Date: 2022-03-04T17:39:12+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 */
     40:   PetscInt       i,j,Ii,J,*blks,m = 4,n;
     41:   PetscMPIInt    rank,size;
     42:   PetscInt       its,nlocal,first,Istart,Iend;
     43:   PetscScalar    v,one = 1.0,none = -1.0;
     44:   PetscBool      isbjacobi;

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

     52:   /* -------------------------------------------------------------------
     53:          Compute the matrix and right-hand-side vector that define
     54:          the linear system, Ax = b.
     55:      ------------------------------------------------------------------- */

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

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

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

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

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

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

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

    117:   /* -------------------------------------------------------------------
    118:                    Define the problem decomposition
    119:      ------------------------------------------------------------------- */

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

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

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

    141:   /* -------------------------------------------------------------------
    142:                Set the linear solvers for the subblocks
    143:      ------------------------------------------------------------------- */

    145:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    146:        Basic method, should be sufficient for the needs of most users.
    147:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    149:      By default, the block Jacobi method uses the same solver on each
    150:      block of the problem.  To set the same solver options on all blocks,
    151:      use the prefix -sub before the usual PC and KSP options, e.g.,
    152:           -sub_pc_type <pc> -sub_ksp_type <ksp> -sub_ksp_rtol 1.e-4
    153:   */

    155:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    156:         Advanced method, setting different solvers for various blocks.
    157:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

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

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

    181:     /*
    182:        Loop over the local blocks, setting various KSP options
    183:        for each block.
    184:     */
    185:     for (i=0; i<nlocal; i++) {
    186:       KSPGetPC(subksp[i],&subpc);
    187:       if (rank == 0) {
    188:         if (i%2) {
    189:           PCSetType(subpc,PCILU);
    190:         } else {
    191:           PCSetType(subpc,PCNONE);
    192:           KSPSetType(subksp[i],KSPBCGS);
    193:           KSPSetTolerances(subksp[i],1.e-6,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
    194:         }
    195:       } else {
    196:         PCSetType(subpc,PCJACOBI);
    197:         KSPSetType(subksp[i],KSPGMRES);
    198:         KSPSetTolerances(subksp[i],1.e-6,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
    199:       }
    200:     }
    201:   }

    203:   /* -------------------------------------------------------------------
    204:                       Solve the linear system
    205:      ------------------------------------------------------------------- */

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

    212:   /* -------------------------------------------------------------------
    213:                       Check solution and clean up
    214:      ------------------------------------------------------------------- */

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

    224:   /*
    225:      Free work space.  All PETSc objects should be destroyed when they
    226:      are no longer needed.
    227:   */
    228:   KSPDestroy(&ksp);
    229:   VecDestroy(&u);  VecDestroy(&x);
    230:   VecDestroy(&b);  MatDestroy(&A);
    231:   PetscFinalize();
    232:   return ierr;
    233: }

    235: /*TEST

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

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

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

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

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

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

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

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

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

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

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

    308: TEST*/