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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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. More...

virtual	~ApproxSchurComplementPreconditioner ()
	Destructor. More...

Public Member Functions inherited from Stokhos::SGPreconditioner
	SGPreconditioner ()
	Constructor. More...

virtual	~SGPreconditioner ()
	Destructor. More...

Protected Types
typedef Stokhos::Sparse3Tensor < int, double >	Cijk_type
	Short-hand for Cijk. More...

Protected Member Functions
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

Protected Attributes
std::string	label
	Label for operator. More...

Teuchos::RCP< const EpetraExt::MultiComm >	sg_comm
	Stores SG parallel communicator. More...

Teuchos::RCP< const Stokhos::OrthogPolyBasis< int, double > >	sg_basis
	Stochastic Galerking basis. More...

Teuchos::RCP< const Stokhos::EpetraSparse3Tensor >	epetraCijk
	Stores Epetra Cijk tensor. More...

Teuchos::RCP< const Epetra_Map >	base_map
	Stores base map. More...

Teuchos::RCP< const Epetra_Map >	sg_map
	Stores SG map. More...

Teuchos::RCP < Stokhos::AbstractPreconditionerFactory >	prec_factory
	Stores factory for building mean preconditioner. More...

Teuchos::RCP< Epetra_Operator >	mean_prec
	Stores mean preconditioner. More...

bool	useTranspose
	Flag indicating whether transpose was selected. More...

Teuchos::RCP< Stokhos::SGOperator >	sg_op
	Pointer to the SG operator. More...

Teuchos::RCP < Stokhos::EpetraOperatorOrthogPoly >	sg_poly
	Pointer to the PCE expansion of Jacobian. More...

Teuchos::RCP< const Cijk_type >	Cijk
	Pointer to triple product. More...

int	P
	Total polynomial order. More...

Teuchos::Array< int >	block_indices
	Starting block indices. More...

Teuchos::Array< Teuchos::RCP < Cijk_type > >	upper_block_Cijk
	Triple product tensor for each sub-block. More...

Teuchos::Array< Teuchos::RCP < Cijk_type > >	lower_block_Cijk

bool	scale_op
	Flag indicating whether operator be scaled with <^2> More...

bool	symmetric
	Use symmetric Gauss-Seidel. More...

bool	only_use_linear
	Limit Gauss-Seidel loop to linear terms. More...

int	max_num_mat_vec
	Maximum number of matvecs in Apply. More...

Teuchos::RCP< Epetra_MultiVector >	tmp
	Temporary vector for storing matrix-vector products. More...

Teuchos::RCP < EpetraExt::BlockMultiVector >	rhs_block
	Temporary vector for storing rhs in Gauss-Seidel loop. More...

Teuchos::Array< double * >	j_ptr

Teuchos::Array< int >	mj_indices

Private Member Functions
	ApproxSchurComplementPreconditioner (const ApproxSchurComplementPreconditioner &)
	Private to prohibit copying. More...

ApproxSchurComplementPreconditioner &	operator= (const ApproxSchurComplementPreconditioner &)
	Private to prohibit copying. More...

Stokhos::SGPreconditioner methods
virtual void	setupPreconditioner (const Teuchos::RCP< Stokhos::SGOperator > &sg_op, const Epetra_Vector &x)
	Setup preconditioner. More...

Epetra_Operator methods
virtual int	SetUseTranspose (bool UseTranspose)
	Set to true if the transpose of the operator is requested. More...

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. More...

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. More...

virtual double	NormInf () const
	Returns an approximate infinity norm of the operator matrix. More...

virtual const char *	Label () const
	Returns a character string describing the operator. More...

virtual bool	UseTranspose () const
	Returns the current UseTranspose setting. More...

virtual bool	HasNormInf () const
	Returns true if the this object can provide an approximate Inf-norm, false otherwise. More...

virtual const Epetra_Comm &	Comm () const
	Returns a reference to the Epetra_Comm communicator associated with this operator. More...

virtual const Epetra_Map &	OperatorDomainMap () const
	Returns the Epetra_Map object associated with the domain of this matrix operator. More...

virtual const Epetra_Map &	OperatorRangeMap () const
	Returns the Epetra_Map object associated with the range of this matrix operator. More...

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.

Definition at line 31 of file Stokhos_ApproxSchurComplementPreconditioner.hpp.

Member Typedef Documentation

typedef Stokhos::Sparse3Tensor<int,double> Stokhos::ApproxSchurComplementPreconditioner::Cijk_type

protected

Short-hand for Cijk.

Definition at line 170 of file Stokhos_ApproxSchurComplementPreconditioner.hpp.

Constructor & Destructor Documentation

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.

Definition at line 17 of file Stokhos_ApproxSchurComplementPreconditioner.cpp.

Stokhos::ApproxSchurComplementPreconditioner::~ApproxSchurComplementPreconditioner ( )

virtual

Destructor.

Definition at line 123 of file Stokhos_ApproxSchurComplementPreconditioner.cpp.

Stokhos::ApproxSchurComplementPreconditioner::ApproxSchurComplementPreconditioner ( const ApproxSchurComplementPreconditioner & )

private

Private to prohibit copying.

Member Function Documentation

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

virtual

Setup preconditioner.

Implements Stokhos::SGPreconditioner.

Definition at line 129 of file Stokhos_ApproxSchurComplementPreconditioner.cpp.

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

virtual

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

Implements Epetra_Operator.

Definition at line 141 of file Stokhos_ApproxSchurComplementPreconditioner.cpp.

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.

Implements Epetra_Operator.

Definition at line 152 of file Stokhos_ApproxSchurComplementPreconditioner.cpp.

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.

Implements Epetra_Operator.

Definition at line 159 of file Stokhos_ApproxSchurComplementPreconditioner.cpp.

double Stokhos::ApproxSchurComplementPreconditioner::NormInf ( ) const

virtual

Returns an approximate infinity norm of the operator matrix.

Implements Epetra_Operator.

Definition at line 227 of file Stokhos_ApproxSchurComplementPreconditioner.cpp.

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

virtual

Returns a character string describing the operator.

Implements Epetra_Operator.

Definition at line 235 of file Stokhos_ApproxSchurComplementPreconditioner.cpp.

bool Stokhos::ApproxSchurComplementPreconditioner::UseTranspose ( ) const

virtual

Returns the current UseTranspose setting.

Implements Epetra_Operator.

Definition at line 242 of file Stokhos_ApproxSchurComplementPreconditioner.cpp.

bool Stokhos::ApproxSchurComplementPreconditioner::HasNormInf ( ) const

virtual

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

Implements Epetra_Operator.

Definition at line 249 of file Stokhos_ApproxSchurComplementPreconditioner.cpp.

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

virtual

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

Implements Epetra_Operator.

Definition at line 256 of file Stokhos_ApproxSchurComplementPreconditioner.cpp.

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

virtual

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

Implements Epetra_Operator.

Definition at line 262 of file Stokhos_ApproxSchurComplementPreconditioner.cpp.

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

virtual

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

Implements Epetra_Operator.

Definition at line 269 of file Stokhos_ApproxSchurComplementPreconditioner.cpp.

void Stokhos::ApproxSchurComplementPreconditioner::multiply_block	(	const Teuchos::RCP< const Stokhos::Sparse3Tensor< int, double > > &	cijk,
		double	alpha,
		const EpetraExt::BlockMultiVector &	Input,
		EpetraExt::BlockMultiVector &	Result
	)		const

protected

Definition at line 276 of file Stokhos_ApproxSchurComplementPreconditioner.cpp.

void Stokhos::ApproxSchurComplementPreconditioner::divide_diagonal_block	(	int	row_begin,
		int	row_end,
		const EpetraExt::BlockMultiVector &	Input,
		EpetraExt::BlockMultiVector &	Result
	)		const