How to construct a linear solver using the "Linear Solver Factory"

(Difference between revisions)
 Revision as of 08:30, 4 July 2013 (view source)Rrossi (Talk | contribs) (→"External" Iterative Solvers (available in some of the applications))← Older edit Revision as of 08:31, 4 July 2013 (view source)Rrossi (Talk | contribs) (→"External" Iterative Solvers (available in some of the applications))Newer edit → Line 52: Line 52: DropTol=1e-4 DropTol=1e-4 FillTol = 1e-2 FillTol = 1e-2 − FillFactor=5 + ilu_level_of_fill = 5 the user is invited to check the SuperLU documentation [[http://crd-legacy.lbl.gov/~xiaoye/SuperLU/]] for an explanation of the meaning of the different parameters the user is invited to check the SuperLU documentation [[http://crd-legacy.lbl.gov/~xiaoye/SuperLU/]] for an explanation of the meaning of the different parameters Line 64: Line 64: max_iteration = 300 max_iteration = 300 gmres_krylov_space_dimension = 100 gmres_krylov_space_dimension = 100 − ilu_level_of_fill = 3 + ilu_level_of_fill = 5 verbosity = 0 verbosity = 0 is_symmetric = False is_symmetric = False

Revision as of 08:31, 4 July 2013

The class "LinearSolverFactory" is designed to help in the construction of the Kratos Linear Solvers, and makes an attempt to unify the construction mechanism.

the essential idea is that the "settings" to be used in the construction of a linear solver are defined by constructing a new python class (with arbitrary name) which contains the settings needed for the construction of the solver

Within kratos there exist different classes of linear solvers.

Iterative Solvers available in the Kratos Core

A first group of iterative solvers is included within the Kratos core and is always available to the user. Available choices for "solver_type"

``` BiConjugate gradient stabilized
GMRES
```

This solvers can be used with or without a preconditioner, which is also available within the Kratos core. Available options for "preconditioner_type" are

``` None
DiagonalPreconditioner
ILU0
```

in order to construct a "BiConjugate gradient stabilized" together with an ILU0 preconditioner using the factory class one shall write

```   ##here we specify the settings to be used in the construction
class custom_settings:
scaling = True
preconditioner_type = "DiagonalPreconditioner"
max_iteration = 500
tolerance = 1e-6

##here we actually construct a new linear solver using the "custom settings" just defined
import linear_solver_factory
new_linear_solver =  linear_solver_factory.ConstructSolver(custom_settings)
```

Note that specifying "True" at the scaling option implies that the matrix coefficients is normalized prior to the solution step

"External" Iterative Solvers (available in some of the applications)

The Kratos also provides interface to external libraries which provide more advanced preconditioners than the ones provided in the Kratos core. Available options are

```  SuperLUIterativeSolver
Pastix
```

SuperLU solver (available in the ExternalSolversApplication) provides a gmres + ILUT preconditioner can be used by creating a configure of the type

```  class solver_configure
solver_type = "SuperLUIterativeSolver"
scaling = False
tolerance = 1e-7
max_iteration = 300
gmres_krylov_space_dimension=100
DropTol=1e-4
FillTol = 1e-2
ilu_level_of_fill = 5
```

the user is invited to check the SuperLU documentation [[1]] for an explanation of the meaning of the different parameters

Iterative Pastix solver (available in the ExternalSolversApplication provided that compilation enabled it) can be obtained with a configure of the type

```  class solver_configure
solver_type = "PastixIterative"
scaling = False
tolerance = 1e-7
max_iteration = 300
gmres_krylov_space_dimension = 100
ilu_level_of_fill = 5
verbosity = 0
is_symmetric = False
```

note that by setting the is_symmetric=True, incomplete Cholesky is used instead of ILU. Pastix solver is OpenMP parallel

Direct solvers included in the Kratos

```  Skyline LU factorization
SuperLUSolver --> requires the ExternalSolversApplication
Parallel MKL Pardiso --> requires kratos to be compiled with Intel MKL and MKLSolversApplication
PastixDirect --> requires the ExternalSolversApplication to be compiled together with the Pastix solver
```

such solvers are appropriate for the solution of relatively small systems of equations which can be conveniently solved by employing a direct solver technology. The Pardiso solver and the Pastix are OpenMP parallel. Since these solvers are direct, tolerance, preconditioner_type and max_iterations make no sense and are not required. a new solver of this type could be constructed as

```   ##here we specify the settings to be used in the construction
class other_settings:
solver_type = "SuperLUSolver"
scaling = False

```

An error is thrown if the required application is not loaded.

Pastix solver is a little specific in that it allows specifying more parameters to handle the case of symmetric matrices and to

```   ##here we specify the settings to be used in the construction
class other_settings:
solver_type = "PastixDirect"
scaling = False
verbosity = 0
is_symmetric = False
```

Algebraic Multigrid Solver

The kratos contains an interface to the AMGCL solver (courtesy of Dr. Denis Demidov). Such solver combines Algebraic Multigrid with krylov methods.

the configuration of the solver is as follows:

```  class solver_configuration:
solver_type = "AMGCL"
scaling = True
max_iteration = 50
tolerance = 1e-5
smoother_type = "ILU0"  #other options are "DAMPED_JACOBI" and "SPAI0"
krylov_type = "GMRES" #other options are "BICGSTAB" and "CG"
verbosity = 0 #OPTIONAL! set to 1 to have some output
gmres_krylov_space_dimension = 50 #OPTIONAL! only read in case GMRES is chosen.
```

and the construction is as in the other cases. The solver automatically detect block structure in the unkowns, and can be used effecitively for multidimensional problems.

Specialized Solvers

The kratos core also provides more advanced solvers, specialized to the case of mixed formulations. An example of this is the

```   Mixed UP
```

solver which implements a SIMPLE-like preconditioner for the monolithic Navier-Stokes equations combined with a GMRES solver. This solver combines different linear solvers to be used for the "U block" and for the "P block" and shall be in some sense optimal in the case of dominating intertia