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@ -57,7 +57,7 @@ linear systems coming from finite-difference discretizations of basic
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elliptic PDE problems, considered as standard tests for multi-level Schwarz
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preconditioners \cite{aaecc_07,apnum_07}. However, this solver does
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not necessarily correspond to the smallest number of iterations of the
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preconditioned Krylov method, which is usually obtained by applying a
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preconditioned Krylov method, which is usually obtained by applying
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a direct solver to the coarsest-level system, e.g.\ based on the LU
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factorization (see Section~\ref{sec:userinterface}
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for the coarsest-level solvers available in MLD2P4).
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@ -77,12 +77,12 @@ compilers.
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\begin{tabular}{|l|l|p{6.4cm}|}
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\hline
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\textsc{type} & \textsc{string} & \textsc{default preconditioner} \\ \hline
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No preconditioner &\verb|'NOPREC'|& (Considered only to use the PSBLAS
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Krylov solvers with no preconditioner.) \\
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Diagonal & \verb|'DIAG'| & --- \\
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Block Jacobi & \verb|'BJAC'| & Block Jacobi with ILU(0) on the local blocks.\\
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No preconditioner &\verb|'NOPREC'|& Considered only to use the PSBLAS
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Krylov solvers with no preconditioner. \\ \hline
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Diagonal & \verb|'DIAG'| & --- \\ \hline
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Block Jacobi & \verb|'BJAC'| & Block Jacobi with ILU(0) on the local blocks.\\ \hline
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Additive Schwarz & \verb|'AS'| & Restricted Additive Schwarz (RAS),
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with overlap 1 and ILU(0) on the local blocks. \\
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with overlap 1 and ILU(0) on the local blocks. \\ \hline
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Multilevel &\verb|'ML'| & Multi-level hybrid preconditioner (additive on the
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same level and multiplicative through the levels),
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with post-smoothing only.
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@ -92,7 +92,7 @@ Multilevel &\verb|'ML'| & Multi-level hybrid preconditioner (additive
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Aggregation: smoothed aggregation with
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threshold $\theta = 0$.
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Coarsest matrix: distributed among the processors.
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Coarse-level solver:
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Coarsest-level solver:
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4 sweeps of the block-Jacobi solver,
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with LU factorization of the blocks
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(UMFPACK for the double precision versions and
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@ -131,7 +131,7 @@ The setup and application of the default multi-level
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preconditioners for the real single precision and the complex, single and double
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precision, versions are obtained with straightforward modifications of the previous
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example (see Section~\ref{sec:userinterface} for details). If these versions are installed,
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the corresponding Fortran 95 codes are available in \verb|examples/fileread/| with these.
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the corresponding Fortran 95 codes are available in \verb|examples/fileread/|.
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\begin{figure}[tbp]
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\begin{center}
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@ -224,7 +224,7 @@ additive Schwarz preconditioner, i.e.\ RAS with overlap 2. The corresponding
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example program is available in \verb|mld_dexample_1lev.f90|.
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For all the previous preconditioners, example programs where the sparse matrix and
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the right-hand side are generated by discretizing a Poisson equation with Dirichlet
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the right-hand side are generated by discretizing a PDE with Dirichlet
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boundary conditions are also available in the directory \verb|examples/pdegen|.
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