Dumux::Detail::StokesPreconditioner< M, X, Y, l > Class Template Reference

A Stokes preconditioner (saddle-point problem) for the problem \(\begin{pmatrix} A & B \\ C & 0 \end{pmatrix} \begin{pmatrix} u \\ p \end{pmatrix} = \begin{pmatrix} f \\ g \end{pmatrix}, \). More...

#include <dumux/linear/stokes_solver.hh>

Inheritance diagram for Dumux::Detail::StokesPreconditioner< M, X, Y, l >:

Description

template<class M, class X, class Y, int l = 2>
class Dumux::Detail::StokesPreconditioner< M, X, Y, l >

where A is the discrete velocity operator and B and C are discrete gradient and divergence operators. This preconditioner is especially suited for solving the incompressible Stokes equations.

Template Parameters

M	Type of the matrix.
X	Type of the update.
Y	Type of the defect.
l	Preconditioner block level

Public Types
using	matrix_type = M
	The matrix type the preconditioner is for.
using	domain_type = X
	The domain type of the preconditioner.
using	range_type = Y
	The range type of the preconditioner.
using	field_type = typename X::field_type
	The field type of the preconditioner.
using	scalar_field_type = Dune::Simd::Scalar<field_type>
	Scalar type underlying the field_type.
using	PressureLinearOperator = Dune::MatrixAdapter<P,V,V>
	the type of the pressure operator

Public Member Functions
	StokesPreconditioner (const std::shared_ptr< const Dune::AssembledLinearOperator< M, X, Y > > &fullLinearOperator, const std::shared_ptr< const PressureLinearOperator > &pressureLinearOperator, const Dune::ParameterTree &params)
	Constructor (sequential).
	StokesPreconditioner (const std::shared_ptr< const Dune::AssembledLinearOperator< M, X, Y > > &fullLinearOperator, const std::shared_ptr< const PressureLinearOperator > &pressureLinearOperator, const Dune::ParameterTree &params, std::shared_ptr< Comm > velComm, std::shared_ptr< Comm > presComm=nullptr)
	Constructor (parallel).
void	pre (X &update, Y &currentDefect) override
	Prepare the preconditioners of the velocity and the pressure block.
void	apply (X &update, const Y &currentDefect) override
	Apply the preconditioner.
void	post (X &update) override
	Clean up the preconditioners of the velocity and the pressure block.
Dune::SolverCategory::Category	category () const override
	Category of the preconditioner (see SolverCategory::Category).
void	setPressureDiagonal (std::shared_ptr< const V > diagonal)
	Add a diagonal to the inverse of the pressure block.

Member Typedef Documentation

domain_type

template<class M, class X, class Y, int l = 2>

using Dumux::Detail::StokesPreconditioner< M, X, Y, l >::domain_type = X

field_type

template<class M, class X, class Y, int l = 2>

using Dumux::Detail::StokesPreconditioner< M, X, Y, l >::field_type = typename X::field_type

matrix_type

template<class M, class X, class Y, int l = 2>

using Dumux::Detail::StokesPreconditioner< M, X, Y, l >::matrix_type = M

PressureLinearOperator

template<class M, class X, class Y, int l = 2>

using Dumux::Detail::StokesPreconditioner< M, X, Y, l >::PressureLinearOperator = Dune::MatrixAdapter<P,V,V>

range_type

template<class M, class X, class Y, int l = 2>

using Dumux::Detail::StokesPreconditioner< M, X, Y, l >::range_type = Y

scalar_field_type

template<class M, class X, class Y, int l = 2>

using Dumux::Detail::StokesPreconditioner< M, X, Y, l >::scalar_field_type = Dune::Simd::Scalar<field_type>

Constructor & Destructor Documentation

StokesPreconditioner() [1/2]

template<class M, class X, class Y, int l = 2>

Dumux::Detail::StokesPreconditioner< M, X, Y, l >::StokesPreconditioner ( const std::shared_ptr< const Dune::AssembledLinearOperator< M, X, Y > > & fullLinearOperator, const std::shared_ptr< const PressureLinearOperator > & pressureLinearOperator, const Dune::ParameterTree & params )

inline

Parameters

fullLinearOperator	the Stokes linear operator
pressureLinearOperator	the linear operator for the pressure space preconditioner
params	a parameter tree for the preconditioner configuration

StokesPreconditioner() [2/2]

template<class M, class X, class Y, int l = 2>

Dumux::Detail::StokesPreconditioner< M, X, Y, l >::StokesPreconditioner ( const std::shared_ptr< const Dune::AssembledLinearOperator< M, X, Y > > & fullLinearOperator, const std::shared_ptr< const PressureLinearOperator > & pressureLinearOperator, const Dune::ParameterTree & params, std::shared_ptr< Comm > velComm, std::shared_ptr< Comm > presComm = nullptr )

inline

Parameters

fullLinearOperator	the Stokes linear operator
pressureLinearOperator	the linear operator for the pressure space preconditioner
params	a parameter tree for the preconditioner configuration
velComm	OwnerOverlapCopy communication for the velocity DOFs
presComm	OwnerOverlapCopy communication for the pressure DOFs

Member Function Documentation

apply()

template<class M, class X, class Y, int l = 2>

void Dumux::Detail::StokesPreconditioner< M, X, Y, l >::apply ( X & update, const Y & currentDefect )

inlineoverride

Parameters

update	The update to be computed.
currentDefect	The current defect.

The currentDefect has be be in a consistent representation, Definition 2.3 Blatt and Bastian (2009) https://doi.org/10.1504/IJCSE.2008.021112 The update is initially zero. At exit the update has to be in a consistent representation. This usually requires communication.

category()

template<class M, class X, class Y, int l = 2>

Dune::SolverCategory::Category Dumux::Detail::StokesPreconditioner< M, X, Y, l >::category ( ) const

inlineoverride

post()

template<class M, class X, class Y, int l = 2>

void Dumux::Detail::StokesPreconditioner< M, X, Y, l >::post ( X & update )

inlineoverride

pre()

template<class M, class X, class Y, int l = 2>

void Dumux::Detail::StokesPreconditioner< M, X, Y, l >::pre ( X & update, Y & currentDefect )

inlineoverride

setPressureDiagonal()

template<class M, class X, class Y, int l = 2>

void Dumux::Detail::StokesPreconditioner< M, X, Y, l >::setPressureDiagonal ( std::shared_ptr< const V > diagonal )

inline

Note

For a transient problem the pressure operator approximates the Schur complement of the storage part of the velocity block. The viscous part contributes a mass matrix scaled by the inverse viscosity, whose inverse is this diagonal; both inverses are summed (Cahouet & Chabard (1988) https://doi.org/10.1002/fld.1650080802).

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

• stokes_solver.hh