|
class | Dumux::Detail::IstlIterativeLinearSolver< LinearSolverTraits, LinearAlgebraTraits, InverseOperator, PreconditionerFactory, convertMultiTypeLATypes > |
| Standard dune-istl iterative linear solvers. More...
|
|
class | Dumux::Detail::DirectIstlSolver< LSTraits, LATraits, Solver, convertMultiTypeVectorAndMatrix > |
| Direct dune-istl linear solvers. More...
|
|
class | Dumux::LinearSolverParameters< LinearSolverTraits > |
| Generates a parameter tree required for the linear solvers and precondioners of the Dune ISTL. More...
|
|
class | Dumux::MatrixConverter< MultiTypeBlockMatrix, Scalar > |
| A helper class that converts a Dune::MultiTypeBlockMatrix into a plain Dune::BCRSMatrix TODO: allow block sizes for BCRSMatrix other than 1x1 ? More...
|
|
class | Dumux::VectorConverter< MultiTypeBlockVector, Scalar > |
| A helper class that converts a Dune::MultiTypeBlockVector into a plain Dune::BlockVector and transfers back values. More...
|
|
class | Dumux::ParallelMatrixHelper< Matrix, GridView, RowDofMapper, rowDofCodim > |
| Helper class for adding up matrix entries for border entities. More...
|
|
class | Dumux::LinearPDESolver< Assembler, LinearSolver, Comm > |
| An implementation of a linear PDE solver. More...
|
|
class | Dumux::SeqUzawa< M, X, Y, l > |
| A preconditioner based on the Uzawa algorithm for saddle-point problems of the form \(
\begin{pmatrix}
A & B \\
C & D
\end{pmatrix}
\begin{pmatrix}
u\\
p
\end{pmatrix}
=
\begin{pmatrix}
f\\
g
\end{pmatrix}
\). More...
|
|
class | Dumux::ScotchBackend< IndexType > |
| A reordering backend using the scotch library. More...
|
|
class | Dumux::IterativePreconditionedSolverImpl |
| A general solver backend allowing arbitrary preconditioners and solvers. More...
|
|
class | Dumux::ExplicitDiagonalSolver |
| Solver for simple block-diagonal matrices (e.g. from explicit time stepping schemes) More...
|
|
class | Dumux::UzawaBiCGSTABBackend< LinearSolverTraits > |
| A Uzawa preconditioned BiCGSTAB solver for saddle-point problems. More...
|
|
class | Dumux::BlockDiagILU0Preconditioner< M, X, Y, blockLevel > |
| A simple ilu0 block diagonal preconditioner. More...
|
|
class | Dumux::BlockDiagILU0BiCGSTABSolver |
| A simple ilu0 block diagonal preconditioned BiCGSTABSolver. More...
|
|
class | Dumux::BlockDiagILU0RestartedGMResSolver |
| A simple ilu0 block diagonal preconditioned RestartedGMResSolver. More...
|
|
class | Dumux::BlockDiagAMGPreconditioner< M, X, Y, blockLevel > |
| A simple ilu0 block diagonal preconditioner. More...
|
|
class | Dumux::BlockDiagAMGBiCGSTABSolver |
| A simple ilu0 block diagonal preconditioned BiCGSTABSolver. More...
|
|
class | Dumux::LinearSolver |
| Base class for linear solvers. More...
|
|
class | Dumux::Detail::StokesPreconditioner< M, X, Y, l > |
| 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...
|
|
class | Dumux::StokesSolver< Matrix, Vector, VelocityGG, PressureGG > |
| Preconditioned iterative solver for the incompressible Stokes problem. More...
|
|
template<class LSTraits , class LATraits >
Initial value:
Detail::IstlIterativeLinearSolver<LSTraits, LATraits,
Dune::BiCGSTABSolver<typename LATraits::SingleTypeVector>,
Detail::IstlSolvers::IstlAmgPreconditionerFactory,
true
>
Solver: The BiCGSTAB (stabilized biconjugate gradients method) solver has faster and smoother convergence than the original BiCG. While, it can be applied to nonsymmetric matrices, the preconditioner SSOR assumes symmetry.
See: Van der Vorst, H. A. (1992). "Bi-CGSTAB: A Fast and Smoothly Converging
Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems". SIAM J. Sci. and Stat. Comput. 13 (2): 631–644. doi:10.1137/0913035.
Preconditioner: AMG (algebraic multigrid)
template<class LSTraits , class LATraits >
Initial value:
Detail::IstlIterativeLinearSolver<LSTraits, LATraits,
Dune::CGSolver<typename LATraits::SingleTypeVector>,
Detail::IstlSolvers::IstlAmgPreconditionerFactory,
true
>
Solver: CG (conjugate gradient) is an iterative method for solving linear systems with a symmetric, positive definite matrix.
See: Helfenstein, R., Koko, J. (2010). "Parallel preconditioned conjugate
gradient algorithm on GPU", Journal of Computational and Applied Mathematics, Volume 236, Issue 15, Pages 3584–3590, http://dx.doi.org/10.1016/j.cam.2011.04.025.
Preconditioner: AMG (algebraic multigrid)
template<class LSTraits , class LATraits >
Initial value:
Detail::IstlIterativeLinearSolver<LSTraits, LATraits,
Dune::BiCGSTABSolver<typename LATraits::SingleTypeVector>,
Detail::IstlSolvers::IstlDefaultBlockLevelPreconditionerFactory<Dune::SeqILU>,
true
>
Solver: The BiCGSTAB (stabilized biconjugate gradients method) solver has faster and smoother convergence than the original BiCG. It can be applied to nonsymmetric matrices.
See: Van der Vorst, H. A. (1992). "Bi-CGSTAB: A Fast and Smoothly Converging
Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems". SIAM J. Sci. and Stat. Comput. 13 (2): 631–644. doi:10.1137/0913035.
Preconditioner: ILU(n) incomplete LU factorization. The order n indicates fill-in. It can be damped by the relaxation parameter LinearSolver.PreconditionerRelaxation.
See: Golub, G. H., and Van Loan, C. F. (2012). Matrix computations. JHU Press.
template<class LSTraits , class LATraits >
Initial value:
Detail::IstlIterativeLinearSolver<LSTraits, LATraits,
Dune::RestartedGMResSolver<typename LATraits::SingleTypeVector>,
Detail::IstlSolvers::IstlDefaultBlockLevelPreconditionerFactory<Dune::SeqILU>,
true
>
Solver: The GMRes (generalized minimal residual) method is an iterative method for the numerical solution of a nonsymmetric system of linear equations.
See: Saad, Y., Schultz, M. H. (1986). "GMRES: A generalized minimal residual
algorithm for solving nonsymmetric linear systems." SIAM J. Sci. and Stat. Comput. 7: 856–869.
Preconditioner: ILU(n) incomplete LU factorization. The order n indicates fill-in. It can be damped by the relaxation parameter LinearSolver.PreconditionerRelaxation.
See: Golub, G. H., and Van Loan, C. F. (2012). Matrix computations. JHU Press.
template<class LSTraits , class LATraits >
Initial value:
Detail::IstlIterativeLinearSolver<LSTraits, LATraits,
Dune::BiCGSTABSolver<typename LATraits::Vector>,
Detail::IstlSolvers::IstlDefaultBlockLevelPreconditionerFactory<Dune::SeqSSOR>
>
Solver: The BiCGSTAB (stabilized biconjugate gradients method) solver has faster and smoother convergence than the original BiCG. While, it can be applied to nonsymmetric matrices, the preconditioner SSOR assumes symmetry.
See: Van der Vorst, H. A. (1992). "Bi-CGSTAB: A Fast and Smoothly Converging
Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems". SIAM J. Sci. and Stat. Comput. 13 (2): 631–644. doi:10.1137/0913035.
Preconditioner: SSOR symmetric successive overrelaxation method. The relaxation is controlled by the parameter LinearSolver.PreconditionerRelaxation. In each preconditioning step, it is applied as often as given by the parameter LinearSolver.PreconditionerIterations.
See: Golub, G. H., and Van Loan, C. F. (2012). Matrix computations. JHU Press.
template<class LSTraits , class LATraits >
Initial value:
Detail::IstlIterativeLinearSolver<LSTraits, LATraits,
Dune::CGSolver<typename LATraits::Vector>,
Detail::IstlSolvers::IstlDefaultBlockLevelPreconditionerFactory<Dune::SeqSSOR>
>
Solver: CG (conjugate gradient) is an iterative method for solving linear systems with a symmetric, positive definite matrix.
See: Helfenstein, R., Koko, J. (2010). "Parallel preconditioned conjugate
gradient algorithm on GPU", Journal of Computational and Applied Mathematics, Volume 236, Issue 15, Pages 3584–3590, http://dx.doi.org/10.1016/j.cam.2011.04.025.
Preconditioner: SSOR symmetric successive overrelaxation method. The relaxation is controlled by the parameter LinearSolver.PreconditionerRelaxation. In each preconditioning step, it is applied as often as given by the parameter LinearSolver.PreconditionerIterations.
See: Golub, G. H., and Van Loan, C. F. (2012). Matrix computations. JHU Press.
template<class LSTraits , class LATraits >
Initial value:
Detail::IstlIterativeLinearSolver<LSTraits, LATraits,
Dune::BiCGSTABSolver<typename LATraits::Vector>,
Detail::IstlSolvers::IstlDefaultBlockLevelPreconditionerFactory<Dumux::SeqUzawa>
>
Solver: The BiCGSTAB (stabilized biconjugate gradients method) solver has faster and smoother convergence than the original BiCG. While, it can be applied to nonsymmetric matrices, the preconditioner SSOR assumes symmetry.
See: Van der Vorst, H. A. (1992). "Bi-CGSTAB: A Fast and Smoothly Converging
Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems". SIAM J. Sci. and Stat. Comput. 13 (2): 631–644. doi:10.1137/0913035.
Preconditioner: Uzawa method for saddle point problems
- Note
- Expects a 2x2 MultiTypeBlockMatrix