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. More...

	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. More...

Public Member Functions inherited from Teko::BlockImplicitLinearOp
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. More...

Related Functions
(Note that these are not member functions.)
ModifiableLinearOp	createDiagnosticLinearOp (const Teuchos::RCP< std::ostream > &os, const ModifiableLinearOp &A, const std::string &label)
	Constructor method for building `DiagnosticLinearOp`. More...

ModifiableLinearOp	createDiagnosticLinearOp (const Teuchos::RCP< std::ostream > &os, const LinearOp &A, const std::string &label)
	Constructor method for building `DiagnosticLinearOp`. More...

ModifiableLinearOp	createDiagnosticLinearOp (const Teuchos::RCP< std::ostream > &os, const Teko::LinearOp &fwdOp, const ModifiableLinearOp &A, const std::string &label)
	Constructor method for building `DiagnosticLinearOp`. More...

LinearOp	createLU2x2InverseOp (BlockedLinearOp &A, LinearOp &invA00, LinearOp &invS)
	Constructor method for building `LU2x2InverseOp`. More...

LinearOp	createLU2x2InverseOp (BlockedLinearOp &A, LinearOp &invA00, LinearOp &invS, const std::string &str)
	Constructor method for building `LU2x2InverseOp`. More...

LinearOp	createLU2x2InverseOp (BlockedLinearOp &A, LinearOp &hatInvA00, LinearOp &tildeInvA00, LinearOp &invS)
	Constructor method for building `LU2x2InverseOp`. More...

LinearOp	createLU2x2InverseOp (BlockedLinearOp &A, LinearOp &hatInvA00, LinearOp &tildeInvA00, LinearOp &invS, const std::string &str)
	Constructor method for building `LU2x2InverseOp`. More...

Inherited methods from Thyra::LinearOpBase
const BlockedLinearOp	A_
	operator More...

const LinearOp	hatInvA00_
	inverse of $A_{00}$ More...

const LinearOp	tildeInvA00_
	inverse of $A_{00}$ More...

const LinearOp	invS_
	inverse of More...

const LinearOp	A10_
	operator $A_{10}$ More...

const LinearOp	A01_
	operator $A_{01}$ More...

Teuchos::RCP< const Thyra::ProductVectorSpaceBase< double > >	productRange_
	Range vector space. More...

Teuchos::RCP< const Thyra::ProductVectorSpaceBase< double > >	productDomain_
	Domain vector space. More...

virtual VectorSpace	range () const
	Range space of this operator. More...

virtual VectorSpace	domain () const
	Domain space of this operator. More...

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. More...

virtual void	describe (Teuchos::FancyOStream &out_arg, const Teuchos::EVerbosityLevel verbLevel) const

virtual void	implicitApply (const BlockedMultiVector &x, BlockedMultiVector &y, const double alpha=1.0, const double beta=0.0) const=0
	Perform a matrix vector multiply with this implicitly defined blocked operator. More...

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. More...

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

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 101 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 63 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 90 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 137 of file Teko_LU2x2InverseOp.hpp.

◆ domain()

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

inlinevirtual

Domain space of this operator.

Implements Teko::BlockImplicitLinearOp.

Definition at line 140 of file Teko_LU2x2InverseOp.hpp.

◆ implicitApply() [1/3]

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 107 of file Teko_LU2x2InverseOp.cpp.

◆ implicitApply() [2/3]

virtual void Teko::BlockImplicitLinearOp::implicitApply

protected

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)

◆ implicitApply() [3/3]

void Teko::BlockImplicitLinearOp::implicitApply

protected

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)

Definition at line 99 of file Teko_BlockImplicitLinearOp.cpp.

Friends And Related Function Documentation

◆ 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 172 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 190 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 209 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 196 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 215 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 237 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 257 of file Teko_LU2x2InverseOp.hpp.

Member Data Documentation

◆ A_

const BlockedLinearOp Teko::LU2x2InverseOp::A_

protected

operator

Definition at line 165 of file Teko_LU2x2InverseOp.hpp.

◆ hatInvA00_

const LinearOp Teko::LU2x2InverseOp::hatInvA00_

protected

inverse of $A_{00}$

Definition at line 166 of file Teko_LU2x2InverseOp.hpp.

◆ tildeInvA00_

const LinearOp Teko::LU2x2InverseOp::tildeInvA00_

protected

inverse of $A_{00}$

Definition at line 167 of file Teko_LU2x2InverseOp.hpp.

◆ invS_

const LinearOp Teko::LU2x2InverseOp::invS_

protected

inverse of

Definition at line 168 of file Teko_LU2x2InverseOp.hpp.

◆ A10_

const LinearOp Teko::LU2x2InverseOp::A10_

protected

operator $A_{10}$

Definition at line 171 of file Teko_LU2x2InverseOp.hpp.

◆ A01_

const LinearOp Teko::LU2x2InverseOp::A01_

protected

operator $A_{01}$

Definition at line 172 of file Teko_LU2x2InverseOp.hpp.

◆ productRange_

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

protected

Range vector space.

Definition at line 174 of file Teko_LU2x2InverseOp.hpp.

◆ productDomain_

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

protected

Domain vector space.

Definition at line 175 of file Teko_LU2x2InverseOp.hpp.

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

Public Member Functions

Related Functions

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() [1/3]

◆ implicitApply() [2/3]

◆ implicitApply() [3/3]

Friends And Related Function 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_