Sparse linear solver parameters

Wherever a record syntax shows [sparselinsolverparams (…)], that stands for the following group of attributes, written directly in the same record.

Syntax

[lstype (in)] [smtype (in)] solverParams (s)

Parameters

[lstype (in)]

Solver for the linear system of equations. Default 0. See Table 3 for the identifiers and Table 4 for the parameters each one takes.

[smtype (in)]

Sparse matrix storage scheme. Default 0, the symmetric skyline (SMT_Skyline). The scheme must be compatible with the solver type; the permitted combinations are in Table 3.

solverParams (s)

The parameters specific to the selected solver, listed in Table 4.

The available storage formats are the symmetric skyline (SMT_Skyline), unsymmetric skyline (SMT_SkylineU), compressed column (SMT_CompCol), dynamically growing compressed column (SMT_DynCompCol), symmetric compressed column (SMT_SymCompCol), dynamically growing compressed row (SMT_DynCompRow), the Spooles library format (SMT_SpoolesMtrx), the PETSc library matrix representation (SMT_PetscMtrx, a sparse serial or parallel matrix in AIJ format), and the DSS-compatible representations (SMT_DSS_*).

Solver identifiers

Table 2 Linear solver types.

lstype	Solver	Compatible storage schemes (smtype)
0	Direct (ST_Direct), the default	0, 1
1	Iterative Method Library (ST_IML)	0, 1, 2, 3, 4, 5; recommended 4 if symmetric, otherwise 2
2	Spooles (ST_Spooles)	6
3	PETSc (ST_Petsc)	7
4	DirectSparseSolver (ST_DSS)	8, 9, 10; recommended 8 if symmetric, otherwise 10
6	Intel MKL Pardiso (ST_MKLPardiso)	2
7	SuperLU_MT (ST_SuperLU_MT)	2
8	Pardiso Project (ST_PardisoProjectOrg)	2

Table 3 Sparse matrix storage schemes.

smtype	Storage format	Compatible solvers (lstype)
0	SMT_Skyline — symmetric skyline, the default	0, 1
1	SMT_SkylineU — unsymmetric skyline	0, 1
2	SMT_CompCol — compressed column	1, 6, 7, 8
3	SMT_DynCompCol — dynamically growing compressed column	1
4	SMT_SymCompCol — symmetric compressed column	1
5	SMT_DynCompRow — dynamically growing compressed row	1
6	SMT_SpoolesMtrx — Spooles library format	2
7	SMT_PetscMtrx — PETSc sparse serial/parallel matrix, AIJ format	3
8	SMT_DSS_sym_LDL — DSS, symmetric LDL	4
9	SMT_DSS_sym_LL — DSS, symmetric LL	4
10	SMT_DSS_unsym_LU — DSS, unsymmetric LU	4

Table 4 Solver parameters.

Solver type	id	Solver parameters and notes
ST_Direct	0	None.
ST_IML	1	lstol (rn), lsiter (in), lsprecond (in), optional stype (in) and precondattributes (s). Included in OOFEM; compile with USE_IML.
ST_Spooles	2	Optional msglvl (in) and msgfile (s). See the Spooles documentation.
ST_Petsc	3	See the PETSc manual, and the run-time options below.
ST_DSS	4	Sparse direct solver included in OOFEM; compile with USE_DSS.
ST_MKLPardiso	6	Requires Intel MKL Pardiso.
ST_SuperLU_MT	7	SuperLU for shared memory machines.
ST_PardisoProjectOrg	8	Requires the Pardiso solver from pardiso-project.org.

Iterative solvers from the IML library

[stype (in)]

Which iterative solver from the IML library to use: 0 (default) the conjugate gradient solver, 1 GMRES.

lstol (rn)

Maximum value of the residual after the final iteration.

lsiter (in)

Maximum number of iterations.

lsprecond (in)

Type of preconditioner; see Table 5.

[precondattributes (s)]

Optional preconditioner parameters; see Table 5.

Table 5 Preconditioning summary.

Precond type	id	Compatible storage	Description and parameters
IML_VoidPrec	0	all	No preconditioning.
IML_DiagPrec	1	all	Diagonal preconditioning.
IML_ILUPrec	2	SMT_CompCol, SMT_DynCompCol	Incomplete LU decomposition with no fill-up.
IML_ILUPrec	3	SMT_DynCompRow	Incomplete LU (ILUT) with fill-up. The precondattributes are droptol (rn), the dropping tolerance, and partfill (in), the level of fill-up.
IML_ICPrec	4	SMT_SymCompCol, SMT_CompCol	Incomplete Cholesky with no fill-up.

PETSc run-time options

With ST_PETSC several run-time options can be set on the command line, for example:

-ksp_type [cg, gmres, bicg, bcgs]
-pc_type  [jacobi, bjacobi, none, ilu, ...]
-ksp_monitor
-ksp_rtol <value>
-ksp_view
-ksp_converged_reason

These options override the defaults, because PETSc’s KSPSetFromOptions() routine is called after any other customization routine.