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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><BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
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<P>
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<BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">The code reported in Figure <A HREF="#fig:ex1">2</A> shows how to set and apply the default
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multilevel 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 the second argument of <code>P%init</code>
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(a call to <code>P%set</code> is not needed) and is applied with the CG
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solver provided by PSBLAS (the matrix of the system to be solved is
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assumed to be positive definite). As previously observed, the modules
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<code>psb_base_mod</code>, <code>mld_prec_mod</code> and <code>psb_krylov_mod</code>
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must be used by the example program.
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</BIG></BIG></BIG>
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<P>
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<BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">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 implementation (see
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Section <A HREF="node11.html#sec:ex_and_test">3.5</A>). A sample test problem along with the relevant
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input data is available in <code>examples/fileread/runs</code>.
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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="node36.html#PSBLASGUIDE">13</A>].
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</BIG></BIG></BIG>
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<P>
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<BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">The setup and application of the default multilevel preconditioner
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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="node18.html#sec:userinterface">6</A> for details). If these versions are installed,
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the corresponding codes are available in <code>examples/fileread/</code>.
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</BIG></BIG></BIG>
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<P>
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<BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
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<DIV ALIGN="CENTER"><A NAME="fig:ex1"></A><A NAME="907"></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 multilevel preconditioner (example 1).
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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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type(psb_d_vect_type) :: 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 spd 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 multilevel preconditioner, i.e. V-cycle
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! with basic smoothed aggregation, 1 hybrid forward/backward
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! GS sweep as pre/post-smoother and UMFPACK as coarsest-level
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! solver
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call P%init('ML',info)
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!
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! build the preconditioner
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call P%hierarchy_build(A,desc_A,info)
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call P%smoothers_build(A,desc_A,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 CG
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call psb_krylov('CG',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 P%free(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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<BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
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<P>
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<BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">Different versions of the multilevel preconditioner 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:ex2">3</A> shows how to set a V-cycle preconditioner
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which applies 1 block-Jacobi sweep as pre- and post-smoother,
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and solves the coarsest-level system with 8 block-Jacobi sweeps.
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Note that the ILU(0) factorization (plus triangular solve) is used as
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local solver for the block-Jacobi sweeps, since this is the default associated
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with block-Jacobi and set by <code>P%init</code>.
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Furthermore, specifying block-Jacobi as coarsest-level
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solver implies that the coarsest-level matrix is distributed
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among the processes.
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Figure <A HREF="#fig:ex3">4</A> shows how to set a W-cycle preconditioner which
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applies 2 hybrid Gauss-Seidel sweeps as pre- and post-smoother,
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and solves the coarsest-level system with the multifrontal LU factorization
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implemented in MUMPS. It is specified that the coarsest-level
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matrix is distributed, since MUMPS can be used on both
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replicated and distributed matrices, and by default
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it is used on replicated ones.
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The code fragments shown in Figures <A HREF="#fig:ex2">3</A> and <A HREF="#fig:ex3">4</A> are
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included in the example program file <code>mld_dexample_ml.f90</code> too.
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</BIG></BIG></BIG>
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<P>
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<BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">Finally, Figure <A HREF="#fig:ex4">5</A> shows the setup of a one-level
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additive Schwarz preconditioner, i.e., RAS with overlap 2.
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Note also that a Krylov method different from CG must be used to solve
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the preconditioned system, since the preconditione in nonsymmetric.
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The corresponding example program is available in the file
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<code>mld_dexample_1lev.f90</code>.
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</BIG></BIG></BIG>
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<P>
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<BIG CLASS="LARGE"><BIG CLASS="LARGE"><BIG CLASS="LARGE">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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</BIG></BIG></BIG>
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<P>
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<BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
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<DIV ALIGN="CENTER"><A NAME="fig:ex2"></A><A NAME="909"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 3:</STRONG>
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setup of a multilevel 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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! build a V-cycle preconditioner with 1 block-Jacobi sweep (with
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! ILU(0) on the blocks) as pre- and post-smoother, and 8 block-Jacobi
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! sweeps (with ILU(0) on the blocks) as coarsest-level solver
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call P%init('ML',info)
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call_P%set('SMOOTHER_TYPE','BJAC',info)
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call P%set('COARSE_SOLVE','BJAC',info)
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call P%set('COARSE_SWEEPS',8,info)
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call P%hierarchy_build(A,desc_A,info)
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call P%smoothers_build(A,desc_A,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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<BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
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<P>
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<BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
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<DIV ALIGN="CENTER"><A NAME="fig:ex3"></A><A NAME="911"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 4:</STRONG>
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setup of a multilevel 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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! build a W-cycle preconditioner with 2 hybrid Gauss-Seidel sweeps
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! as pre- and post-smoother, a distributed coarsest
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! matrix, and MUMPS as coarsest-level solver
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call P%init('ML',info)
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call P%set('ML_CYCLE','WCYCLE',info)
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call P%set('SMOOTHER_TYPE','FBGS',info)
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call P%set('SMOOTHER_SWEEPS',2,info)
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call P%set('COARSE_SOLVE','MUMPS',info)
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call P%set('COARSE_MAT','DIST',info)
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call P%hierarchy_build(A,desc_A,info)
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call P%smoothers_build(A,desc_A,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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</DIV>
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<BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
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<P>
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<BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
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<DIV ALIGN="CENTER"><A NAME="fig:ex4"></A><A NAME="913"></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 P%init('AS',info)
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call P%set('SUB_OVR',2,info)
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call P%bld(A,desc_A,info)
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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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</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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<BIG CLASS="LARGE"><BIG CLASS="LARGE"></BIG></BIG>
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<P>
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