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

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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
 Conjugate gradient

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


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:
      solver_type = "BiConjugate gradient stabilized"
      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

Direct solvers included in the Kratos

Admissible values for "solver_type" are

  Skyline LU factorization
  SuperLUSolver --> requires the ExternalSolversApplication
  Parallel MKL Pardiso --> requires kratos to be compiled with Intel MKL and MKLSolversApplication
  Pastix --> 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
   ##here we actually construct a new linear solver using the "other settings" just defined
   import linear_solver_factory
   new_direct_solver =  linear_solver_factory.ConstructSolver(other_settings)

An error is thrown if the required application is not loaded

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

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