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@ -75,77 +75,7 @@ $ptype$ string as follows\footnote{The string is case-insensitive}:
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by the data allocation boundaries for each process; requires no
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communication. Only the incomplete factorization $ILU(0)$ is
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currently implemented.
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%% \item[AS] Additive Schwarz preconditioner (see~\cite{PARA04}); in this
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%% case the user may specify additional flags through the integer
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%% vector \verb|ir| as follows:
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%% \begin{description}
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%% \item[$iv(1)$] Number of overlap levels, an integer $novr>=0$, default
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%% $novr=1$.
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%% \item[$iv(2)$] Restriction operator, legal values: \verb|psb_halo_|,
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%% \verb|psb_none_|; default: \verb|psb_halo_|
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%% \item[$iv(3)$] Prolongation operator, legal values: \verb|psb_none_|,
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%% \verb|psb_sum_|, \verb|psb_avg_|, default: \verb|psb_none_|
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%% \item[$iv(4)$] Factorization type, legal values: \verb|f_ilu_n_|,
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%% \verb|f_slu_|, \verb|f_umf_|, default: \verb|f_ilu_n_|.
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%% \end{description}
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%% Note that the default corresponds to a Restricted Additive Schwarz
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%% preconditioner with $ILU(0)$ and 1 level of overlap.
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%% \item[2L] Second level of a multilevel preconditioner, see below
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%% \end{description}
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%% If a multilevel preconditioner is desired, the user should call
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%% \verb|psb_precset| twice, the first time choosing an AS variant, and
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%% a second time specifying
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%% $ptype=2L$ with the following optional parameters in $iv$ (see
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%% also~\cite{APNUM06,DD2}):
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%% \begin{description}
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%% \item[$iv(1)$] Type of multilevel correction, legal values: \verb|no_ml_|,
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%% \verb|add_ml_prec_|, \verb|mult_ml_prec_|,
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%% default: \verb|mult_ml_prec_|;
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%% \item[$iv(2)$] Aggregation algorithm, legal values: \verb|loc_aggr_|;
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%% \item[$iv(3)$] Smoother type, legal values: \verb|no_smth_|,
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%% \verb|smth_omg_|, default: \verb|smth_omg_|;
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%% \item[$iv(4)$] Coarse matrix allocation, legal values:
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%% \verb|mat_distr_|, \verb|mat_repl_|, default: \verb|mat_distr_|
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%% \item[$iv(5)$] Smoother position, legal values: \verb|pre_smooth_|,
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%% \verb|post_smooth_|, \verb|smooth_both_|, default:
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%% \verb|post_smooth_|
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%% \item[$iv(6)$] Factorization type (for coarse matrix), legal values: \verb|f_ilu_n_|,
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%% \verb|f_slu_|, \verb|f_umf_|, default: \verb|f_ilu_n_|;
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%% \item[$iv(7)$] Number of Jacobi sweeps for coarse system correction,
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%% default 1.
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%% \item[$rs$] Set the smoother parameter $\omega$ a user defined value;
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%% default: esitimate with the infinity norm of matrix $A$.
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\end{description}
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%% The 2-level preconditioners are based on the idea of building a
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%% coarse-space approximation $A_C$ of the matrix $A$; given a set $W_C$
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%% of coarse vertices, with size $n_C$, and a suitable restriction
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%% operator $R_C \in \Re^{n_C \times n}$, $A_C$ is defined as
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%% \[
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%% A_C=R_C A R_C^T .
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%% \]
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%% The prolongator $R_C^T$ is built with the smoothed aggregation technique,
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%% in which we start from a tentative prolongator that simply maps
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%% fine-level entries onto their aggregates $P_C$; if the user chooses
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%% \verb|no_smth_| this is the prolongator used, otherwise it is
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%% multiplied by a smoother \[ S = I - \omega D^{-1} A \], where $D$ is
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%% the diagonal of $A$ and $\omega$ may be imposed by the user or
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%% estimated internally.
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%% The coarse space correction may be added to the fine level solution
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%% \verb|add_ml_prec_|
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%% \[
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%% M_{2L-A}^{-1} = M_{C}^{-1} + M_{1L}^{-1}.
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%% \]
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%% or it can be composed in a multiplicative framework
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%% (\verb|mult_ml_prec_|)as a pre-smoothed correction (\verb|pre_smooth_|)
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%% \[
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%% M_{2L-H1}^{-1} = M_{C}^{-1} + \left( I - M_{C}^{-1}A \right) M_{1L}^{-1},
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%% \]
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%% post-smoothed correction (\verb|post_smooth_|)
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%% \[
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%% M_{2L-H2}^{-1} = M_{1L}^{-1} + \left( I - M_{1L}^{-1}A \right) M_{C}^{-1}.
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%% \]
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%% or two-sided for symmetric matrices (\verb|smooth_both_|).
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\subroutine{psb\_precbld}{Builds a preconditioner}
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Salvatore Filippone
17 years ago