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< h4 class = "subsectionHead" > < span class = "titlemark" > < span
class="cmr-12">4.1 < / span > < / span > < a
id="x15-140004.1">< / a > < span
class="cmr-12">Examples< / span > < / h4 >
<!-- l. 116 --> < p class = "noindent" > < span
class="cmr-12">The code reported in Figure< / span > < span
class="cmr-12">  < / span > < a
href="#x15-14001r1">< span
class="cmr-12">1< / 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 AMG4PSBLAS< / span >
< span
class="cmr-12">(see Table< / span > < span
class="cmr-12">  < / span > < a
href="userhtmlse4.html#x14-13015r1">< span
class="cmr-12">1< / span > <!-- tex4ht:ref: tab:precinit --> < / a > < span
class="cmr-12">). This preconditioner is chosen by simply specifying < / span > < code class = "lstinline" > < span style = "color:#000000" > ’ < / span > < span style = "color:#000000" > ML< / span > < span style = "color:#000000" > ’ < / span > < / code > < span
class="cmr-12">as the< / span >
< span
class="cmr-12">second argument of < / span > < code class = "lstinline" > < span style = "color:#000000" > P< / span > < span style = "color:#000000" > %< / span > < span style = "color:#000000" > init< / span > < / code > < span
class="cmr-12">(a call to < / span > < code class = "lstinline" > < span style = "color:#000000" > P< / span > < span style = "color:#000000" > %< / span > < span style = "color:#000000" > set< / span > < / code > < span
class="cmr-12">is not needed) and is applied< / span >
< span
class="cmr-12">with the CG solver provided by PSBLAS (the matrix of the system to be< / span >
< span
class="cmr-12">solved is assumed to be positive definite). As previously observed, the modules< / span >
< code class = "lstinline" > < span style = "color:#000000" > psb_base_mod< / span > < / code > < span
class="cmr-12">, < / span > < code class = "lstinline" > < span style = "color:#000000" > amg_prec_mod< / span > < / code > < span
class="cmr-12">and < / span > < code class = "lstinline" > < span style = "color:#000000" > psb_krylov_mod< / span > < / code > < span
class="cmr-12">must be used by the example< / span >
< span
class="cmr-12">program.< / span >
<!-- l. 126 --> < p class = "indent" > < span
class="cmr-12">The part of the code dealing with reading and assembling the sparse matrix and the< / span >
< span
class="cmr-12">right-hand side vector and the deallocation of the relevant data structures, performed< / span >
< span
class="cmr-12">through the PSBLAS routines for sparse matrix and vector management,< / span >
< span
class="cmr-12">is not reported here for the sake of conciseness. The complete code can be< / span >
< span
class="cmr-12">found in the example program file < / span > < span class = "obeylines-h" > < code class = "verb" > amg_dexample_ml.f90< / code > < / span > < span
class="cmr-12">, in the directory< / span >
< span class = "obeylines-h" > < code class = "verb" > samples/simple/file< / code > < / span > < span class = "obeylines-h" > < code class = "verb" > read< / code > < / span > < span
class="cmr-12">of the AMG4PSBLAS implementation (see Section< / span > < span
class="cmr-12">  < / span > < a
href="userhtmlsu5.html#x13-120003.5">< span
class="cmr-12">3.5< / span > <!-- tex4ht:ref: sec:ex_and_test --> < / a > < span
class="cmr-12">). A< / span >
< span
class="cmr-12">sample test problem along with the relevant input data is available in< / span >
< span class = "obeylines-h" > < code class = "verb" > samples/simple/fileread/runs< / code > < / span > < span
class="cmr-12">. For details on the use of the PSBLAS routines, see< / span >
< span
class="cmr-12">the PSBLAS User’ s Guide< / span > < span
class="cmr-12">  < / span > < span class = "cite" > < span
class="cmr-12">[< / span > < a
href="userhtmlli5.html#XPSBLASGUIDE">< span
class="cmr-12">21< / span > < / a > < span
class="cmr-12">]< / span > < / span > < span
class="cmr-12">.< / span >
<!-- l. 138 --> < 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="userhtmlse5.html#x17-160005">< span
class="cmr-12">5< / 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" > < code class = "verb" > samples/simple/file< / code > < / span > < span class = "obeylines-h" > < code class = "verb" > read< / code > < / span > < span
class="cmr-12">.< / span >
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< div class = "minipage" > < pre class = "verbatim" id = "verbatim-7" >
    use  psb_base_mod
    use  amg_prec_mod
    use  psb_krylov_mod
...  ...
!
!  sparse  matrix
    type(psb_dspmat_type)  ::  A
!  sparse  matrix  descriptor
    type(psb_desc_type)      ::  desc_A
!  preconditioner
    type(amg_dprec_type)    ::  P
!  right-hand  side  and  solution  vectors
    type(psb_d_vect_type)  ::  b,  x
...  ...
!
!  initialize  the  parallel  environment
    call  psb_init(ctxt)
    call  psb_info(ctxt,iam,np)
...  ...
!
!  read  and  assemble  the  spd  matrix  A  and  the  right-hand  side  b
!  using  PSBLAS  routines  for  sparse  matrix  /  vector  management
...  ...
!
!  initialize  the  default  multilevel  preconditioner,  i.e.  V-cycle
!  with  basic  smoothed  aggregation,  1  hybrid  forward/backward
!  GS  sweep  as  pre/post-smoother  and  UMFPACK  as  coarsest-level
!  solver
    call  P%init(ctxt,’ ML’ ,info)
!
!  build  the  preconditioner
    call  P%hierarchy_build(A,desc_A,info)
    call  P%smoothers_build(A,desc_A,info)
!
!  set  the  solver  parameters  and  the  initial  guess
    ...  ...
!
!  solve  Ax=b  with  preconditioned  FCG
    call  psb_krylov(’ FCG’ ,A,P,b,x,tol,desc_A,info)
    ...  ...
!
!  deallocate  the  preconditioner
    call  P%free(info)
!
!  deallocate  other  data  structures
    ...  ...
!
!  exit  the  parallel  environment
    call  psb_exit(ctxt)
    stop
< / pre >
<!-- l. 255 --> < p class = "nopar" > < / div >
< br / > < div class = "caption"
>< span class = "id" > Listing 1: < / span > < span
class="content">setup and application of the default multilevel preconditioner (example 1).
< / span > < / div > <!-- tex4ht:label?: x15 - 14001r1 -->
< / div >
< / div > < hr class = "endfloat" / >
<!-- l. 264 --> < 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="#x15-14002r2">< span
class="cmr-12">2< / 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-< / span >
< span
class="cmr-12">and post-smoother, and solves the coarsest-level system with 8 block-Jacobi< / span >
< span
class="cmr-12">sweeps. Note that the ILU(0) factorization (plus triangular solve) is used as< / span >
< span
class="cmr-12">local solver for the block-Jacobi sweeps, since this is the default associated< / span >
< span
class="cmr-12">with block-Jacobi and set by< / span > < span
class="cmr-12">  < / span > < code class = "lstinline" > < span style = "color:#000000" > P< / span > < span style = "color:#000000" > %< / span > < span style = "color:#000000" > init< / span > < / code > < span
class="cmr-12">. Furthermore, specifying block-Jacobi as< / span >
< span
class="cmr-12">coarsest-level solver implies that the coarsest-level matrix is distributed among< / span >
< span
class="cmr-12">the processes. Figure< / span > < span
class="cmr-12">  < / span > < a
href="#x15-14003r3">< span
class="cmr-12">3< / span > <!-- tex4ht:ref: fig:ex3 --> < / a > < span
class="cmr-12">shows how to set a W-cycle preconditioner using the< / span >
< span
class="cmr-12">Coarsening based on Compatible Weighted Matching, aggregates of size at< / span >
< span
class="cmr-12">most 8 and smoothed prolongators. It applies 2 hybrid Gauss-Seidel sweeps as< / span >
< span
class="cmr-12">pre- and post-smoother, and solves the coarsest-level system with the parallel< / span >
< span
class="cmr-12">flexible Conjugate Gradient method (KRM) coupled with the block-Jacobi< / span >
< span
class="cmr-12">preconditioner having ILU(0) on the blocks. Default parameters are used for stopping< / span >
< span
class="cmr-12">criterion of the coarsest solver. Note that, also in this case, specifying KRM as< / span >
< span
class="cmr-12">coarsest-level solver implies that the coarsest-level matrix is distributed among the< / span >
< span
class="cmr-12">processes.< / span >
<!-- l. 291 --> < p class = "indent" > < span
class="cmr-12">The code fragments shown in Figures< / span > < span
class="cmr-12">  < / span > < a
href="#x15-14002r2">< span
class="cmr-12">2< / span > <!-- tex4ht:ref: fig:ex2 --> < / a > < span
class="cmr-12">and < / span > < a
href="#x15-14003r3">< span
class="cmr-12">3< / span > <!-- tex4ht:ref: fig:ex3 --> < / a > < span
class="cmr-12">are included in the example program< / span >
< span
class="cmr-12">file < / span > < span class = "obeylines-h" > < code class = "verb" > amg_dexample_ml.f90< / code > < / span > < span
class="cmr-12">too.< / span >
<!-- l. 294 --> < p class = "indent" > < span
class="cmr-12">Finally, Figure< / span > < span
class="cmr-12">  < / span > < a
href="#x15-14004r4">< span
class="cmr-12">4< / 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" > < code class = "verb" > amg_dexample_1lev.f90< / code > < / span > < span
class="cmr-12">.< / span >
<!-- l. 301 --> < p class = "indent" > < span
class="cmr-12">For all the previous preconditioners, example programs where the sparse matrix< / span >
< span
class="cmr-12">and the right-hand side are generated by discretizing a PDE with Dirichlet< / span >
< span
class="cmr-12">boundary conditions are also available in the directory < / span > < span class = "obeylines-h" > < code class = "verb" > samples/simple/pdegen< / code > < / span > < span
class="cmr-12">.< / span >
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id="x15-14002r2">< / a > < hr class = "float" > < div class = "float"
>
< div class = "center"
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< div class = "minipage" > < pre class = "verbatim" id = "verbatim-8" >
...  ...
!  build  a  V-cycle  preconditioner  with  1  block-Jacobi  sweep  (with
!  ILU(0)  on  the  blocks)  as  pre-  and  post-smoother,  and  8    block-Jacobi
!  sweeps  (with  ILU(0)  on  the  blocks)  as  coarsest-level  solver
    call  P%init(ctxt,’ ML’ ,info)
    call  P%set(’ SMOOTHER_TYPE’ ,’ BJAC’ ,info)
    call  P%set(’ COARSE_SOLVE’ ,’ BJAC’ ,info)
    call  P%set(’ COARSE_SWEEPS’ ,8,info)
    call  P%hierarchy_build(A,desc_A,info)
    call  P%smoothers_build(A,desc_A,info)
...  ...
< / pre >
<!-- l. 333 --> < p class = "nopar" > < / div > < / div >
< br / > < div class = "caption"
>< span class = "id" > Listing 2: < / span > < span
class="content">setup of a multilevel preconditioner based on the default decoupled coarsening< / span > < / div > <!-- tex4ht:label?: x15 - 14002r2 -->
< / div > < hr class = "endfloat" / >
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id="x15-14003r3">< / a > < hr class = "float" > < div class = "float"
>
< div class = "center"
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...  ...
!  build  a  W-cycle  preconditioner  with  2  hybrid  Gauss-Seidel  sweeps
!  as  pre-  and  post-smoother,  a  distributed  coarsest
!  matrix,  and  MUMPS  as  coarsest-level  solver
    call  P%init(ctxt,’ ML’ ,info)
    call  P%set(’ PAR_AGGR_ALG’ ,’ COUPLED’ ,info)
    call  P%set(’ AGGR_TYPE’ ,’ MATCHBOXP’ ,info)
    call  P%set(’ AGGR_SIZE’ ,8,info)
    call  P%set(’ ML_CYCLE’ ,’ WCYCLE’ ,info)
    call  P%set(’ SMOOTHER_TYPE’ ,’ FBGS’ ,info)
    call  P%set(’ SMOOTHER_SWEEPS’ ,2,info)
    call  P%set(’ COARSE_SOLVE’ ,’ KRM’ ,info)
    call  P%set(’ COARSE_MAT’ ,’ DIST’ ,info)
    call  P%set(’ KRM_METHOD’ ,’ FCG’ ,info)
    call  P%hierarchy_build(A,desc_A,info)
    call  P%smoothers_build(A,desc_A,info)
...  ...
< / pre >
<!-- l. 383 --> < p class = "nopar" > < / div > < / div >
< br / > < div class = "caption"
>< span class = "id" > Listing 3: < / span > < span
class="content">setup of a multilevel preconditioner based on the coupled coarsening using
weighted matching< / span > < / div > <!-- tex4ht:label?: x15 - 14003r3 -->
< / div > < hr class = "endfloat" / >
<!-- l. 390 --> < p class = "indent" > < a
id="x15-14004r4">< / a > < hr class = "float" > < div class = "float"
>
< div class = "center"
>
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< div class = "minipage" > < pre class = "verbatim" id = "verbatim-10" >
...  ...
!  set  RAS  with  overlap  2  and  ILU(0)  on  the  local  blocks
    call  P%init(ctxt,’ AS’ ,info)
    call  P%set(’ SUB_OVR’ ,2,info)
    call  P%bld(A,desc_A,info)
...  ...
!  solve  Ax=b  with  preconditioned  BiCGSTAB
    call  psb_krylov(’ BICGSTAB’ ,A,P,b,x,tol,desc_A,info)
< / pre >
<!-- l. 414 --> < p class = "nopar" > < / div > < / div >
< br / > < div class = "caption"
>< span class = "id" > Listing 4: < / span > < span
class="content">setup of a one-level Schwarz preconditioner.< / span > < / div > <!-- tex4ht:label?: x15 - 14004r4 -->
< / div > < hr class = "endfloat" / >
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