Date: 2022-08-02T03:14:46+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: /*
     16:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
     17:   automatically includes:
     18:      petscsys.h       - base PETSc routines   petscvec.h - vectors
     19:      petscmat.h - matrices
     20:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     21:      petscviewer.h - viewers               petscpc.h  - preconditioners
     22: */
     23: #include <petscksp.h>

     25: int main(int argc,char **args)
     26: {
     27:   Vec            x,b,u;      /* approx solution, RHS, exact solution */
     28:   Mat            A;            /* linear system matrix */
     29:   KSP            ksp;         /* KSP context */
     30:   KSP            *subksp;     /* array of local KSP contexts on this processor */
     31:   PC             pc;           /* PC context */
     32:   PC             subpc;        /* PC context for subdomain */
     33:   PetscReal      norm;         /* norm of solution error */
     34:   PetscInt       i,j,Ii,J,*blks,m = 4,n;
     35:   PetscMPIInt    rank,size;
     36:   PetscInt       its,nlocal,first,Istart,Iend;
     37:   PetscScalar    v,one = 1.0,none = -1.0;
     38:   PetscBool      isbjacobi;

     40:   PetscInitialize(&argc,&args,(char*)0,help);
     41:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
     42:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
     43:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
     44:   n    = m+2;

     46:   /* -------------------------------------------------------------------
     47:          Compute the matrix and right-hand-side vector that define
     48:          the linear system, Ax = b.
     49:      ------------------------------------------------------------------- */

     51:   /*
     52:      Create and assemble parallel matrix
     53:   */
     54:   MatCreate(PETSC_COMM_WORLD,&A);
     55:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
     56:   MatSetFromOptions(A);
     57:   MatMPIAIJSetPreallocation(A,5,NULL,5,NULL);
     58:   MatSeqAIJSetPreallocation(A,5,NULL);
     59:   MatGetOwnershipRange(A,&Istart,&Iend);
     60:   for (Ii=Istart; Ii<Iend; Ii++) {
     61:     v = -1.0; i = Ii/n; j = Ii - i*n;
     62:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
     63:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
     64:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
     65:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
     66:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);
     67:   }
     68:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     69:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
     70:   MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);

     72:   /*
     73:      Create parallel vectors
     74:   */
     75:   MatCreateVecs(A,&u,&b);
     76:   VecDuplicate(u,&x);

     78:   /*
     79:      Set exact solution; then compute right-hand-side vector.
     80:   */
     81:   VecSet(u,one);
     82:   MatMult(A,u,b);

     84:   /*
     85:      Create linear solver context
     86:   */
     87:   KSPCreate(PETSC_COMM_WORLD,&ksp);

     89:   /*
     90:      Set operators. Here the matrix that defines the linear system
     91:      also serves as the preconditioning matrix.
     92:   */
     93:   KSPSetOperators(ksp,A,A);

     95:   /*
     96:      Set default preconditioner for this program to be block Jacobi.
     97:      This choice can be overridden at runtime with the option
     98:         -pc_type <type>

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

    111:   /* -------------------------------------------------------------------
    112:                    Define the problem decomposition
    113:      ------------------------------------------------------------------- */

    115:   /*
    116:      Call PCBJacobiSetTotalBlocks() to set individually the size of
    117:      each block in the preconditioner.  This could also be done with
    118:      the runtime option
    119:          -pc_bjacobi_blocks <blocks>
    120:      Also, see the command PCBJacobiSetLocalBlocks() to set the
    121:      local blocks.

    123:       Note: The default decomposition is 1 block per processor.
    124:   */
    125:   PetscMalloc1(m,&blks);
    126:   for (i=0; i<m; i++) blks[i] = n;
    127:   PCBJacobiSetTotalBlocks(pc,m,blks);
    128:   PetscFree(blks);

    130:   /*
    131:     Set runtime options
    132:   */
    133:   KSPSetFromOptions(ksp);

    135:   /* -------------------------------------------------------------------
    136:                Set the linear solvers for the subblocks
    137:      ------------------------------------------------------------------- */

    139:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    140:        Basic method, should be sufficient for the needs of most users.
    141:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    143:      By default, the block Jacobi method uses the same solver on each
    144:      block of the problem.  To set the same solver options on all blocks,
    145:      use the prefix -sub before the usual PC and KSP options, e.g.,
    146:           -sub_pc_type <pc> -sub_ksp_type <ksp> -sub_ksp_rtol 1.e-4
    147:   */

    149:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    150:         Advanced method, setting different solvers for various blocks.
    151:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

    166:        Note: KSPSetUp() MUST be called before PCBJacobiGetSubKSP().
    167:     */
    168:     KSPSetUp(ksp);

    170:     /*
    171:        Extract the array of KSP contexts for the local blocks
    172:     */
    173:     PCBJacobiGetSubKSP(pc,&nlocal,&first,&subksp);

    175:     /*
    176:        Loop over the local blocks, setting various KSP options
    177:        for each block.
    178:     */
    179:     for (i=0; i<nlocal; i++) {
    180:       KSPGetPC(subksp[i],&subpc);
    181:       if (rank == 0) {
    182:         if (i%2) {
    183:           PCSetType(subpc,PCILU);
    184:         } else {
    185:           PCSetType(subpc,PCNONE);
    186:           KSPSetType(subksp[i],KSPBCGS);
    187:           KSPSetTolerances(subksp[i],1.e-6,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
    188:         }
    189:       } else {
    190:         PCSetType(subpc,PCJACOBI);
    191:         KSPSetType(subksp[i],KSPGMRES);
    192:         KSPSetTolerances(subksp[i],1.e-6,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
    193:       }
    194:     }
    195:   }

    197:   /* -------------------------------------------------------------------
    198:                       Solve the linear system
    199:      ------------------------------------------------------------------- */

    201:   /*
    202:      Solve the linear system
    203:   */
    204:   KSPSolve(ksp,b,x);

    206:   /* -------------------------------------------------------------------
    207:                       Check solution and clean up
    208:      ------------------------------------------------------------------- */

    210:   /*
    211:      Check the error
    212:   */
    213:   VecAXPY(x,none,u);
    214:   VecNorm(x,NORM_2,&norm);
    215:   KSPGetIterationNumber(ksp,&its);
    216:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);

    218:   /*
    219:      Free work space.  All PETSc objects should be destroyed when they
    220:      are no longer needed.
    221:   */
    222:   KSPDestroy(&ksp);
    223:   VecDestroy(&u));  PetscCall(VecDestroy(&x);
    224:   VecDestroy(&b));  PetscCall(MatDestroy(&A);
    225:   PetscFinalize();
    226:   return 0;
    227: }

    229: /*TEST

    231:    test:
    232:       suffix: 1
    233:       nsize: 2
    234:       args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    236:    test:
    237:       suffix: 2
    238:       nsize: 2
    239:       args: -ksp_view ::ascii_info_detail

    241:    test:
    242:       suffix: viennacl
    243:       requires: viennacl
    244:       args: -ksp_monitor_short -mat_type aijviennacl
    245:       output_file: output/ex7_mpiaijcusparse.out

    247:    test:
    248:       suffix: viennacl_2
    249:       nsize: 2
    250:       requires: viennacl
    251:       args: -ksp_monitor_short -mat_type aijviennacl
    252:       output_file: output/ex7_mpiaijcusparse_2.out

    254:    test:
    255:       suffix: mpiaijcusparse
    256:       requires: cuda
    257:       args: -ksp_monitor_short -mat_type aijcusparse

    259:    test:
    260:       suffix: mpiaijcusparse_2
    261:       nsize: 2
    262:       requires: cuda
    263:       args: -ksp_monitor_short -mat_type aijcusparse

    265:    test:
    266:       suffix: mpiaijcusparse_simple
    267:       requires: cuda
    268:       args: -ksp_monitor_short -mat_type aijcusparse -sub_pc_factor_mat_solver_type cusparse -sub_ksp_type preonly -sub_pc_type ilu

    270:    test:
    271:       suffix: mpiaijcusparse_simple_2
    272:       nsize: 2
    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_3
    278:       requires: cuda
    279:       args: -ksp_monitor_short -mat_type aijcusparse -sub_pc_factor_mat_solver_type cusparse

    281:    test:
    282:       suffix: mpiaijcusparse_4
    283:       nsize: 2
    284:       requires: cuda
    285:       args: -ksp_monitor_short -mat_type aijcusparse -sub_pc_factor_mat_solver_type cusparse

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

    302: TEST*/