrainedOperator::mem_class

protected

Definition at line 901 of file operator.hpp.

◆ own_A

bool mfem::ConstrainedOperator::own_A

protected

Ownership flag for A.

Definition at line 899 of file operator.hpp.

◆ w

Vector mfem::ConstrainedOperator::w

protected

Auxiliary vectors.

Definition at line 900 of file operator.hpp.

◆ z

Vector mfem::ConstrainedOperator::z

mutableprotected

Definition at line 900 of file operator.hpp.

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

linalg/operator.hpp
linalg/operator.cpp

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ ConstrainedOperator()

◆ ~ConstrainedOperator()

Member Function Documentation

◆ AddMult()

◆ AssembleDiagonal()

◆ ConstrainedMult()

◆ EliminateRHS()

◆ GetMemoryClass()

◆ Mult()

◆ MultTranspose()

◆ SetDiagonalPolicy()

Member Data Documentation

◆ A

◆ constraint_list

◆ diag_policy

◆ mem_class

◆ own_A

◆ w

◆ z