A stochastic preconditioner based on applying the approximate Schur complement preconditioner as defined by Sousedik, Ghanem, and Phipps, Numerical Linear Algebra and Applications, 2012. More...

#include <Stokhos_ApproxSchurComplementPreconditioner.hpp>

Inheritance diagram for Stokhos::ApproxSchurComplementPreconditioner:

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Collaboration diagram for Stokhos::ApproxSchurComplementPreconditioner:

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Public Member Functions
	ApproxSchurComplementPreconditioner (const Teuchos::RCP< const EpetraExt::MultiComm > &sg_comm, const Teuchos::RCP< const Stokhos::OrthogPolyBasis< int, double > > &sg_basis, const Teuchos::RCP< const Stokhos::EpetraSparse3Tensor > &epetraCijk, const Teuchos::RCP< const Epetra_Map > &base_map, const Teuchos::RCP< const Epetra_Map > &sg_map, const Teuchos::RCP< Stokhos::AbstractPreconditionerFactory > &prec_factory, const Teuchos::RCP< Teuchos::ParameterList > &params)
	Constructor.
virtual	~ApproxSchurComplementPreconditioner ()
	Destructor.
Stokhos::SGPreconditioner methods
virtual void	setupPreconditioner (const Teuchos::RCP< Stokhos::SGOperator > &sg_op, const Epetra_Vector &x)
	Setup preconditioner.
Public Member Functions inherited from Stokhos::SGPreconditioner
	SGPreconditioner ()
	Constructor.
virtual	~SGPreconditioner ()
	Destructor.

Epetra_Operator methods
typedef Stokhos::Sparse3Tensor< int, double >	Cijk_type
	Short-hand for Cijk.
std::string	label
	Label for operator.
Teuchos::RCP< const EpetraExt::MultiComm >	sg_comm
	Stores SG parallel communicator.
Teuchos::RCP< const Stokhos::OrthogPolyBasis< int, double > >	sg_basis
	Stochastic Galerking basis.
Teuchos::RCP< const Stokhos::EpetraSparse3Tensor >	epetraCijk
	Stores Epetra Cijk tensor.
Teuchos::RCP< const Epetra_Map >	base_map
	Stores base map.
Teuchos::RCP< const Epetra_Map >	sg_map
	Stores SG map.
Teuchos::RCP< Stokhos::AbstractPreconditionerFactory >	prec_factory
	Stores factory for building mean preconditioner.
Teuchos::RCP< Epetra_Operator >	mean_prec
	Stores mean preconditioner.
bool	useTranspose
	Flag indicating whether transpose was selected.
Teuchos::RCP< Stokhos::SGOperator >	sg_op
	Pointer to the SG operator.
Teuchos::RCP< Stokhos::EpetraOperatorOrthogPoly >	sg_poly
	Pointer to the PCE expansion of Jacobian.
Teuchos::RCP< const Cijk_type >	Cijk
	Pointer to triple product.
int	P
	Total polynomial order.
Teuchos::Array< int >	block_indices
	Starting block indices.
Teuchos::Array< Teuchos::RCP< Cijk_type > >	upper_block_Cijk
	Triple product tensor for each sub-block.
Teuchos::Array< Teuchos::RCP< Cijk_type > >	lower_block_Cijk
bool	scale_op
	Flag indicating whether operator be scaled with <\psi_i^2>.
bool	symmetric
	Use symmetric Gauss-Seidel.
bool	only_use_linear
	Limit Gauss-Seidel loop to linear terms.
int	max_num_mat_vec
	Maximum number of matvecs in Apply.
Teuchos::RCP< Epetra_MultiVector >	tmp
	Temporary vector for storing matrix-vector products.
Teuchos::RCP< EpetraExt::BlockMultiVector >	rhs_block
	Temporary vector for storing rhs in Gauss-Seidel loop.
Teuchos::Array< double * >	j_ptr
Teuchos::Array< int >	mj_indices
virtual int	SetUseTranspose (bool UseTranspose)
	Set to true if the transpose of the operator is requested.
virtual int	Apply (const Epetra_MultiVector &Input, Epetra_MultiVector &Result) const
	Returns the result of a Epetra_Operator applied to a Epetra_MultiVector Input in Result as described above.
virtual int	ApplyInverse (const Epetra_MultiVector &X, Epetra_MultiVector &Y) const
	Returns the result of the inverse of the operator applied to a Epetra_MultiVector Input in Result as described above.
virtual double	NormInf () const
	Returns an approximate infinity norm of the operator matrix.
virtual const char *	Label () const
	Returns a character string describing the operator.
virtual bool	UseTranspose () const
	Returns the current UseTranspose setting.
virtual bool	HasNormInf () const
	Returns true if the this object can provide an approximate Inf-norm, false otherwise.
virtual const Epetra_Comm &	Comm () const
	Returns a reference to the Epetra_Comm communicator associated with this operator.
virtual const Epetra_Map &	OperatorDomainMap () const
	Returns the Epetra_Map object associated with the domain of this matrix operator.
virtual const Epetra_Map &	OperatorRangeMap () const
	Returns the Epetra_Map object associated with the range of this matrix operator.
void	multiply_block (const Teuchos::RCP< const Stokhos::Sparse3Tensor< int, double > > &cijk, double alpha, const EpetraExt::BlockMultiVector &Input, EpetraExt::BlockMultiVector &Result) const
void	divide_diagonal_block (int row_begin, int row_end, const EpetraExt::BlockMultiVector &Input, EpetraExt::BlockMultiVector &Result) const

Detailed Description

A stochastic preconditioner based on applying the approximate Schur complement preconditioner as defined by Sousedik, Ghanem, and Phipps, Numerical Linear Algebra and Applications, 2012.

Constructor & Destructor Documentation

◆ ApproxSchurComplementPreconditioner()

Stokhos::ApproxSchurComplementPreconditioner::ApproxSchurComplementPreconditioner	(	const Teuchos::RCP< const EpetraExt::MultiComm > &	sg_comm,
		const Teuchos::RCP< const Stokhos::OrthogPolyBasis< int, double > > &	sg_basis,
		const Teuchos::RCP< const Stokhos::EpetraSparse3Tensor > &	epetraCijk,
		const Teuchos::RCP< const Epetra_Map > &	base_map,
		const Teuchos::RCP< const Epetra_Map > &	sg_map,
		const Teuchos::RCP< Stokhos::AbstractPreconditionerFactory > &	prec_factory,
		const Teuchos::RCP< Teuchos::ParameterList > &	params )

Constructor.

References base_map, block_indices, Cijk, epetraCijk, label, max_num_mat_vec, mean_prec, only_use_linear, P, prec_factory, rhs_block, scale_op, sg_basis, sg_comm, sg_map, sg_op, sg_poly, symmetric, upper_block_Cijk, and useTranspose.

Member Function Documentation

◆ Apply()

int Stokhos::ApproxSchurComplementPreconditioner::Apply	(	const Epetra_MultiVector &	Input,
		Epetra_MultiVector &	Result ) const

virtual

Returns the result of a Epetra_Operator applied to a Epetra_MultiVector Input in Result as described above.

References sg_op.

◆ ApplyInverse()

int Stokhos::ApproxSchurComplementPreconditioner::ApplyInverse	(	const Epetra_MultiVector &	X,
		Epetra_MultiVector &	Y ) const

virtual

Returns the result of the inverse of the operator applied to a Epetra_MultiVector Input in Result as described above.

References base_map, block_indices, max_num_mat_vec, P, rhs_block, sg_map, tmp, and upper_block_Cijk.

◆ Comm()

const Epetra_Comm & Stokhos::ApproxSchurComplementPreconditioner::Comm ( ) const

virtual

Returns a reference to the Epetra_Comm communicator associated with this operator.

References sg_comm.

◆ HasNormInf()

bool Stokhos::ApproxSchurComplementPreconditioner::HasNormInf ( ) const

virtual

Returns true if the this object can provide an approximate Inf-norm, false otherwise.

References sg_op.

◆ Label()

const char * Stokhos::ApproxSchurComplementPreconditioner::Label ( ) const

virtual

Returns a character string describing the operator.

References label.

◆ NormInf()

double Stokhos::ApproxSchurComplementPreconditioner::NormInf ( ) const

virtual

Returns an approximate infinity norm of the operator matrix.

References sg_op.

◆ OperatorDomainMap()

const Epetra_Map & Stokhos::ApproxSchurComplementPreconditioner::OperatorDomainMap ( ) const

virtual

Returns the Epetra_Map object associated with the domain of this matrix operator.

References sg_map.

◆ OperatorRangeMap()

const Epetra_Map & Stokhos::ApproxSchurComplementPreconditioner::OperatorRangeMap ( ) const

virtual

Returns the Epetra_Map object associated with the range of this matrix operator.

References sg_map.

◆ setupPreconditioner()

void Stokhos::ApproxSchurComplementPreconditioner::setupPreconditioner	(	const Teuchos::RCP< Stokhos::SGOperator > &	sg_op,
		const Epetra_Vector &	x )

virtual

Setup preconditioner.

Implements Stokhos::SGPreconditioner.

References label, mean_prec, prec_factory, sg_op, and sg_poly.

◆ SetUseTranspose()

int Stokhos::ApproxSchurComplementPreconditioner::SetUseTranspose ( bool UseTranspose )

virtual

Set to true if the transpose of the operator is requested.

References mean_prec, sg_op, UseTranspose(), and useTranspose.

◆ UseTranspose()

bool Stokhos::ApproxSchurComplementPreconditioner::UseTranspose ( ) const

virtual

Returns the current UseTranspose setting.

References useTranspose.

Referenced by SetUseTranspose().

Member Data Documentation

◆ base_map

Teuchos::RCP<const Epetra_Map> Stokhos::ApproxSchurComplementPreconditioner::base_map

protected

Stores base map.

Referenced by ApplyInverse(), and ApproxSchurComplementPreconditioner().

◆ block_indices

Teuchos::Array<int> Stokhos::ApproxSchurComplementPreconditioner::block_indices

protected

Starting block indices.

Referenced by ApplyInverse(), and ApproxSchurComplementPreconditioner().

◆ Cijk

Teuchos::RCP<const Cijk_type > Stokhos::ApproxSchurComplementPreconditioner::Cijk

protected

Pointer to triple product.

Referenced by ApproxSchurComplementPreconditioner().

◆ epetraCijk

Teuchos::RCP<const Stokhos::EpetraSparse3Tensor> Stokhos::ApproxSchurComplementPreconditioner::epetraCijk

protected

Stores Epetra Cijk tensor.

Referenced by ApproxSchurComplementPreconditioner().

◆ label

std::string Stokhos::ApproxSchurComplementPreconditioner::label

protected

Label for operator.

Referenced by ApproxSchurComplementPreconditioner(), Label(), and setupPreconditioner().

◆ max_num_mat_vec

int Stokhos::ApproxSchurComplementPreconditioner::max_num_mat_vec

protected

Maximum number of matvecs in Apply.

Referenced by ApplyInverse(), and ApproxSchurComplementPreconditioner().

◆ mean_prec

Teuchos::RCP<Epetra_Operator> Stokhos::ApproxSchurComplementPreconditioner::mean_prec

protected

Stores mean preconditioner.

Referenced by ApproxSchurComplementPreconditioner(), setupPreconditioner(), and SetUseTranspose().

◆ only_use_linear

bool Stokhos::ApproxSchurComplementPreconditioner::only_use_linear

protected

Limit Gauss-Seidel loop to linear terms.

Referenced by ApproxSchurComplementPreconditioner().

◆ P

int Stokhos::ApproxSchurComplementPreconditioner::P

protected

Total polynomial order.

Referenced by ApplyInverse(), and ApproxSchurComplementPreconditioner().

◆ prec_factory

Teuchos::RCP<Stokhos::AbstractPreconditionerFactory> Stokhos::ApproxSchurComplementPreconditioner::prec_factory

protected

Stores factory for building mean preconditioner.

Referenced by ApproxSchurComplementPreconditioner(), and setupPreconditioner().

◆ rhs_block

Teuchos::RCP<EpetraExt::BlockMultiVector> Stokhos::ApproxSchurComplementPreconditioner::rhs_block

mutableprotected

Temporary vector for storing rhs in Gauss-Seidel loop.

Referenced by ApplyInverse(), and ApproxSchurComplementPreconditioner().

◆ scale_op

bool Stokhos::ApproxSchurComplementPreconditioner::scale_op

protected

Flag indicating whether operator be scaled with <\psi_i^2>.

Referenced by ApproxSchurComplementPreconditioner().

◆ sg_basis

Teuchos::RCP<const Stokhos::OrthogPolyBasis<int,double> > Stokhos::ApproxSchurComplementPreconditioner::sg_basis

protected

Stochastic Galerking basis.

Referenced by ApproxSchurComplementPreconditioner().

◆ sg_comm

Teuchos::RCP<const EpetraExt::MultiComm> Stokhos::ApproxSchurComplementPreconditioner::sg_comm

protected

Stores SG parallel communicator.

Referenced by ApproxSchurComplementPreconditioner(), and Comm().

◆ sg_map

Teuchos::RCP<const Epetra_Map> Stokhos::ApproxSchurComplementPreconditioner::sg_map

protected

Stores SG map.

Referenced by ApplyInverse(), ApproxSchurComplementPreconditioner(), OperatorDomainMap(), and OperatorRangeMap().

◆ sg_op

Teuchos::RCP<Stokhos::SGOperator> Stokhos::ApproxSchurComplementPreconditioner::sg_op

protected

Pointer to the SG operator.

Referenced by Apply(), ApproxSchurComplementPreconditioner(), HasNormInf(), NormInf(), setupPreconditioner(), and SetUseTranspose().

◆ sg_poly

Teuchos::RCP<Stokhos::EpetraOperatorOrthogPoly > Stokhos::ApproxSchurComplementPreconditioner::sg_poly

protected

Pointer to the PCE expansion of Jacobian.

Referenced by ApproxSchurComplementPreconditioner(), and setupPreconditioner().

◆ symmetric

bool Stokhos::ApproxSchurComplementPreconditioner::symmetric

protected

Use symmetric Gauss-Seidel.

Referenced by ApproxSchurComplementPreconditioner().

◆ tmp

Teuchos::RCP<Epetra_MultiVector> Stokhos::ApproxSchurComplementPreconditioner::tmp

mutableprotected

Temporary vector for storing matrix-vector products.

Referenced by ApplyInverse().

◆ upper_block_Cijk

Teuchos::Array< Teuchos::RCP<Cijk_type> > Stokhos::ApproxSchurComplementPreconditioner::upper_block_Cijk

protected

Triple product tensor for each sub-block.

Referenced by ApplyInverse(), and ApproxSchurComplementPreconditioner().

◆ useTranspose

bool Stokhos::ApproxSchurComplementPreconditioner::useTranspose

protected

Flag indicating whether transpose was selected.

Referenced by ApproxSchurComplementPreconditioner(), SetUseTranspose(), and UseTranspose().

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

Stokhos_ApproxSchurComplementPreconditioner.hpp
Stokhos_ApproxSchurComplementPreconditioner.cpp

Public Member Functions

Epetra_Operator methods

Detailed Description

Constructor & Destructor Documentation

◆ ApproxSchurComplementPreconditioner()

Member Function Documentation

◆ Apply()

◆ ApplyInverse()

◆ Comm()

◆ HasNormInf()

◆ Label()

◆ NormInf()

◆ OperatorDomainMap()

◆ OperatorRangeMap()

◆ setupPreconditioner()

◆ SetUseTranspose()

◆ UseTranspose()

Member Data Documentation

◆ base_map

◆ block_indices

◆ Cijk

◆ epetraCijk

◆ label

◆ max_num_mat_vec

◆ mean_prec

◆ only_use_linear

◆ P

◆ prec_factory

◆ rhs_block

◆ scale_op

◆ sg_basis

◆ sg_comm

◆ sg_map

◆ sg_op

◆ sg_poly

◆ symmetric

◆ tmp

◆ upper_block_Cijk

◆ useTranspose