UMFPACK Saddle-Point Mean solver class. More...

#include <umfpack.hpp>

Inheritance diagram for FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >:

Public Types
typedef SolverBase< VectorType >	BaseClass
	our base class More...

typedef LAFEM::SaddlePointMatrix< MatrixTypeA, MatrixTypeB, MatrixTypeD >	MatrixType

typedef LAFEM::SparseMatrixBCSR< DT_, IT_, dim_, dim_ >	MatrixTypeA
	compatible matrix type More...

typedef LAFEM::SparseMatrixBCSR< DT_, IT_, dim_, 1 >	MatrixTypeB

typedef LAFEM::SparseMatrixBCSR< DT_, IT_, 1, dim_ >	MatrixTypeD

typedef LAFEM::SparseMatrixCSR< double, Index >	UmfMatrixType

typedef LAFEM::DenseVector< double, Index >	UmfVectorType

typedef LAFEM::TupleVector< VectorTypeV, VectorTypeP >	VectorType

typedef LAFEM::DenseVector< DT_, IT_ >	VectorTypeP

typedef LAFEM::DenseVectorBlocked< DT_, IT_, dim_ >	VectorTypeV
	compatible vector type More...

Public Member Functions
	SaddleUmfpackMean (const MatrixType &system_matrix, const LAFEM::MeanFilter< DT_, IT_ > &mean_filter)
	Constructor. More...

	SaddleUmfpackMean (const MatrixType &system_matrix, const VectorTypeP &weight_vector)
	Constructor. More...

virtual Status	apply (LAFEM::TupleVector< LAFEM::DenseVectorBlocked< DT_, IT_, dim_ >, LAFEM::DenseVector< DT_, IT_ > > &vec_cor, const LAFEM::TupleVector< LAFEM::DenseVectorBlocked< DT_, IT_, dim_ >, LAFEM::DenseVector< DT_, IT_ > > &vec_def)=0
	Solver application method. More...

virtual Status	apply (VectorType &vec_sol, const VectorType &vec_rhs) override
	Solves a linear system with the factorized system matrix. More...

virtual void	done ()
	Finalization method. More...

virtual void	done_numeric () override
	Numeric finalization method. More...

virtual void	done_symbolic () override
	Symbolic finalization method. More...

virtual void	init ()
	Initialization method. More...

virtual void	init_numeric () override
	Numeric initialization method. More...

virtual void	init_symbolic () override
	Symbolic initialization method. More...

virtual String	name () const override
	Returns the name of the solver. More...

Private Attributes
UmfMatrixType	_solver_matrix
	our extended system matrix More...

const MatrixType &	_system_matrix
	system matrix More...

Umfpack	_umfpack
	our internal Umfpack solver object More...

UmfVectorType	_vec_b

UmfVectorType	_vec_x
	two temporary extended vectors More...

const VectorTypeP &	_weight_vector
	weight vector from mean filter More...

Detailed Description

template<typename DT_, typename IT_, int dim_>
class FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >

UMFPACK Saddle-Point Mean solver class.

This class implements a variant of the Umfpack solver, which is capable of solving linear systems on SaddlePointMatrix objects including the integral mean constraint or any other constraint that can be expressed as a scalar Lagrange multiplier to the second solution component (usually the pressure) of the original system.

This class can be used to solve (Navier-)Stokes systems with full Dirichlet boundary conditions for the velocity, which in turn requires a MeanFilter constraint for the pressure to make the system regular. In this case, the sub-matrix blocks A and B are required to be filtered by the corresponding UnitFilterBlocked by the caller, whereas the MeanFilter is passed to this solver class.

This class offers two constructors:

A CTOR which takes a SaddlePointMatrix and a MeanFilter for the second component as input
A CTOR which takes a SaddlePointMatrix and a DenseVector representing the Lagrange multiplier as input.

Author: Peter Zajac

Definition at line 276 of file umfpack.hpp.

Member Typedef Documentation

◆ BaseClass

template<typename DT_ , typename IT_ , int dim_>

typedef SolverBase<VectorType> FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::BaseClass

our base class

Definition at line 295 of file umfpack.hpp.

◆ MatrixType

template<typename DT_ , typename IT_ , int dim_>

typedef LAFEM::SaddlePointMatrix<MatrixTypeA, MatrixTypeB, MatrixTypeD> FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::MatrixType

Definition at line 284 of file umfpack.hpp.

◆ MatrixTypeA

template<typename DT_ , typename IT_ , int dim_>

typedef LAFEM::SparseMatrixBCSR<DT_, IT_, dim_, dim_> FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::MatrixTypeA

compatible matrix type

Definition at line 281 of file umfpack.hpp.

◆ MatrixTypeB

template<typename DT_ , typename IT_ , int dim_>

typedef LAFEM::SparseMatrixBCSR<DT_, IT_, dim_, 1> FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::MatrixTypeB

Definition at line 282 of file umfpack.hpp.

◆ MatrixTypeD

template<typename DT_ , typename IT_ , int dim_>

typedef LAFEM::SparseMatrixBCSR<DT_, IT_, 1, dim_> FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::MatrixTypeD

Definition at line 283 of file umfpack.hpp.

◆ UmfMatrixType

template<typename DT_ , typename IT_ , int dim_>

typedef LAFEM::SparseMatrixCSR<double, Index> FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::UmfMatrixType

Definition at line 291 of file umfpack.hpp.

◆ UmfVectorType

template<typename DT_ , typename IT_ , int dim_>

typedef LAFEM::DenseVector<double, Index> FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::UmfVectorType

Definition at line 292 of file umfpack.hpp.

◆ VectorType

template<typename DT_ , typename IT_ , int dim_>

typedef LAFEM::TupleVector<VectorTypeV, VectorTypeP> FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::VectorType

Definition at line 289 of file umfpack.hpp.

◆ VectorTypeP

template<typename DT_ , typename IT_ , int dim_>

typedef LAFEM::DenseVector<DT_, IT_> FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::VectorTypeP

Definition at line 288 of file umfpack.hpp.

◆ VectorTypeV

template<typename DT_ , typename IT_ , int dim_>

typedef LAFEM::DenseVectorBlocked<DT_, IT_, dim_> FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::VectorTypeV

compatible vector type

Definition at line 287 of file umfpack.hpp.

Constructor & Destructor Documentation

◆ SaddleUmfpackMean() [1/2]

template<typename DT_ , typename IT_ , int dim_>

FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::SaddleUmfpackMean	(	const MatrixType &	system_matrix,
		const VectorTypeP &	weight_vector
	)

inlineexplicit

Constructor.

Parameters

[in]	system_matrix	A reference to the system matrix to be factorized.
[in]	weight_vector	The weight vector to be used as a Lagrange multiplier.

Definition at line 319 of file umfpack.hpp.

◆ SaddleUmfpackMean() [2/2]

template<typename DT_ , typename IT_ , int dim_>

FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::SaddleUmfpackMean	(	const MatrixType &	system_matrix,
		const LAFEM::MeanFilter< DT_, IT_ > &	mean_filter
	)

inlineexplicit

Constructor.

Parameters

[in]	system_matrix	A reference to the system matrix to be factorized.
[in]	mean_filter	A reference to the pressure mean filter containing the weight vector.

Definition at line 336 of file umfpack.hpp.

Member Function Documentation

◆ apply() [1/2]

virtual Status FEAT::Solver::SolverBase< LAFEM::TupleVector< LAFEM::DenseVectorBlocked< DT_, IT_, dim_ >, LAFEM::DenseVector< DT_, IT_ > > >::apply	(	LAFEM::TupleVector< LAFEM::DenseVectorBlocked< DT_, IT_, dim_ >, LAFEM::DenseVector< DT_, IT_ > > &	vec_cor,
		const LAFEM::TupleVector< LAFEM::DenseVectorBlocked< DT_, IT_, dim_ >, LAFEM::DenseVector< DT_, IT_ > > &	vec_def
	)

pure virtualinherited

Solver application method.

This method applies the solver represented by this object onto a given defect vector and returns the corresponding correction vector.

Note: Solvers which derive from the IterativeSolver base class also provide a correct() method which corrects an initial solution instead of starting with the null vector.

Parameters

[out]	vec_cor	The vector that shall receive the solution of the linear system. It is assumed to be allocated, but its numerical contents may be undefined upon calling this method.
[in]	vec_def	The vector that represents the right-hand-side of the linear system to be solved.

Attention: vec_cor and vec_def must not refer to the same vector object!

Returns: A Status code that represents the status of the solution step.

◆ apply() [2/2]

template<typename DT_ , typename IT_ , int dim_>

virtual Status FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::apply	(	VectorType &	vec_sol,
		const VectorType &	vec_rhs
	)

inlineoverridevirtual

Solves a linear system with the factorized system matrix.

Parameters

[in,out]	vec_sol	A reference to the solution vector. The vector must be allocated to the correct length, but its initial contents are ignored.
[in]	vec_rhs	A reference to the right-hand-side of the linear system.

Definition at line 551 of file umfpack.hpp.

References FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::_umfpack, FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::_vec_x, FEAT::Solver::Umfpack::apply(), FEAT::LAFEM::DenseVector< DT_, IT_ >::elements(), and FEAT::LAFEM::TupleVector< First_, Rest_ >::size().

◆ done()

virtual void FEAT::Solver::SolverBase< LAFEM::TupleVector< LAFEM::DenseVectorBlocked< DT_, IT_, dim_ >, LAFEM::DenseVector< DT_, IT_ > > >::done ( )

inlinevirtualinherited

Finalization method.

This function performs both the symbolic and numeric finalization, i.e. it simply performs

this->done_numeric();
this->done_symbolic();

Definition at line 283 of file base.hpp.

◆ done_numeric()

template<typename DT_ , typename IT_ , int dim_>

virtual void FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::done_numeric ( )

inlineoverridevirtual

Numeric finalization method.

This method is called to release any data allocated in the numeric initialization step.

Reimplemented from FEAT::Solver::SolverBase< LAFEM::TupleVector< LAFEM::DenseVectorBlocked< DT_, IT_, dim_ >, LAFEM::DenseVector< DT_, IT_ > > >.

Definition at line 534 of file umfpack.hpp.

References FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::_umfpack, FEAT::Solver::SolverBase< Vector_ >::done_numeric(), and FEAT::Solver::Umfpack::done_numeric().

◆ done_symbolic()

template<typename DT_ , typename IT_ , int dim_>

virtual void FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::done_symbolic ( )

inlineoverridevirtual

Symbolic finalization method.

This method is called to release any data allocated in the symbolic initialization step.

Reimplemented from FEAT::Solver::SolverBase< LAFEM::TupleVector< LAFEM::DenseVectorBlocked< DT_, IT_, dim_ >, LAFEM::DenseVector< DT_, IT_ > > >.

Definition at line 449 of file umfpack.hpp.

References FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::_solver_matrix, FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::_umfpack, FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::_vec_x, FEAT::LAFEM::Container< DT_, IT_ >::clear(), FEAT::Solver::SolverBase< Vector_ >::done_symbolic(), and FEAT::Solver::Umfpack::done_symbolic().

◆ init()

virtual void FEAT::Solver::SolverBase< LAFEM::TupleVector< LAFEM::DenseVectorBlocked< DT_, IT_, dim_ >, LAFEM::DenseVector< DT_, IT_ > > >::init ( )

inlinevirtualinherited

Initialization method.

This function performs both the symbolic and numeric initialization, i.e. it simply performs

this->init_symbolic();
this->init_numeric();

Definition at line 268 of file base.hpp.

◆ init_numeric()

template<typename DT_ , typename IT_ , int dim_>

virtual void FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::init_numeric ( )

inlineoverridevirtual

Numeric initialization method.

This method is called to perform numeric initialization of the solver.
Before this function can be called, the symbolic initialization must be performed.

Reimplemented from FEAT::Solver::SolverBase< LAFEM::TupleVector< LAFEM::DenseVectorBlocked< DT_, IT_, dim_ >, LAFEM::DenseVector< DT_, IT_ > > >.

Definition at line 459 of file umfpack.hpp.

References FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::_solver_matrix, FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::_system_matrix, FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::_umfpack, FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::_weight_vector, FEAT::LAFEM::SaddlePointMatrix< MatrixA_, MatrixB_, MatrixD_ >::block_a(), FEAT::LAFEM::SaddlePointMatrix< MatrixA_, MatrixB_, MatrixD_ >::block_b(), FEAT::LAFEM::SaddlePointMatrix< MatrixA_, MatrixB_, MatrixD_ >::block_d(), FEAT::LAFEM::SparseMatrixBCSR< DT_, IT_, BlockHeight_, BlockWidth_ >::columns(), FEAT::LAFEM::DenseVector< DT_, IT_ >::elements(), FEAT::Solver::SolverBase< Vector_ >::init_numeric(), FEAT::Solver::Umfpack::init_numeric(), FEAT::LAFEM::SparseMatrixBCSR< DT_, IT_, BlockHeight_, BlockWidth_ >::row_ptr(), FEAT::LAFEM::SparseMatrixCSR< DT_, IT_ >::row_ptr(), FEAT::LAFEM::SparseMatrixBCSR< DT_, IT_, BlockHeight_, BlockWidth_ >::rows(), FEAT::LAFEM::SparseMatrixCSR< DT_, IT_ >::val(), and FEAT::LAFEM::SparseMatrixBCSR< DT_, IT_, BlockHeight_, BlockWidth_ >::val().

◆ init_symbolic()

template<typename DT_ , typename IT_ , int dim_>

virtual void FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::init_symbolic ( )

inlineoverridevirtual

Symbolic initialization method.

This method is called to perform symbolic initialization of the solver.

Reimplemented from FEAT::Solver::SolverBase< LAFEM::TupleVector< LAFEM::DenseVectorBlocked< DT_, IT_, dim_ >, LAFEM::DenseVector< DT_, IT_ > > >.

Definition at line 349 of file umfpack.hpp.

◆ name()

template<typename DT_ , typename IT_ , int dim_>

virtual String FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::name ( ) const

inlineoverridevirtual

Returns the name of the solver.

Implements FEAT::Solver::SolverBase< LAFEM::TupleVector< LAFEM::DenseVectorBlocked< DT_, IT_, dim_ >, LAFEM::DenseVector< DT_, IT_ > > >.

Definition at line 344 of file umfpack.hpp.

Member Data Documentation

◆ _solver_matrix

template<typename DT_ , typename IT_ , int dim_>

UmfMatrixType FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::_solver_matrix

private

our extended system matrix

Definition at line 303 of file umfpack.hpp.

Referenced by FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::done_symbolic(), FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::init_numeric(), and FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::init_symbolic().

◆ _system_matrix

template<typename DT_ , typename IT_ , int dim_>

const MatrixType& FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::_system_matrix

private

system matrix

Definition at line 299 of file umfpack.hpp.

Referenced by FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::init_numeric(), and FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::init_symbolic().

◆ _umfpack

template<typename DT_ , typename IT_ , int dim_>

Umfpack FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::_umfpack

private

our internal Umfpack solver object

Definition at line 307 of file umfpack.hpp.

Referenced by FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::apply(), FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::done_numeric(), FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::done_symbolic(), FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::init_numeric(), and FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::init_symbolic().

◆ _vec_b

template<typename DT_ , typename IT_ , int dim_>

UmfVectorType FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::_vec_b

private

Definition at line 305 of file umfpack.hpp.

◆ _vec_x

template<typename DT_ , typename IT_ , int dim_>

UmfVectorType FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::_vec_x

private

two temporary extended vectors

Definition at line 305 of file umfpack.hpp.

Referenced by FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::apply(), FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::done_symbolic(), and FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::init_symbolic().

◆ _weight_vector

template<typename DT_ , typename IT_ , int dim_>

const VectorTypeP& FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::_weight_vector

private

weight vector from mean filter

Definition at line 301 of file umfpack.hpp.

Referenced by FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::init_numeric(), and FEAT::Solver::SaddleUmfpackMean< DT_, IT_, dim_ >::init_symbolic().

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

kernel/solver/umfpack.hpp

Public Types

Public Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ BaseClass

◆ MatrixType

◆ MatrixTypeA

◆ MatrixTypeB

◆ MatrixTypeD

◆ UmfMatrixType

◆ UmfVectorType

◆ VectorType

◆ VectorTypeP

◆ VectorTypeV

Constructor & Destructor Documentation

◆ SaddleUmfpackMean() [1/2]

◆ SaddleUmfpackMean() [2/2]

Member Function Documentation

◆ apply() [1/2]

◆ apply() [2/2]

◆ done()

◆ done_numeric()

◆ done_symbolic()

◆ init()

◆ init_numeric()

◆ init_symbolic()

◆ name()

Member Data Documentation

◆ _solver_matrix

◆ _system_matrix

◆ _umfpack

◆ _vec_b

◆ _vec_x

◆ _weight_vector