Date: 2022-03-31T04:48:19+00:00

Actual source code: ex7.c

      1: static char help[] = "Block Jacobi preconditioner for solving a linear system in parallel with KSP.\n\
      2: The code indicates the\n\
      3: procedures for setting the particular block sizes and for using different\n\
      4: linear solvers on the individual blocks.\n\n";

      6: /*
      7:    Note:  This example focuses on ways to customize the block Jacobi
      8:    preconditioner. See ex1.c and ex2.c for more detailed comments on
      9:    the basic usage of KSP (including working with matrices and vectors).

     11:    Recall: The block Jacobi method is equivalent to the ASM preconditioner
     12:    with zero overlap.
     13:  */

     15: /*T
     16:    Concepts: KSP^customizing the block Jacobi preconditioner
     17:    Processors: n
     18: T*/

     20: /*
     21:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
     22:   automatically includes:
     23:      petscsys.h       - base PETSc routines   petscvec.h - vectors
     24:      petscmat.h - matrices
     25:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     26:      petscviewer.h - viewers               petscpc.h  - preconditioners
     27: */
     28: #include <petscksp.h>

     30: int main(int argc,char **args)
     31: {
     32:   Vec            x,b,u;      /* approx solution, RHS, exact solution */
     33:   Mat            A;            /* linear system matrix */
     34:   KSP            ksp;         /* KSP context */
     35:   KSP            *subksp;     /* array of local KSP contexts on this processor */
     36:   PC             pc;           /* PC context */
     37:   PC             subpc;        /* PC context for subdomain */
     38:   PetscReal      norm;         /* norm of solution error */
     39:   PetscInt       i,j,Ii,J,*blks,m = 4,n;
     40:   PetscMPIInt    rank,size;
     41:   PetscInt       its,nlocal,first,Istart,Iend;
     42:   PetscScalar    v,one = 1.0,none = -1.0;
     43:   PetscBool      isbjacobi;

     45:   PetscInitialize(&argc,&args,(char*)0,help);
     46:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
     47:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
     48:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
     49:   n    = m+2;

     51:   /* -------------------------------------------------------------------
     52:          Compute the matrix and right-hand-side vector that define
     53:          the linear system, Ax = b.
     54:      ------------------------------------------------------------------- */

     56:   /*
     57:      Create and assemble parallel matrix
     58:   */
     59:   MatCreate(PETSC_COMM_WORLD,&A);
     60:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
     61:   MatSetFromOptions(A);
     62:   MatMPIAIJSetPreallocation(A,5,NULL,5,NULL);
     63:   MatSeqAIJSetPreallocation(A,5,NULL);
     64:   MatGetOwnershipRange(A,&Istart,&Iend);
     65:   for (Ii=Istart; Ii<Iend; Ii++) {
     66:     v = -1.0; i = Ii/n; j = Ii - i*n;
     67:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
     68:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
     69:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
     70:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
     71:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);
     72:   }
     73:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     74:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
     75:   MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);

     77:   /*
     78:      Create parallel vectors
     79:   */
     80:   MatCreateVecs(A,&u,&b);
     81:   VecDuplicate(u,&x);

     83:   /*
     84:      Set exact solution; then compute right-hand-side vector.
     85:   */
     86:   VecSet(u,one);
     87:   MatMult(A,u,b);

     89:   /*
     90:      Create linear solver context
     91:   */
     92:   KSPCreate(PETSC_COMM_WORLD,&ksp);

     94:   /*
     95:      Set operators. Here the matrix that defines the linear system
     96:      also serves as the preconditioning matrix.
     97:   */
     98:   KSPSetOperators(ksp,A,A);

    100:   /*
    101:      Set default preconditioner for this program to be block Jacobi.
    102:      This choice can be overridden at runtime with the option
    103:         -pc_type <type>

    105:      IMPORTANT NOTE: Since the inners solves below are constructed to use
    106:      iterative methods (such as KSPGMRES) the outer Krylov method should
    107:      be set to use KSPFGMRES since it is the only Krylov method (plus KSPFCG)
    108:      that allows the preconditioners to be nonlinear (that is have iterative methods
    109:      inside them). The reason these examples work is because the number of
    110:      iterations on the inner solves is left at the default (which is 10,000)
    111:      and the tolerance on the inner solves is set to be a tight value of around 10^-6.
    112:   */
    113:   KSPGetPC(ksp,&pc);
    114:   PCSetType(pc,PCBJACOBI);

    116:   /* -------------------------------------------------------------------
    117:                    Define the problem decomposition
    118:      ------------------------------------------------------------------- */

    120:   /*
    121:      Call PCBJacobiSetTotalBlocks() to set individually the size of
    122:      each block in the preconditioner.  This could also be done with
    123:      the runtime option
    124:          -pc_bjacobi_blocks <blocks>
    125:      Also, see the command PCBJacobiSetLocalBlocks() to set the
    126:      local blocks.

    128:       Note: The default decomposition is 1 block per processor.
    129:   */
    130:   PetscMalloc1(m,&blks);
    131:   for (i=0; i<m; i++) blks[i] = n;
    132:   PCBJacobiSetTotalBlocks(pc,m,blks);
    133:   PetscFree(blks);

    135:   /*
    136:     Set runtime options
    137:   */
    138:   KSPSetFromOptions(ksp);

    140:   /* -------------------------------------------------------------------
    141:                Set the linear solvers for the subblocks
    142:      ------------------------------------------------------------------- */

    144:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    145:        Basic method, should be sufficient for the needs of most users.
    146:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    148:      By default, the block Jacobi method uses the same solver on each
    149:      block of the problem.  To set the same solver options on all blocks,
    150:      use the prefix -sub before the usual PC and KSP options, e.g.,
    151:           -sub_pc_type <pc> -sub_ksp_type <ksp> -sub_ksp_rtol 1.e-4
    152:   */

    154:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    155:         Advanced method, setting different solvers for various blocks.
    156:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    158:      Note that each block's KSP context is completely independent of
    159:      the others, and the full range of uniprocessor KSP options is
    160:      available for each block. The following section of code is intended
    161:      to be a simple illustration of setting different linear solvers for
    162:      the individual blocks.  These choices are obviously not recommended
    163:      for solving this particular problem.
    164:   */
    165:   PetscObjectTypeCompare((PetscObject)pc,PCBJACOBI,&isbjacobi);
    166:   if (isbjacobi) {
    167:     /*
    168:        Call KSPSetUp() to set the block Jacobi data structures (including
    169:        creation of an internal KSP context for each block).

    171:        Note: KSPSetUp() MUST be called before PCBJacobiGetSubKSP().
    172:     */
    173:     KSPSetUp(ksp);

    175:     /*
    176:        Extract the array of KSP contexts for the local blocks
    177:     */
    178:     PCBJacobiGetSubKSP(pc,&nlocal,&first,&subksp);

    180:     /*
    181:        Loop over the local blocks, setting various KSP options
    182:        for each block.
    183:     */
    184:     for (i=0; i<nlocal; i++) {
    185:       KSPGetPC(subksp[i],&subpc);
    186:       if (rank == 0) {
    187:         if (i%2) {
    188:           PCSetType(subpc,PCILU);
    189:         } else {
    190:           PCSetType(subpc,PCNONE);
    191:           KSPSetType(subksp[i],KSPBCGS);
    192:           KSPSetTolerances(subksp[i],1.e-6,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
    193:         }
    194:       } else {
    195:         PCSetType(subpc,PCJACOBI);
    196:         KSPSetType(subksp[i],KSPGMRES);
    197:         KSPSetTolerances(subksp[i],1.e-6,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
    198:       }
    199:     }
    200:   }

    202:   /* -------------------------------------------------------------------
    203:                       Solve the linear system
    204:      ------------------------------------------------------------------- */

    206:   /*
    207:      Solve the linear system
    208:   */
    209:   KSPSolve(ksp,b,x);

    211:   /* -------------------------------------------------------------------
    212:                       Check solution and clean up
    213:      ------------------------------------------------------------------- */

    215:   /*
    216:      Check the error
    217:   */
    218:   VecAXPY(x,none,u);
    219:   VecNorm(x,NORM_2,&norm);
    220:   KSPGetIterationNumber(ksp,&its);
    221:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);

    223:   /*
    224:      Free work space.  All PETSc objects should be destroyed when they
    225:      are no longer needed.
    226:   */
    227:   KSPDestroy(&ksp);
    228:   VecDestroy(&u));  PetscCall(VecDestroy(&x);
    229:   VecDestroy(&b));  PetscCall(MatDestroy(&A);
    230:   PetscFinalize();
    231:   return 0;
    232: }

    234: /*TEST

    236:    test:
    237:       suffix: 1
    238:       nsize: 2
    239:       args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    241:    test:
    242:       suffix: 2
    243:       nsize: 2
    244:       args: -ksp_view ::ascii_info_detail

    246:    test:
    247:       suffix: viennacl
    248:       requires: viennacl
    249:       args: -ksp_monitor_short -mat_type aijviennacl
    250:       output_file: output/ex7_mpiaijcusparse.out

    252:    test:
    253:       suffix: viennacl_2
    254:       nsize: 2
    255:       requires: viennacl
    256:       args: -ksp_monitor_short -mat_type aijviennacl
    257:       output_file: output/ex7_mpiaijcusparse_2.out

    259:    test:
    260:       suffix: mpiaijcusparse
    261:       requires: cuda
    262:       args: -ksp_monitor_short -mat_type aijcusparse

    264:    test:
    265:       suffix: mpiaijcusparse_2
    266:       nsize: 2
    267:       requires: cuda
    268:       args: -ksp_monitor_short -mat_type aijcusparse

    270:    test:
    271:       suffix: mpiaijcusparse_simple
    272:       requires: cuda
    273:       args: -ksp_monitor_short -mat_type aijcusparse -sub_pc_factor_mat_solver_type cusparse -sub_ksp_type preonly -sub_pc_type ilu

    275:    test:
    276:       suffix: mpiaijcusparse_simple_2
    277:       nsize: 2
    278:       requires: cuda
    279:       args: -ksp_monitor_short -mat_type aijcusparse -sub_pc_factor_mat_solver_type cusparse -sub_ksp_type preonly -sub_pc_type ilu

    281:    test:
    282:       suffix: mpiaijcusparse_3
    283:       requires: cuda
    284:       args: -ksp_monitor_short -mat_type aijcusparse -sub_pc_factor_mat_solver_type cusparse

    286:    test:
    287:       suffix: mpiaijcusparse_4
    288:       nsize: 2
    289:       requires: cuda
    290:       args: -ksp_monitor_short -mat_type aijcusparse -sub_pc_factor_mat_solver_type cusparse

    292:    testset:
    293:       args: -ksp_monitor_short -pc_type gamg -ksp_view -pc_gamg_esteig_ksp_type cg -pc_gamg_esteig_ksp_max_it 10
    294:       test:
    295:         suffix: gamg_cuda
    296:         nsize: {{1 2}separate output}
    297:         requires: cuda
    298:         args: -mat_type aijcusparse
    299:         # triggers cusparse MatTransposeMat operation when squaring the graph
    300:         args: -pc_gamg_sym_graph 0 -pc_gamg_threshold -1 -pc_gamg_square_graph 1
    301:       test:
    302:         suffix: gamg_kokkos
    303:         nsize: {{1 2}separate output}
    304:         requires: !sycl kokkos_kernels
    305:         args: -mat_type aijkokkos

    307: TEST*/