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<H2><A NAME="SECTION00071000000000000000"></A><A NAME="sec:examples"></A>
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<BR>
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Examples
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</H2>
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<P>
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The code reported in Figure <A HREF="#fig:ex_default">2</A> shows how to set and apply the default
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multi-level preconditioner available in the real double precision version
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of MLD2P4 (see Table <A HREF="#tab:precinit">1</A>). This preconditioner is chosen
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by simply specifying <code>'ML'</code> as second argument of <code>mld_precinit</code>
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(a call to <code>mld_precset</code> is not needed) and is applied with the BiCGSTAB
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solver provided by PSBLAS. As previously observed, the modules <code>psb_base_mod</code>,
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<code>mld_prec_mod</code> and <code>psb_krylov_mod</code> must be used by the example program.
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<P>
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The part of the code concerning the
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reading and assembling of the sparse matrix and the right-hand side vector, performed
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through the PSBLAS routines for sparse matrix and vector management, is not reported
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here for brevity; the statements concerning the deallocation of the PSBLAS
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data structure are neglected too.
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The complete code can be found in the example program file <code>mld_dexample_ml.f90</code>,
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in the directory <code>examples/fileread</code> of the MLD2P4 tree (see
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Section <A HREF="node10.html#sec:ex_and_test">3.5</A>).
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For details on the use of the PSBLAS routines, see the PSBLAS User's
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Guide [<A
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HREF="node25.html#PSBLASGUIDE">15</A>].
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<P>
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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 <A HREF="node16.html#sec:userinterface">6</A> for details). If these versions are installed,
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the corresponding Fortran 95 codes are available in <code>examples/fileread/</code>.
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig:ex_default"></A><A NAME="931"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 2:</STRONG>
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Setup and application of the default multi-level Schwarz preconditioner.
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</CAPTION>
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<TR><TD>
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<DIV ALIGN="CENTER">
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</DIV><TABLE WIDTH="90%">
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<TR><TD>
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<PRE>
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use psb_base_mod
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use mld_prec_mod
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use psb_krylov_mod
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... ...
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!
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! sparse matrix
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type(psb_dspmat_type) :: A
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! sparse matrix descriptor
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type(psb_desc_type) :: desc_A
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! preconditioner
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type(mld_dprec_type) :: P
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! right-hand side and solution vectors
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real(kind(1.d0)) :: b(:), x(:)
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... ...
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!
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! initialize the parallel environment
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call psb_init(ictxt)
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call psb_info(ictxt,iam,np)
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... ...
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!
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! read and assemble the matrix A and the right-hand side b
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! using PSBLAS routines for sparse matrix / vector management
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... ...
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!
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! initialize the default multi-level preconditioner, i.e. hybrid
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! Schwarz, using RAS (with overlap 1 and ILU(0) on the blocks)
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! as post-smoother and 4 block-Jacobi sweeps (with UMFPACK LU
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! on the blocks) as distributed coarse-level solver
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call mld_precinit(P,'ML',info)
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!
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! build the preconditioner
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call mld_precbld(A,desc_A,P,info)
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!
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! set the solver parameters and the initial guess
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... ...
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!
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! solve Ax=b with preconditioned BiCGSTAB
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call psb_krylov('BICGSTAB',A,P,b,x,tol,desc_A,info)
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... ...
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!
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! deallocate the preconditioner
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call mld_precfree(P,info)
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!
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! deallocate other data structures
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... ...
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!
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! exit the parallel environment
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call psb_exit(ictxt)
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stop
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</PRE>
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</TD></TR>
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</TABLE>
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<DIV ALIGN="CENTER">
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</DIV></TD></TR>
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</TABLE>
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</DIV>
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<P>
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Different versions of multi-level preconditioners can be obtained by changing
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the default values of the preconditioner parameters. The code reported in
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Figure <A HREF="#fig:ex_3lh">3</A> shows how to set a three-level hybrid Schwarz
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preconditioner, which uses block Jacobi with ILU(0) on the
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local blocks as post-smoother, has a coarsest matrix replicated on the processors,
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and solves the coarsest-level system with the LU factorization from UMFPACK [<A
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HREF="node25.html#UMFPACK">9</A>].
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The number of levels is specified by using <code>mld_precinit</code>; the other
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preconditioner parameters are set by calling <code>mld_precset</code>. Note that
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the type of multilevel framework (i.e. multiplicative among the levels
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with post-smoothing only) is not specified since it is the default
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set by <code>mld_precinit</code>.
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<P>
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Figure <A HREF="#fig:ex_3la">4</A> shows how to
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set a three-level additive Schwarz preconditioner,
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which uses RAS, with overlap 1 and ILU(0) on the blocks,
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as pre- and post-smoother, and applies five block-Jacobi sweeps, with
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the UMFPACK LU factorization on the blocks, as distributed coarsest-level
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solver. Again, <code>mld_precset</code> is used only to set
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non-default values of the parameters (see Tables <A HREF="#tab:p_type">2</A>-<A HREF="#tab:p_coarse">5</A>).
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In both cases, the construction and the application of the preconditioner
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are carried out as for the default multi-level preconditioner.
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The code fragments shown in in Figures <A HREF="#fig:ex_3lh">3</A>-<A HREF="#fig:ex_3la">4</A> are
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included in the example program file <code>mld_dexample_ml.f90</code> too.
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<P>
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Finally, Figure <A HREF="#fig:ex_1l">5</A> shows the setup of a one-level
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additive Schwarz preconditioner, i.e. RAS with overlap 2. The corresponding
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example program is available in <code>mld_dexample_</code> <code>1lev.f90</code>.
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<P>
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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 PDE with Dirichlet
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boundary conditions are also available in the directory <code>examples/pdegen</code>.
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<P>
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<BR><B>Remark 3.</B> Any PSBLAS-based program using the basic preconditioners
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implemented in PSBLAS 2.0, i.e. the diagonal and block-Jacobi ones,
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can use the diagonal and block-Jacobi preconditioners
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implemented in MLD2P4 without any change in the code.
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The PSBLAS-based program must be only recompiled
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and linked to the MLD2P4 library.
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<BR>
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig:ex_3lh"></A><A NAME="933"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 3:</STRONG>
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Setup of a hybrid three-level Schwarz preconditioner.</CAPTION>
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<TR><TD>
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<DIV ALIGN="CENTER">
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</DIV><TABLE WIDTH="90%">
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<TR><TD>
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<PRE>
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... ...
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! set a three-level hybrid Schwarz preconditioner, which uses
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! block Jacobi (with ILU(0) on the blocks) as post-smoother,
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! a coarsest matrix replicated on the processors, and the
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! LU factorization from UMFPACK as coarse-level solver
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call mld_precinit(P,'ML',info,nlev=3)
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call_mld_precset(P,mld_smoother_type_,'BJAC',info)
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call mld_precset(P,mld_coarse_mat_,'REPL',info)
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call mld_precset(P,mld_coarse_solve_,'UMF',info)
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... ...
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</PRE>
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</TD></TR>
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</TABLE>
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<DIV ALIGN="CENTER">
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</DIV>
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<P>
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<DIV ALIGN="CENTER">
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</DIV></TD></TR>
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</TABLE>
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</DIV>
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig:ex_3la"></A><A NAME="935"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 4:</STRONG>
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Setup of an additive three-level Schwarz preconditioner.</CAPTION>
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<TR><TD>
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<DIV ALIGN="CENTER">
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</DIV><TABLE WIDTH="90%">
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<TR><TD>
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<PRE>
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... ...
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! set a three-level additive Schwarz preconditioner, which uses
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! RAS (with overlap 1 and ILU(0) on the blocks) as pre- and
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! post-smoother, and 5 block-Jacobi sweeps (with UMFPACK LU
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! on the blocks) as distributed coarsest-level solver
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call mld_precinit(P,'ML',info,nlev=3)
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call mld_precset(P,mld_ml_type_,'ADD',info)
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call_mld_precset(P,mld_smoother_pos_,'TWOSIDE',info)
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call mld_precset(P,mld_coarse_sweeps_,5,info)
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... ...
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</PRE>
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</TD></TR>
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</TABLE>
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<DIV ALIGN="CENTER">
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</DIV>
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<P>
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<DIV ALIGN="CENTER">
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</DIV></TD></TR>
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</TABLE>
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</DIV>
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig:ex_1l"></A><A NAME="937"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 5:</STRONG>
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Setup of a one-level Schwarz preconditioner.</CAPTION>
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<TR><TD>
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<DIV ALIGN="CENTER">
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</DIV><TABLE WIDTH="90%">
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<TR><TD>
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<PRE>
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... ...
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! set RAS with overlap 2 and ILU(0) on the local blocks
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call mld_precinit(P,'AS',info)
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call mld_precset(P,mld_sub_ovr_,2,info)
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... ...
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</PRE>
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</TD></TR>
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</TABLE>
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<DIV ALIGN="CENTER">
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</DIV></TD></TR>
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</TABLE>
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