This linear operator approximates the inverse of a block $2\times 2$ operator using a block decomposition. More...

#include <Teko_LU2x2InverseOp.hpp>

Inheritance diagram for Teko::LU2x2InverseOp:

Public Member Functions
	LU2x2InverseOp (const BlockedLinearOp &A, const LinearOp &invA00, const LinearOp &invS)
	This constructor explicitly takes the parts of required to build the inverse operator.
	LU2x2InverseOp (const BlockedLinearOp &A, const LinearOp &hatInvA00, const LinearOp &tildeInvA00, const LinearOp &invS)
	This constructor explicitly takes the parts of required to build the inverse operator.

Related Symbols
(Note that these are not member symbols.)
ModifiableLinearOp	createDiagnosticLinearOp (const Teuchos::RCP< std::ostream > &os, const ModifiableLinearOp &A, const std::string &label)
	Constructor method for building `DiagnosticLinearOp`.
ModifiableLinearOp	createDiagnosticLinearOp (const Teuchos::RCP< std::ostream > &os, const LinearOp &A, const std::string &label)
	Constructor method for building `DiagnosticLinearOp`.
ModifiableLinearOp	createDiagnosticLinearOp (const Teuchos::RCP< std::ostream > &os, const Teko::LinearOp &fwdOp, const ModifiableLinearOp &A, const std::string &label)
	Constructor method for building `DiagnosticLinearOp`.
LinearOp	createLU2x2InverseOp (BlockedLinearOp &A, LinearOp &invA00, LinearOp &invS)
	Constructor method for building `LU2x2InverseOp`.
LinearOp	createLU2x2InverseOp (BlockedLinearOp &A, LinearOp &invA00, LinearOp &invS, const std::string &str)
	Constructor method for building `LU2x2InverseOp`.
LinearOp	createLU2x2InverseOp (BlockedLinearOp &A, LinearOp &hatInvA00, LinearOp &tildeInvA00, LinearOp &invS)
	Constructor method for building `LU2x2InverseOp`.
LinearOp	createLU2x2InverseOp (BlockedLinearOp &A, LinearOp &hatInvA00, LinearOp &tildeInvA00, LinearOp &invS, const std::string &str)
	Constructor method for building `LU2x2InverseOp`.

Inherited methods from Thyra::LinearOpBase
const BlockedLinearOp	A_
	operator
const LinearOp	hatInvA00_
	inverse of $A_{00}$
const LinearOp	tildeInvA00_
	inverse of $A_{00}$
const LinearOp	invS_
	inverse of
const LinearOp	A10_
	operator $A_{10}$
const LinearOp	A01_
	operator $A_{01}$
Teuchos::RCP< const Thyra::ProductVectorSpaceBase< double > >	productRange_
	Range vector space.
Teuchos::RCP< const Thyra::ProductVectorSpaceBase< double > >	productDomain_
	Domain vector space.
virtual VectorSpace	range () const
	Range space of this operator.
virtual VectorSpace	domain () const
	Domain space of this operator.
virtual void	implicitApply (const BlockedMultiVector &x, BlockedMultiVector &y, const double alpha=1.0, const double beta=0.0) const
	Perform a matrix vector multiply with this operator.
virtual void	implicitApply (const Thyra::EOpTransp M_trans, const BlockedMultiVector &x, BlockedMultiVector &y, const double alpha=1.0, const double beta=0.0) const
	Perform a matrix vector multiply with this implicitly defined blocked operator.

Additional Inherited Members
Protected Member Functions inherited from Teko::BlockImplicitLinearOp
virtual bool	opSupportedImpl (const Thyra::EOpTransp M_trans) const
	Functions required by Thyra::LinearOpBase.

Detailed Description

This linear operator approximates the inverse of a block $2\times 2$ operator using a block decomposition.

For a matrix that is blocked like

$A = \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{10} & A_{11} \end{array}\right]$

this class evaluates the $A^{-1}$ given $A_{00}^{-1}$ and the inverse of the Schur complement. The factorization is defined as

$A = \left[ \begin{array}{cc} I & 0 \\ A_{10} A_{00}^{-1} & I \end{array} \right] \left[ \begin{array}{cc} A_{00} & 0 \\ 0 & -S \end{array} \right] \left[ \begin{array}{cc} I & A_{00}^{-1} A_{01} \\ 0 & I \end{array} \right]$

where the Schur complement is $S=-A_{11}+A_{10} A_{00}^{-1} A_{01}$ . In order to do this 2 evaluations of $A_{00}^{-1}$ and a single evalution of $S^{-1}$ are needed. For increased flexibility both evaluations of $A_{00}^{-1}$ can be specified independently. For righthand side vector and solution vector the two inverses ( -hat and -tilde) are needed to evaluate

$\hat{A}_{00} u^* = f$ ,

$\tilde{A}_{00} v = A_{01} v$

where is an intermediate step.

Definition at line 64 of file Teko_LU2x2InverseOp.hpp.

Constructor & Destructor Documentation

◆ LU2x2InverseOp() [1/2]

Teko::LU2x2InverseOp::LU2x2InverseOp	(	const BlockedLinearOp &	A,
		const LinearOp &	invA00,
		const LinearOp &	invS )

This constructor explicitly takes the parts of required to build the inverse operator.

Parameters

[in]	A	The block $2 \times 2$ operator.
[in]	invA00	An approximate inverse of $A_{00}$ , used for both $\hat{A}_{00}$ and $\tilde{A}_{00}$
[in]	invS	An approximate inverse of $S = -A_{11} + A_{10} A_{00}^{-1} A_{01}$ .

Definition at line 26 of file Teko_LU2x2InverseOp.cpp.

◆ LU2x2InverseOp() [2/2]

Teko::LU2x2InverseOp::LU2x2InverseOp	(	const BlockedLinearOp &	A,
		const LinearOp &	hatInvA00,
		const LinearOp &	tildeInvA00,
		const LinearOp &	invS )

This constructor explicitly takes the parts of required to build the inverse operator.

Parameters

[in]	A	The block $2 \times 2$ operator.
[in]	hatInvA00	An approximate inverse of $\hat{A}_{00}$
[in]	tildeInvA00	An approximate inverse of $\tilde{A}_{00}$
[in]	invS	An approximate inverse of $S = -A_{11} + A_{10} A_{00}^{-1} A_{01}$ .

Definition at line 55 of file Teko_LU2x2InverseOp.cpp.

Member Function Documentation

◆ range()

virtual VectorSpace Teko::LU2x2InverseOp::range ( ) const

inlinevirtual

Range space of this operator.

Implements Teko::BlockImplicitLinearOp.

Definition at line 97 of file Teko_LU2x2InverseOp.hpp.

◆ domain()

virtual VectorSpace Teko::LU2x2InverseOp::domain ( ) const

inlinevirtual

Domain space of this operator.

Implements Teko::BlockImplicitLinearOp.

Definition at line 100 of file Teko_LU2x2InverseOp.hpp.

◆ implicitApply() [1/2]

void Teko::LU2x2InverseOp::implicitApply	(	const BlockedMultiVector &	x,
		BlockedMultiVector &	y,
		const double	alpha = 1.0,
		const double	beta = 0.0 ) const

virtual

Perform a matrix vector multiply with this operator.

The apply function takes one vector as input and applies the inverse decomposition. The result is returned in . If this operator is reprsented as then $y = \alpha M x + \beta y$ (ignoring conjugation!).

Parameters

[in]	x
[in,out]	y
[in]	alpha	(default=1)
[in]	beta	(default=0)

Implements Teko::BlockImplicitLinearOp.

Definition at line 73 of file Teko_LU2x2InverseOp.cpp.

◆ implicitApply() [2/2]

void Teko::BlockImplicitLinearOp::implicitApply	(	const Thyra::EOpTransp	M_trans,
		const BlockedMultiVector &	x,
		BlockedMultiVector &	y,
		const double	alpha = 1.0,
		const double	beta = 0.0 ) const

protectedvirtual

Perform a matrix vector multiply with this implicitly defined blocked operator.

The apply function takes one vector as input and applies a linear operator. The result is returned in . If this operator is reprsented as then $y = \alpha M x + \beta y$

Parameters

[in]	x
[in,out]	y
[in]	alpha	(default=1)
[in]	beta	(default=0)

Reimplemented from Teko::BlockImplicitLinearOp.

Definition at line 61 of file Teko_BlockImplicitLinearOp.cpp.

◆ createDiagnosticLinearOp() [1/3]

ModifiableLinearOp createDiagnosticLinearOp	(	const Teuchos::RCP< std::ostream > &	os,
		const ModifiableLinearOp &	A,
		const std::string &	label )

Constructor method for building DiagnosticLinearOp.

Parameters

[in]	os	Output stream to print diagnostics to
[in]	A	Operator to be wrapped
[in]	label	String for outputing with diagnostics

Returns: A linear operator that wrapping A that will print diagnostics on descruction.

Definition at line 137 of file Teko_DiagnosticLinearOp.hpp.

◆ createDiagnosticLinearOp() [2/3]

ModifiableLinearOp createDiagnosticLinearOp	(	const Teuchos::RCP< std::ostream > &	os,
		const LinearOp &	A,
		const std::string &	label )

Constructor method for building DiagnosticLinearOp.

Parameters

[in]	os	Output stream to print diagnostics to
[in]	A	Operator to be wrapped
[in]	label	String for outputing with diagnostics

Returns: A linear operator that wrapping A that will print diagnostics on descruction.

Definition at line 156 of file Teko_DiagnosticLinearOp.hpp.

◆ createDiagnosticLinearOp() [3/3]

ModifiableLinearOp createDiagnosticLinearOp	(	const Teuchos::RCP< std::ostream > &	os,
		const Teko::LinearOp &	fwdOp,
		const ModifiableLinearOp &	A,
		const std::string &	label )

Constructor method for building DiagnosticLinearOp.

Parameters

[in]	os	Output stream to print diagnostics to
[in]	fwdOp	Forward operator to compute residual with
[in]	A	Operator to be wrapped
[in]	label	String for outputing with diagnostics

Returns: A linear operator that wrapping A that will print diagnostics on descruction.

Definition at line 175 of file Teko_DiagnosticLinearOp.hpp.

◆ createLU2x2InverseOp() [1/4]

LinearOp createLU2x2InverseOp	(	BlockedLinearOp &	A,
		LinearOp &	invA00,
		LinearOp &	invS )

Constructor method for building LU2x2InverseOp.

Parameters

[in]	A	2x2 Operator to be decomposed
[in]	invA00	Approximate inverse of the operators block.
[in]	invS	Approximate inverse of the Schur complement

Returns: A linear operator that behaves like the inverse of the LU decomposition.

Definition at line 158 of file Teko_LU2x2InverseOp.hpp.

◆ createLU2x2InverseOp() [2/4]

LinearOp createLU2x2InverseOp	(	BlockedLinearOp &	A,
		LinearOp &	invA00,
		LinearOp &	invS,
		const std::string &	str )

Constructor method for building LU2x2InverseOp.

Parameters

[in]	A	2x2 Operator to be decomposed
[in]	invA00	Approximate inverse of the operators block.
[in]	invS	Approximate inverse of the Schur complement
[in]	str	String to label the operator

Returns: A linear operator that behaves like the inverse of the LU decomposition.

Definition at line 176 of file Teko_LU2x2InverseOp.hpp.

◆ createLU2x2InverseOp() [3/4]

LinearOp createLU2x2InverseOp	(	BlockedLinearOp &	A,
		LinearOp &	hatInvA00,
		LinearOp &	tildeInvA00,
		LinearOp &	invS )

Constructor method for building LU2x2InverseOp.

Parameters

[in]	A	2x2 Operator to be decomposed
[in]	hatInvA00	First approximate inverse of the operators block.
[in]	tildeInvA00	Second approximate inverse of the operators block.
[in]	invS	Approximate inverse of the Schur complement

Returns: A linear operator that behaves like the inverse of the LU decomposition.

Definition at line 199 of file Teko_LU2x2InverseOp.hpp.

◆ createLU2x2InverseOp() [4/4]

LinearOp createLU2x2InverseOp	(	BlockedLinearOp &	A,
		LinearOp &	hatInvA00,
		LinearOp &	tildeInvA00,
		LinearOp &	invS,
		const std::string &	str )

Constructor method for building LU2x2InverseOp.

Parameters

[in]	A	2x2 Operator to be decomposed
[in]	hatInvA00	First approximate inverse of the operators block.
[in]	tildeInvA00	Second approximate inverse of the operators block.
[in]	invS	Approximate inverse of the Schur complement
[in]	str	String to label the operator

Returns: A linear operator that behaves like the inverse of the LU decomposition.

Definition at line 219 of file Teko_LU2x2InverseOp.hpp.

Member Data Documentation

◆ A_

const BlockedLinearOp Teko::LU2x2InverseOp::A_

protected

operator

Definition at line 125 of file Teko_LU2x2InverseOp.hpp.

◆ hatInvA00_

const LinearOp Teko::LU2x2InverseOp::hatInvA00_

protected

inverse of $A_{00}$

Definition at line 126 of file Teko_LU2x2InverseOp.hpp.

◆ tildeInvA00_

const LinearOp Teko::LU2x2InverseOp::tildeInvA00_

protected

inverse of $A_{00}$

Definition at line 127 of file Teko_LU2x2InverseOp.hpp.

◆ invS_

const LinearOp Teko::LU2x2InverseOp::invS_

protected

inverse of

Definition at line 128 of file Teko_LU2x2InverseOp.hpp.

◆ A10_

const LinearOp Teko::LU2x2InverseOp::A10_

protected

operator $A_{10}$

Definition at line 131 of file Teko_LU2x2InverseOp.hpp.

◆ A01_

const LinearOp Teko::LU2x2InverseOp::A01_

protected

operator $A_{01}$

Definition at line 132 of file Teko_LU2x2InverseOp.hpp.

◆ productRange_

Teuchos::RCP<const Thyra::ProductVectorSpaceBase<double> > Teko::LU2x2InverseOp::productRange_

protected

Range vector space.

Definition at line 135 of file Teko_LU2x2InverseOp.hpp.

◆ productDomain_

Teuchos::RCP<const Thyra::ProductVectorSpaceBase<double> > Teko::LU2x2InverseOp::productDomain_

protected

Domain vector space.

Definition at line 137 of file Teko_LU2x2InverseOp.hpp.

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

Public Member Functions

Related Symbols

Inherited methods from Thyra::LinearOpBase

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ LU2x2InverseOp() [1/2]

◆ LU2x2InverseOp() [2/2]

Member Function Documentation

◆ range()

◆ domain()

◆ implicitApply() [1/2]

◆ implicitApply() [2/2]

Friends And Related Symbol Documentation

◆ createDiagnosticLinearOp() [1/3]

◆ createDiagnosticLinearOp() [2/3]

◆ createDiagnosticLinearOp() [3/3]

◆ createLU2x2InverseOp() [1/4]

◆ createLU2x2InverseOp() [2/4]

◆ createLU2x2InverseOp() [3/4]

◆ createLU2x2InverseOp() [4/4]

Member Data Documentation

◆ A_

◆ hatInvA00_

◆ tildeInvA00_

◆ invS_

◆ A10_

◆ A01_

◆ productRange_

◆ productDomain_