Subroutine mld_precset

call mld_precset(p,what,val,info)

This routine sets the parameters defining the preconditioner. More precisely, the parameter identified by what is assigned the value contained in val.

The routine may also be invoked as a method of the preconditioner object as in the following:

call p%set(what,val,info [,ilev])
In this case it is also possible to specify an optional ilev argument that restricts the effect of the call to the specified level.

Finally, if the user has developed a new type of smoother and/or solver by extending one of the base MLD2P4 types, and has declared a variable of the new type in the main program, it is possible to pass the new smoother/solver variable to the setup routine as follows:

call p%set(smoother,info [,ilev])
call p%set(solver,info [,ilev])
In this way, the variable will act as a mold to which the preconditioner will conform, even though the MLD2P4 library is not modified, and thus has no direct knowledge about the new type.

Arguments

p type(mld_xprec_type), intent(inout).
  The preconditioner data structure. Note that x must be chosen according to the real/complex, single/double precision version of MLD2P4 under use.
what integer, intent(in) or character(len=*).
  The parameter to be set. It can be specified by a predefined constant, or through its name; the string is case-insensitive. See also Tables 2-5.
val integer or character(len=*) or real(psb_spk_) or real(psb_dpk_), intent(in).
  The value of the parameter to be set. The list of allowed values and the corresponding data types is given in Tables 2-5. When the value is of type character(len=*), it is also treated as case insensitive.
smoother class(mld_x_base_smoother_type)
  The user-defined new smoother to be employed in the preconditioner.
solver class(mld_x_base_solver_type)
  The user-defined new solver to be employed in the preconditioner.
info integer, intent(out).
  Error code. If no error, 0 is returned. See Section 7 for details.


A variety of (one-level and multi-level) preconditioners can be obtained by a suitable setting of the preconditioner parameters. These parameters can be logically divided into four groups, i.e. parameters defining

  1. the type of multi-level preconditioner;
  2. the one-level preconditioner used as smoother;
  3. the aggregation algorithm;
  4. the coarse-space correction at the coarsest level.
A list of the parameters that can be set, along with their allowed and default values, is given in Tables 2-5. For a detailed description of the meaning of the parameters, please refer to Section 4.

The smoother and solver objects are arranged in a hierarchical manner; when specifying a smoother object, its parameters including the contained solver are set to default values, and when a solver object is specified its defaults are also set, overriding in both cases any previous settings even if explicitly specified. Therefore if the user sets a new smoother, and wishes to use a solver different from the default one, the call to set the solver must come after the call to set the smoother.

The combination of a Jacobi smoother with a Diagonal Scaling local solver is equivalent to the strategy called Point Jacobi in the literature; similarly, having a Jacobi smoother with a Gauss-Seidel local solver is equivalent to a ``hybrid Gauss-Seidel'' solver.

Completely new smoother and/or solver class derived from the base objects in the library may be used without recompiling the library itself. Once the new smoother/solver class has been developed, the user can declare a variable of that new type in the application, and pass that variable to the p%set(solver,info) call; the new solver object is then dynamically included in the preconditioner structure.

The what,val pairs described here are those of the predefined smoother/solver objects; newly developed solvers may define new pairs according to their needs.


Table 2: Parameters defining the type of multi-level preconditioner.
what DATA TYPE val DEFAULT COMMENTS
mld_ml_type_
ML_TYPE
character(len=*) 'ADD' 'MULT' 'MULT' Basic multi-level framework: additive or multiplicative among the levels (always additive inside a level).
mld_smoother_type_
SMOOTHER_TYPE
character(len=*) 'JACOBI' 'BJAC' 'AS' 'AS' Basic predefined one-level preconditioner (i.e. smoother): Jacobi, block Jacobi, AS.
mld_smoother_pos_
SMOOTHER_POS
character(len=*) 'PRE' 'POST' 'TWOSIDE' 'TWOSIDE' ``Position'' of the smoother: pre-smoother, post-smoother, pre- and post-smoother.



Table 3: Parameters defining the one-level preconditioner used as smoother.
what DATA TYPE val DEFAULT COMMENTS
mld_sub_ovr_
SUB_OVR
integer any int. num. $\ge 0$ 1 Number of overlap layers.
mld_sub_restr_
SUB_RESTR
character(len=*) 'HALO' 'NONE' 'HALO' Type of restriction operator: 'HALO' for taking into account the overlap, 'NONE' for neglecting it.
mld_sub_prol_
SUB_PROL
character(len=*) 'SUM' 'NONE' 'NONE' Type of prolongation operator: 'SUM' for adding the contributions from the overlap, 'NONE' for neglecting them.
mld_sub_solve_
SUB_SOLVE
character(len=*) 'DIAG' 'GS' 'ILU' 'MILU' 'ILUT' 'UMF' 'SLU' 'ILU' Predefined local solver: pointwise Jacobi (diagonal scaling), Gauss-Seidel, ILU($p$), MILU($p$), ILU($p,t$), LU from UMFPACK, LU from SuperLU (plus triangular solve).
mld_sub_fillin_
SUB_FILLIN
integer Any int. num. $\ge 0$ 0 Fill-in level $p$ of the incomplete LU factorizations.
mld_sub_iluthrs_
SUB_ILUTHRS
real(kind_parameter) Any real num. $\ge 0$ 0 Drop tolerance $t$ in the ILU($p,t$) factorization.
mld_sub_ren_
SUB_REN
character(len=*) 'RENUM_NONE' 'RENUM_GLOBAL' 'RENUM_NONE' Row and column reordering of the local submatrices: no reordering, reordering according to the global numbering of the rows and columns of the whole matrix.
mld_solver_sweeps_
SOLVER_SWEEPS
integer Any int. num. $\ge 1$ 1 Number of sweeps for iterative local solver (currently only Gauss-Seidel).



Table 4: Parameters defining the aggregation algorithm.
what DATA TYPE val DEFAULT COMMENTS
mld_coarse_aggr_size_
COARSE_AGGR_SIZE
integer A positive number 0, meaning that the size is fixed at precinit time Coarse size threshold. Disregard the original specification of number of levels in precinit and continue aggregation until either the global number of variables is below this threshold, or the aggregation does not reduce the size any longer.
mld_aggr_alg_
AGGR_ALG
character(len=*) 'DEC' 'DEC' Aggregation algorithm. Currently, only the decoupled aggregation is available.
mld_aggr_kind_
AGGR_KIND
character(len=*) 'SMOOTHED' 'NONSMOOTHED' 'SMOOTHED' Type of aggregation: smoothed, nonsmoothed (i.e. using the tentative prolongator).
mld_aggr_thresh_
AGGR_THRESH
real(kind_parameter) Any real num. $\in [0, 1]$ 0.05 Threshold $\theta$ in the aggregation algorithm.
mld_aggr_scale_
AGGR_SCALE
real(kind_parameter) Any real num. $\in [0, 1]$ 1.0 Scale factor applied to the threshold going from level $ilev$ to level $ilev+1$.
mld_aggr_omega_alg_
AGGR_OMEGA_ALG
character(len=*) 'EIG_EST' 'USER_CHOICE' 'EIG_EST' How the damping parameter $\omega$ in the smoothed aggregation should be computed: either via an estimate of the spectral radius of $D^{-1}A$, or explicily specified by the user.
mld_aggr_eig_
AGGR_EIG
character(len=*) 'A_NORMI' 'A_NORMI' How to estimate the spectral radius of $D^{-1}A$. Currently only the infinity norm estimate is available.
mld_aggr_omega_val_
AGGR_OMEGA_VAL
real(kind_parameter) Any nonnegative real num. $4/(3\rho(D^{-1}A))$ Damping parameter $\omega$ in the smoothed aggregation algorithm. It must be set by the user if USER_CHOICE was specified for mld_aggr_omega_alg_, otherwise it is computed by the library, using the selected estimate of the spectral radius $\rho(D^{-1}A)$ of $D^{-1}A$.



Table 5: Parameters defining the coarse-space correction at the coarsest level.
what DATA TYPE val DEFAULT COMMENTS
mld_coarse_mat_
COARSE_MAT
character(len=*) 'DISTR' 'REPL' 'DISTR' Coarsest matrix: distributed among the processors or replicated on each of them.
mld_coarse_solve_
COARSE_SOLVE
character(len=*) 'BJAC' 'UMF' 'SLU' 'SLUDIST' 'BJAC' Solver used at the coarsest level: block Jacobi, sequential LU from UMFPACK, sequential LU from SuperLU, distributed LU from SuperLU_Dist. 'SLUDIST' requires the coarsest matrix to be distributed, while 'UMF' and 'SLU' require it to be replicated.
mld_coarse_subsolve_
COARSE_SUBSOLVE
character(len=*) 'ILU' 'MILU' 'ILUT' 'UMF' 'SLU' See note Solver for the diagonal blocks of the coarse matrix, in case the block Jacobi solver is chosen as coarsest-level solver: ILU($p$), MILU($p$), ILU($p,t$), LU from UMFPACK, LU from SuperLU, plus triangular solve.
mld_coarse_sweeps_
COARSE_SWEEPS
integer Any int. num. $> 0$ 4 Number of Block-Jacobi sweeps when 'BJAC' is used as coarsest-level solver.
mld_coarse_fillin_
COARSE_FILLIN
integer Any int. num. $\ge 0$ 0 Fill-in level $p$ of the incomplete LU factorizations.
mld_coarse_iluthrs_
COARSE_ILUTHRS
real(kind_parameter) Any real. num. $\ge 0$ 0 Drop tolerance $t$ in the ILU($p,t$) factorization.
Note: defaults for mld_coarse_subsolve_ are chosen as
single precision version: 'SLU' if installed, 'ILU' otherwise
double precision version: 'UMF' if installed, else 'SLU' if installed, 'ILU' otherwise