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

A preconditioner based on the Uzawa algorithm for saddle-point problems of the form \( \begin{pmatrix} A & B \\ C & D \end{pmatrix} \begin{pmatrix} u\\ p \end{pmatrix} = \begin{pmatrix} f\\ g \end{pmatrix} \). More...

#include <dumux/linear/preconditioners.hh>

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

Description

template<class M, class X, class Y, int l = 1>
class Dumux::SeqUzawa< M, X, Y, l >

A preconditioner based on the Uzawa algorithm for saddle-point problems of the form \( \begin{pmatrix} A & B \\ C & D \end{pmatrix} \begin{pmatrix} u\\ p \end{pmatrix} = \begin{pmatrix} f\\ g \end{pmatrix} \).

This preconditioner is especially suited for solving the incompressible (Navier-)Stokes equations. Here, \(D = 0\) and \(B = C^T\) if \(\rho = 1\). We do not expect good convergence if energy or mass transport is considered.

See: Benzi, M., Golub, G. H., & Liesen, J. (2005). Numerical solution of saddle point problems. Acta numerica, 14, 1-137 [10] and
Ho, N., Olson, S. D., & Walker, H. F. (2017). Accelerating the Uzawa algorithm. SIAM Journal on Scientific Computing, 39(5), S461-S476 [29]

Template Parameters

M	Type of the matrix.
X	Type of the update.
Y	Type of the defect.
l	Preconditioner block level (for compatibility reasons, unused).

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

Public Member Functions
	SeqUzawa (const M &mat, const Dune::ParameterTree &params)
	Constructor. More...
virtual void	pre (X &x, Y &b)
	Prepare the preconditioner. More...
virtual void	apply (X &update, const Y &currentDefect)
	Apply the preconditioner. More...
virtual void	post (X &x)
	Clean up. More...
virtual Dune::SolverCategory::Category	category () const
	Category of the preconditioner (see SolverCategory::Category) More...

Member Typedef Documentation

domain_type

template<class M , class X , class Y , int l = 1>

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

The domain type of the preconditioner.

field_type

template<class M , class X , class Y , int l = 1>

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

The field type of the preconditioner.

matrix_type

template<class M , class X , class Y , int l = 1>

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

The matrix type the preconditioner is for.

range_type

template<class M , class X , class Y , int l = 1>

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

The range type of the preconditioner.

scalar_field_type

template<class M , class X , class Y , int l = 1>

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

Scalar type underlying the field_type.

Constructor & Destructor Documentation

SeqUzawa()

template<class M , class X , class Y , int l = 1>

Dumux::SeqUzawa< M, X, Y, l >::SeqUzawa ( const M &  mat, const Dune::ParameterTree &  params  )

inline

Constructor.

Parameters

mat	The matrix to operate on.
params	Collection of paramters.

Member Function Documentation

apply()

template<class M , class X , class Y , int l = 1>

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

inlinevirtual

Apply the preconditioner.

Parameters

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

category()

template<class M , class X , class Y , int l = 1>

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

inlinevirtual

Category of the preconditioner (see SolverCategory::Category)

post()

template<class M , class X , class Y , int l = 1>

virtual void Dumux::SeqUzawa< M, X, Y, l >::post ( X &  x )

inlinevirtual

Clean up.

pre()

template<class M , class X , class Y , int l = 1>

virtual void Dumux::SeqUzawa< M, X, Y, l >::pre ( X &  x, Y &  b  )

inlinevirtual

Prepare the preconditioner.

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

• preconditioners.hh