An inexact Uzawa type solver for solving symmetric saddle point systems. More...
#include <uzawa.hh>
Detailed Description
class Kaskade::UzawaSolver< X, Y >
An inexact Uzawa type solver for solving symmetric saddle point systems.
\[ \begin{array}{cc} A & B^T \\ B & \end{array}\begin{matrix}{c} u \\ \lambda \end{matrix} = \begin{matrix}{c} f \\ g \end{matrix} \]
It implements an inexact preconditioned conjugate gradient method for the Schur complement \( S = BA^{-1}B^T\). The iteration is terminated once the preconditioned residual energy drops below a prescribed reduction factor times the solution energy, i.e. \( r^T\hat S^{-1} S \hat S^{-1} r \le \mathrm{TOL}^2 p^T S p \).
- Template Parameters
-
X the linear space of the primal variable \( u \) Y the linear space of the dual variable \( \lambda \)
Public Types | |
| using | domain_type = LinearProductSpace< typename X::field_type, boost::fusion::vector< X, Y > > |
| The domain type \( X \times Y \) of the Uzawa iteration. More... | |
| using | range_type = domain_type |
| typedef X::field_type | field_type |
| typedef field_type | Scalar |
| typedef domain_type | Domain |
| typedef range_type | Range |
Public Member Functions | |
| UzawaSolver (Dune::LinearOperator< X, X > &A_, Dune::InverseOperator< X, X > &invA_, Dune::LinearOperator< X, Y > &B_, Dune::LinearOperator< Y, X > &Bt_, Dune::Preconditioner< Y, Y > &precS_, double reduction_, int maxit_, int verbose_) | |
| Constructor. More... | |
| virtual void | apply (Domain &x, Range &b, Dune::InverseOperatorResult &res) override |
| Solves the saddle point system \( K x = b \). More... | |
| virtual void | apply (Domain &x, Range &b, double reduction_, Dune::InverseOperatorResult &res) |
| void | apply (Domain &x, Range &b) |
| virtual Dune::SolverCategory::Category | category () const override |
| returns the category of the operator More... | |
Member Typedef Documentation
◆ Domain
| typedef domain_type Kaskade::UzawaSolver< X, Y >::Domain |
◆ domain_type
| using Kaskade::UzawaSolver< X, Y >::domain_type = LinearProductSpace<typename X::field_type,boost::fusion::vector<X,Y> > |
The domain type \( X \times Y \) of the Uzawa iteration.
This is the LinearProductSpace of X and Y
◆ field_type
| typedef X::field_type Kaskade::UzawaSolver< X, Y >::field_type |
◆ Range
| typedef range_type Kaskade::UzawaSolver< X, Y >::Range |
◆ range_type
| using Kaskade::UzawaSolver< X, Y >::range_type = domain_type |
◆ Scalar
| typedef field_type Kaskade::UzawaSolver< X, Y >::Scalar |
Constructor & Destructor Documentation
◆ UzawaSolver()
|
inline |
Constructor.
- Parameters
-
A_ the linear operator \( A : X \to X \) invA_ the (approximate) inverse operator \( A^{-1}: X \to X \), needs to be a subclass of Dune::InverseOperator<X,X> B_ the linear operaotr \( B: X\to Y \) Bt_ the linear operator \( B^T : Y\to X\) precS_ the Schur complement preconditioner \( P: Y\to Y \), \( P\approx S \) reduction_ the default required reduction in preconditioned Schur complement's residual maxit_ the maximum number of iterations verbose_ printing level to stdout (0=silent, 1=result, 2=every iteration)
All the given linear operators and the Schur preconditioner are kept by reference, and have to exist during the lifetime of the UzawaSolver object.
Member Function Documentation
◆ apply() [1/3]
|
inline |
◆ apply() [2/3]
|
inlinevirtual |
◆ apply() [3/3]
|
inlineoverridevirtual |
Solves the saddle point system \( K x = b \).
- Parameters
-
[in,out] x solution. On entry, an initial guess is provided. [in] b right hand side. This will not be modified.
- Returns
- the initial preconditioned residual energy norm squared
Definition at line 112 of file uzawa.hh.
Referenced by Kaskade::UzawaSolver< X, Y >::apply().
◆ category()
|
inlineoverridevirtual |
The documentation for this class was generated from the following file:
