Subroutine mld_precset

mld_precset(p,what,val,info)
mld_precset(p,smoother,info)
mld_precset(p,solver,info)

This routine sets the parameters defining the preconditioner. More precisely, the parameter identified by what is assigned the value contained in val. The other two forms of this routine are designed to allow extensions of the library by passing new smoothers and solvers to be employed in the preconditioner.

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).
	The number identifying the parameter to be set. A mnemonic constant has been associated to each of these numbers, as reported in 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 new smoother object, its parameters including the contained solver are set to default values, and when a new solver object is specified its defaults are also set, overriding in both cases any previous settings even if explicitly specified. Therefore if the user specifies a new smoother, and whishes to use a new solver which is not the default one, the call to set the solver must come after the call to set the smoother.

Table 2: Parameters defining the type of multi-level preconditioner.

what	DATA TYPE	val	DEFAULT	COMMENTS
mld_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_	character(len=*)	'DIAG' 'BJAC' 'AS'	'AS'	Basic predefined one-level preconditioner (i.e. smoother): diagonal, block Jacobi, AS.
mld_smoother_pos_	character(len=*)	'PRE' 'POST' 'TWOSIDE'	'POST'	``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_	integer	any int. num. $\ge 0$	1	Number of overlap layers.
mld_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_	character(len=*)	'SUM' 'NONE'	'NONE'	Type of prolongation operator: 'SUM' for adding the contributions from the overlap, 'NONE' for neglecting them.
mld_sub_solve_	character(len=*)	'ILU' 'MILU' 'ILUT' 'UMF' 'SLU'	'ILU'	Predefined local solver: ILU($p$), MILU($p$), ILU($p,t$), LU from UMFPACK, LU from SuperLU (plus triangular solve).
mld_sub_fillin_	integer	Any int. num. $\ge 0$	0	Fill-in level $p$ of the incomplete LU factorizations.
mld_sub_iluthrs_	real(kind_parameter)	Any real num. $\ge 0$	0	Drop tolerance $t$ in the ILU($p,t$) factorization.
mld_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.

Table 4: Parameters defining the aggregation algorithm.

what	DATA TYPE	val	DEFAULT	COMMENTS
mld_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_	character(len=*)	'DEC'	'DEC'	Aggregation algorithm. Currently, only the decoupled aggregation is available.
mld_aggr_kind_	character(len=*)	'SMOOTHED' 'NONSMOOTHED'	'SMOOTHED'	Type of aggregation: smoothed, nonsmoothed (i.e. using the tentative prolongator).
mld_aggr_thresh_	real(kind_parameter)	Any real num. $\in [0, 1]$	0	Threshold $\theta$ in the aggregation algorithm.
mld_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_	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_	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_	character(len=*)	'DISTR' 'REPL'	'DISTR'	Coarsest matrix: distributed among the processors or replicated on each of them.
mld_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_	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_	integer	Any int. num. $> 0$	4	Number of Block-Jacobi sweeps when 'BJAC' is used as coarsest-level solver.
mld_coarse_fillin_	integer	Any int. num. $\ge 0$	0	Fill-in level $p$ of the incomplete LU factorizations.
mld_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