<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> <html > <head><title>Examples</title> <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> <meta name="generator" content="TeX4ht (http://www.tug.org/tex4ht/)"> <meta name="originator" content="TeX4ht (http://www.tug.org/tex4ht/)"> <!-- html,3 --> <meta name="src" content="userhtml.tex"> <link rel="stylesheet" type="text/css" href="userhtml.css"> </head><body > <!--l. 122--><div class="crosslinks"><p class="noindent"><span class="cmr-12">[</span><a href="#tailuserhtmlsu9.html"><span class="cmr-12">tail</span></a><span class="cmr-12">] [</span><a href="userhtmlse5.html#userhtmlsu9.html" ><span class="cmr-12">up</span></a><span class="cmr-12">] </span></p></div> <h4 class="subsectionHead"><span class="titlemark"><span class="cmr-12">5.1 </span></span> <a id="x18-170005.1"></a><span class="cmr-12">Examples</span></h4> <!--l. 124--><p class="noindent" ><span class="cmr-12">The code reported in Figure</span><span class="cmr-12"> </span><a href="#x18-170012"><span class="cmr-12">2</span><!--tex4ht:ref: fig:ex1 --></a> <span class="cmr-12">shows how to set and apply the default multilevel</span> <span class="cmr-12">preconditioner available in the real double precision version of MLD2P4 (see Table</span><span class="cmr-12"> </span><a href="userhtmlse5.html#x17-160151"><span class="cmr-12">1</span><!--tex4ht:ref: tab:precinit --></a><span class="cmr-12">).</span> <span class="cmr-12">This preconditioner is chosen by simply specifying </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">’ML’</span></span></span> <span class="cmr-12">as the second argument of</span> <span class="obeylines-h"><span class="verb"><span class="cmtt-12">P%init</span></span></span> <span class="cmr-12">(a call to </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">P%set</span></span></span> <span class="cmr-12">is not needed) and is applied with the CG solver provided by</span> <span class="cmr-12">PSBLAS (the matrix of the system to be solved is assumed to be positive definite). As</span> <span class="cmr-12">previously observed, the modules </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">psb_base_mod</span></span></span><span class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">mld_prec_mod</span></span></span> <span class="cmr-12">and </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">psb_krylov_mod</span></span></span> <span class="cmr-12">must be used by the example program.</span> <!--l. 134--><p class="indent" > <span class="cmr-12">The part of the code concerning the reading and assembling of the sparse matrix</span> <span class="cmr-12">and the right-hand side vector, performed through the PSBLAS routines for sparse</span> <span class="cmr-12">matrix and vector management, is not reported here for brevity; the statements</span> <span class="cmr-12">concerning the deallocation of the PSBLAS data structure are neglected too. The</span> <span class="cmr-12">complete code can be found in the example program file </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">mld_dexample_ml.f90</span></span></span><span class="cmr-12">,</span> <span class="cmr-12">in the directory </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">examples/fileread</span></span></span> <span class="cmr-12">of the MLD2P4 implementation (see</span> <span class="cmr-12">Section</span><span class="cmr-12"> </span><a href="userhtmlsu5.html#x12-110003.5"><span class="cmr-12">3.5</span><!--tex4ht:ref: sec:ex_and_test --></a><span class="cmr-12">). A sample test problem along with the relevant input data is available in</span> <span class="obeylines-h"><span class="verb"><span class="cmtt-12">examples/fileread/runs</span></span></span><span class="cmr-12">. For details on the use of the PSBLAS routines, see the</span> <span class="cmr-12">PSBLAS User’s Guide</span><span class="cmr-12"> </span><span class="cite"><span class="cmr-12">[</span><a href="userhtmlli4.html#XPSBLASGUIDE"><span class="cmr-12">13</span></a><span class="cmr-12">]</span></span><span class="cmr-12">.</span> <!--l. 146--><p class="indent" > <span class="cmr-12">The setup and application of the default multilevel preconditioner for the real single</span> <span class="cmr-12">precision and the complex, single and double precision, versions are obtained</span> <span class="cmr-12">with straightforward modifications of the previous example (see Section</span><span class="cmr-12"> </span><a href="userhtmlse6.html#x19-180006"><span class="cmr-12">6</span><!--tex4ht:ref: sec:userinterface --></a> <span class="cmr-12">for</span> <span class="cmr-12">details). If these versions are installed, the corresponding codes are available in</span> <span class="obeylines-h"><span class="verb"><span class="cmtt-12">examples/fileread/</span></span></span><span class="cmr-12">.</span> <!--l. 152--><p class="indent" > <hr class="figure"><div class="figure" > <a id="x18-170012"></a> <div class="center" > <!--l. 153--><p class="noindent" > <div class="minipage"><div class="verbatim" id="verbatim-6">   use psb_base_mod  <br />  use mld_prec_mod  <br />  use psb_krylov_mod  <br />... ...  <br />!  <br />! sparse matrix  <br />  type(psb_dspmat_type) :: A  <br />! sparse matrix descriptor  <br />  type(psb_desc_type)   :: desc_A  <br />! preconditioner  <br />  type(mld_dprec_type)  :: P  <br />! right-hand side and solution vectors  <br />  type(psb_d_vect_type) :: b, x  <br />... ...  <br />!  <br />! initialize the parallel environment  <br />  call psb_init(ictxt)  <br />  call psb_info(ictxt,iam,np)  <br />... ...  <br />!  <br />! read and assemble the spd matrix A and the right-hand side b  <br />! using PSBLAS routines for sparse matrix / vector management  <br />... ...  <br />!  <br />! initialize the default multilevel preconditioner, i.e. V-cycle  <br />! with basic smoothed aggregation, 1 hybrid forward/backward  <br />! GS sweep as pre/post-smoother and UMFPACK as coarsest-level  <br />! solver  <br />  call P%init(’ML’,info)  <br />!  <br />! build the preconditioner  <br />  call P%hierarchy_build(A,desc_A,info)  <br />  call P%smoothers_build(A,desc_A,info)  <br />  <br />!  <br />! set the solver parameters and the initial guess  <br />  ... ...  <br />!  <br />! solve Ax=b with preconditioned CG  <br />  call psb_krylov(’CG’,A,P,b,x,tol,desc_A,info)  <br />  ... ...  <br />!  <br />! deallocate the preconditioner  <br />  call P%free(info)  <br />!  <br />! deallocate other data structures  <br />  ... ...  <br />!  <br />! exit the parallel environment  <br />  call psb_exit(ictxt)  <br />  stop </div> <!--l. 208--><p class="nopar" > </div> <br /> <div class="caption" ><span class="id">Figure 2: </span><span class="content">setup and application of the default multilevel preconditioner (example 1). </span></div><!--tex4ht:label?: x18-170012 --> </div> <!--l. 214--><p class="indent" > </div><hr class="endfigure"> <!--l. 216--><p class="indent" > <span class="cmr-12">Different versions of the multilevel preconditioner can be obtained by changing the</span> <span class="cmr-12">default values of the preconditioner parameters. The code reported in Figure</span><span class="cmr-12"> </span><a href="#x18-170023"><span class="cmr-12">3</span><!--tex4ht:ref: fig:ex2 --></a> <span class="cmr-12">shows</span> <span class="cmr-12">how to set a V-cycle preconditioner which applies 1 block-Jacobi sweep as pre- and</span> <span class="cmr-12">post-smoother, and solves the coarsest-level system with 8 block-Jacobi sweeps. Note</span> <span class="cmr-12">that the ILU(0) factorization (plus triangular solve) is used as local solver for the</span> <span class="cmr-12">block-Jacobi sweeps, since this is the default associated with block-Jacobi and set</span> <span class="cmr-12">by</span><span class="cmr-12"> </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">P%init</span></span></span><span class="cmr-12">. Furthermore, specifying block-Jacobi as coarsest-level solver implies that</span> <span class="cmr-12">the coarsest-level matrix is distributed among the processes. Figure</span><span class="cmr-12"> </span><a href="#x18-170034"><span class="cmr-12">4</span><!--tex4ht:ref: fig:ex3 --></a> <span class="cmr-12">shows how to set</span> <span class="cmr-12">a W-cycle preconditioner which applies 2 hybrid Gauss-Seidel sweeps as pre- and</span> <span class="cmr-12">post-smoother, and solves the coarsest-level system with the multifrontal LU</span> <span class="cmr-12">factorization implemented in MUMPS. It is specified that the coarsest-level matrix is</span> <span class="cmr-12">distributed, since MUMPS can be used on both replicated and distributed matrices,</span> <span class="cmr-12">and by default it is used on replicated ones. The code fragments shown in</span> <span class="cmr-12">Figures</span><span class="cmr-12"> </span><a href="#x18-170023"><span class="cmr-12">3</span><!--tex4ht:ref: fig:ex2 --></a> <span class="cmr-12">and </span><a href="#x18-170034"><span class="cmr-12">4</span><!--tex4ht:ref: fig:ex3 --></a> <span class="cmr-12">are included in the example program file </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">mld_dexample_ml.f90</span></span></span> <span class="cmr-12">too.</span> <!--l. 240--><p class="indent" > <span class="cmr-12">Finally, Figure</span><span class="cmr-12"> </span><a href="#x18-170045"><span class="cmr-12">5</span><!--tex4ht:ref: fig:ex4 --></a> <span class="cmr-12">shows the setup of a one-level additive Schwarz preconditioner,</span> <span class="cmr-12">i.e., RAS with overlap 2. Note also that a Krylov method different from CG</span> <span class="cmr-12">must be used to solve the preconditioned system, since the preconditione in</span> <span class="cmr-12">nonsymmetric. The corresponding example program is available in the file</span> <span class="obeylines-h"><span class="verb"><span class="cmtt-12">mld_dexample_1lev.f90</span></span></span><span class="cmr-12">.</span> <!--l. 247--><p class="indent" > <span class="cmr-12">For all the previous preconditioners, example programs where the sparse matrix and</span> <span class="cmr-12">the right-hand side are generated by discretizing a PDE with Dirichlet boundary</span> <span class="cmr-12">conditions are also available in the directory </span><span class="obeylines-h"><span class="verb"><span class="cmtt-12">examples/pdegen</span></span></span><span class="cmr-12">.</span> <!--l. 261--><p class="indent" > <hr class="figure"><div class="figure" > <a id="x18-170023"></a> <div class="center" > <!--l. 262--><p class="noindent" > <div class="minipage"><div class="verbatim" id="verbatim-7"> ... ...  <br />! build a V-cycle preconditioner with 1 block-Jacobi sweep (with  <br />! ILU(0) on the blocks) as pre- and post-smoother, and 8  block-Jacobi  <br />! sweeps (with ILU(0) on the blocks) as coarsest-level solver  <br />  call P%init(’ML’,info)  <br />  call_P%set(’SMOOTHER_TYPE’,’BJAC’,info)  <br />  call P%set(’COARSE_SOLVE’,’BJAC’,info)  <br />  call P%set(’COARSE_SWEEPS’,8,info)  <br />  call P%hierarchy_build(A,desc_A,info)  <br />  call P%smoothers_build(A,desc_A,info)  <br />... ... </div> <!--l. 277--><p class="nopar" ></div> <br /> <div class="caption" ><span class="id">Figure 3: </span><span class="content">setup of a multilevel preconditioner</span></div><!--tex4ht:label?: x18-170023 --> </div> <!--l. 283--><p class="indent" > </div><hr class="endfigure"> <!--l. 285--><p class="indent" > <hr class="figure"><div class="figure" > <a id="x18-170034"></a> <div class="center" > <!--l. 286--><p class="noindent" > <div class="minipage"><div class="verbatim" id="verbatim-8"> ... ...  <br />! build a W-cycle preconditioner with 2 hybrid Gauss-Seidel sweeps  <br />! as pre- and post-smoother, a distributed coarsest  <br />! matrix, and MUMPS as coarsest-level solver  <br />  call P%init(’ML’,info)  <br />  call P%set(’ML_CYCLE’,’WCYCLE’,info)  <br />  call P%set(’SMOOTHER_TYPE’,’FBGS’,info)  <br />  call P%set(’SMOOTHER_SWEEPS’,2,info)  <br />  call P%set(’COARSE_SOLVE’,’MUMPS’,info)  <br />  call P%set(’COARSE_MAT’,’DIST’,info)  <br />  call P%hierarchy_build(A,desc_A,info)  <br />  call P%smoothers_build(A,desc_A,info)  <br />... ... </div> <!--l. 303--><p class="nopar" ></div> <br /> <div class="caption" ><span class="id">Figure 4: </span><span class="content">setup of a multilevel preconditioner</span></div><!--tex4ht:label?: x18-170034 --> </div> <!--l. 308--><p class="indent" > </div><hr class="endfigure"> <!--l. 310--><p class="indent" > <hr class="figure"><div class="figure" > <a id="x18-170045"></a> <div class="center" > <!--l. 311--><p class="noindent" > <div class="minipage"><div class="verbatim" id="verbatim-9"> ... ...  <br />! set RAS with overlap 2 and ILU(0) on the local blocks  <br />  call P%init(’AS’,info)  <br />  call P%set(’SUB_OVR’,2,info)  <br />  call P%bld(A,desc_A,info)  <br />... ...  <br />! solve Ax=b with preconditioned BiCGSTAB  <br />  call psb_krylov(’BICGSTAB’,A,P,b,x,tol,desc_A,info) </div> <!--l. 323--><p class="nopar" ></div> <br /> <div class="caption" ><span class="id">Figure 5: </span><span class="content">setup of a one-level Schwarz preconditioner.</span></div><!--tex4ht:label?: x18-170045 --> </div> <!--l. 328--><p class="indent" > </div><hr class="endfigure"> <!--l. 1--><div class="crosslinks"><p class="noindent"><span class="cmr-12">[</span><a href="userhtmlsu9.html" ><span class="cmr-12">front</span></a><span class="cmr-12">] [</span><a href="userhtmlse5.html#userhtmlsu9.html" ><span class="cmr-12">up</span></a><span class="cmr-12">] </span></p></div> <!--l. 1--><p class="indent" > <a id="tailuserhtmlsu9.html"></a> </body></html>