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

#include <operator.hpp>

Inheritance diagram for mfem::RectangularConstrainedOperator:

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Collaboration diagram for mfem::RectangularConstrainedOperator:

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

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

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

virtual void	Mult (const Vector &x, Vector &y) const
	Rectangular-constrained operator action.

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	~RectangularConstrainedOperator ()

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	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.

Protected Attributes
Array< int >	trial_constraints

Array< int >	test_constraints

Operator *	A

bool	own_A

Vector	z

Vector	w

MemoryClass	mem_class

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

Rectangular Operator for imposing essential boundary conditions on the input space using only the action, Mult(), of a given unconstrained Operator.

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

Definition at line 969 of file operator.hpp.

Constructor & Destructor Documentation

◆ RectangularConstrainedOperator()

mfem::RectangularConstrainedOperator::RectangularConstrainedOperator	(	Operator *	A,
		const Array< int > &	trial_list,
		const Array< int > &	test_list,
		bool	own_A = false )

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

Specify the unconstrained operator *A and two lists of indices to constrain, i.e. each entry trial_list[i] represents an essential trial dof. If the ownership flag own_A is true, the operator *A will be destroyed when this object is destroyed.

Definition at line 667 of file operator.cpp.

◆ ~RectangularConstrainedOperator()

virtual mfem::RectangularConstrainedOperator::~RectangularConstrainedOperator ( )

inlinevirtual

Definition at line 1012 of file operator.hpp.

Member Function Documentation

◆ EliminateRHS()

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

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

Performs the following steps:

b -= A((0,x_b));
b_j = 0

where the "_b" subscripts denote the essential (boundary) indices and the "_j" subscript denotes the essential test indices

Definition at line 686 of file operator.cpp.

◆ GetMemoryClass()

virtual MemoryClass mfem::RectangularConstrainedOperator::GetMemoryClass ( ) const

inlinevirtual

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

Reimplemented from mfem::Operator.

Definition at line 989 of file operator.hpp.

◆ Mult()

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

virtual

Rectangular-constrained operator action.

Performs the following steps:

y = A((x_i,0));
y_j = 0

where the "_i" subscripts denote all the nonessential (boundary) trial indices and the "_j" subscript denotes the essential test indices

Implements mfem::Operator.

Definition at line 712 of file operator.cpp.

◆ MultTranspose()

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

virtual

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 746 of file operator.cpp.

Member Data Documentation

◆ A

Operator* mfem::RectangularConstrainedOperator::A

protected

Definition at line 973 of file operator.hpp.

◆ mem_class

MemoryClass mfem::RectangularConstrainedOperator::mem_class

protected

Definition at line 976 of file operator.hpp.

◆ own_A

bool mfem::RectangularConstrainedOperator::own_A

protected

Definition at line 974 of file operator.hpp.

◆ test_constraints

Array<int> mfem::RectangularConstrainedOperator::test_constraints

protected

Definition at line 972 of file operator.hpp.

◆ trial_constraints

Array<int> mfem::RectangularConstrainedOperator::trial_constraints

protected

Definition at line 972 of file operator.hpp.

◆ w

Vector mfem::RectangularConstrainedOperator::w

protected

Definition at line 975 of file operator.hpp.

◆ z

Vector mfem::RectangularConstrainedOperator::z

mutableprotected

Definition at line 975 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

◆ RectangularConstrainedOperator()

◆ ~RectangularConstrainedOperator()

Member Function Documentation

◆ EliminateRHS()

◆ GetMemoryClass()

◆ Mult()

◆ MultTranspose()

Member Data Documentation

◆ A

◆ mem_class

◆ own_A

◆ test_constraints

◆ trial_constraints

◆ w

◆ z