Actual source code: ex7.c
petsc-3.13.6 2020-09-29
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      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*/

     22: /*
     23:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
     24:   automatically includes:
     25:      petscsys.h       - base PETSc routines   petscvec.h - vectors
     26:      petscmat.h - matrices
     27:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     28:      petscviewer.h - viewers               petscpc.h  - preconditioners
     29: */
     30:  #include <petscksp.h>

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

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

     54:   /* -------------------------------------------------------------------
     55:          Compute the matrix and right-hand-side vector that define
     56:          the linear system, Ax = b.
     57:      ------------------------------------------------------------------- */

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

     79:   /*
     80:      Create parallel vectors
     81:   */
     82:   VecCreate(PETSC_COMM_WORLD,&u);
     83:   VecSetSizes(u,PETSC_DECIDE,m*n);
     84:   VecSetFromOptions(u);
     85:   VecDuplicate(u,&b);
     86:   VecDuplicate(b,&x);

     88:   /*
     89:      Set exact solution; then compute right-hand-side vector.
     90:   */
     91:   VecSet(u,one);
     92:   MatMult(A,u,b);

     94:   /*
     95:      Create linear solver context
     96:   */
     97:   KSPCreate(PETSC_COMM_WORLD,&ksp);

     99:   /*
    100:      Set operators. Here the matrix that defines the linear system
    101:      also serves as the preconditioning matrix.
    102:   */
    103:   KSPSetOperators(ksp,A,A);

    105:   /*
    106:      Set default preconditioner for this program to be block Jacobi.
    107:      This choice can be overridden at runtime with the option
    108:         -pc_type <type>
    109:
    110:      IMPORTANT NOTE: Since the inners solves below are constructed to use
    111:      iterative methods (such as KSPGMRES) the outer Krylov method should
    112:      be set to use KSPFGMRES since it is the only Krylov method (plus KSPFCG)
    113:      that allows the preconditioners to be nonlinear (that is have iterative methods
    114:      inside them). The reason these examples work is because the number of
    115:      iterations on the inner solves is left at the default (which is 10,000)
    116:      and the tolerance on the inner solves is set to be a tight value of around 10^-6.
    117:   */
    118:   KSPGetPC(ksp,&pc);
    119:   PCSetType(pc,PCBJACOBI);

    122:   /* -------------------------------------------------------------------
    123:                    Define the problem decomposition
    124:      ------------------------------------------------------------------- */

    126:   /*
    127:      Call PCBJacobiSetTotalBlocks() to set individually the size of
    128:      each block in the preconditioner.  This could also be done with
    129:      the runtime option
    130:          -pc_bjacobi_blocks <blocks>
    131:      Also, see the command PCBJacobiSetLocalBlocks() to set the
    132:      local blocks.

    134:       Note: The default decomposition is 1 block per processor.
    135:   */
    136:   PetscMalloc1(m,&blks);
    137:   for (i=0; i<m; i++) blks[i] = n;
    138:   PCBJacobiSetTotalBlocks(pc,m,blks);
    139:   PetscFree(blks);

    142:   /* -------------------------------------------------------------------
    143:                Set the linear solvers for the subblocks
    144:      ------------------------------------------------------------------- */

    146:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    147:        Basic method, should be sufficient for the needs of most users.
    148:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    150:      By default, the block Jacobi method uses the same solver on each
    151:      block of the problem.  To set the same solver options on all blocks,
    152:      use the prefix -sub before the usual PC and KSP options, e.g.,
    153:           -sub_pc_type <pc> -sub_ksp_type <ksp> -sub_ksp_rtol 1.e-4
    154:   */

    156:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    157:         Advanced method, setting different solvers for various blocks.
    158:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

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

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

    182:     /*
    183:        Loop over the local blocks, setting various KSP options
    184:        for each block.
    185:     */
    186:     for (i=0; i<nlocal; i++) {
    187:       KSPGetPC(subksp[i],&subpc);
    188:       if (!rank) {
    189:         if (i%2) {
    190:           PCSetType(subpc,PCILU);
    191:         } else {
    192:           PCSetType(subpc,PCNONE);
    193:           KSPSetType(subksp[i],KSPBCGS);
    194:           KSPSetTolerances(subksp[i],1.e-6,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
    195:         }
    196:       } else {
    197:         PCSetType(subpc,PCJACOBI);
    198:         KSPSetType(subksp[i],KSPGMRES);
    199:         KSPSetTolerances(subksp[i],1.e-6,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
    200:       }
    201:     }
    202:   }

    204:   /* -------------------------------------------------------------------
    205:                       Solve the linear system
    206:      ------------------------------------------------------------------- */

    208:   /*
    209:     Set runtime options
    210:   */
    211:   KSPSetFromOptions(ksp);

    213:   /*
    214:      Solve the linear system
    215:   */
    216:   KSPSolve(ksp,b,x);

    218:   /* -------------------------------------------------------------------
    219:                       Check solution and clean up
    220:      ------------------------------------------------------------------- */

    222:   /*
    223:      Check the error
    224:   */
    225:   VecAXPY(x,none,u);
    226:   VecNorm(x,NORM_2,&norm);
    227:   KSPGetIterationNumber(ksp,&its);
    228:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);

    230:   /*
    231:      Free work space.  All PETSc objects should be destroyed when they
    232:      are no longer needed.
    233:   */
    234:   KSPDestroy(&ksp);
    235:   VecDestroy(&u);  VecDestroy(&x);
    236:   VecDestroy(&b);  MatDestroy(&A);
    237:   PetscFinalize();
    238:   return ierr;
    239: }

    242: /*TEST

    244:    test:
    245:       nsize: 2
    246:       args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always> ex7_1.tmp 2>&1

    248:    test:
    249:       suffix: 2
    250:       nsize: 2
    251:       args: -ksp_view

    253:    test:
    254:       suffix: viennacl
    255:       requires: viennacl
    256:       args: -ksp_monitor_short -mat_type aijviennacl -vec_type viennacl
    257:       output_file: output/ex7_mpiaijcusparse.out

    259:    test:
    260:       suffix: viennacl_2
    261:       nsize: 2
    262:       requires: viennacl
    263:       args: -ksp_monitor_short -mat_type aijviennacl -vec_type viennacl
    264:       output_file: output/ex7_mpiaijcusparse_2.out

    266:    test:
    267:       suffix: mpiaijcusparse
    268:       requires: cuda
    269:       args: -ksp_monitor_short -mat_type aijcusparse -vec_type cuda

    271:    test:
    272:       suffix: mpiaijcusparse_2
    273:       nsize: 2
    274:       requires: cuda
    275:       args: -ksp_monitor_short -mat_type aijcusparse -vec_type cuda

    277:    test:
    278:       suffix: mpiaijcusparse_simple
    279:       requires: cuda
    280:       args: -ksp_monitor_short -mat_type aijcusparse -sub_pc_factor_mat_solver_type cusparse -vec_type cuda -sub_ksp_type preonly -sub_pc_type ilu

    282:    test:
    283:       suffix: mpiaijcusparse_simple_2
    284:       nsize: 2
    285:       requires: cuda
    286:       args: -ksp_monitor_short -mat_type aijcusparse -sub_pc_factor_mat_solver_type cusparse -vec_type cuda -sub_ksp_type preonly -sub_pc_type ilu

    288:    test:
    289:       suffix: mpiaijcusparse_3
    290:       requires: cuda
    291:       args: -ksp_monitor_short -mat_type aijcusparse -sub_pc_factor_mat_solver_type cusparse -vec_type cuda

    293:    test:
    294:       suffix: mpiaijcusparse_4
    295:       nsize: 2
    296:       requires: cuda
    297:       args: -ksp_monitor_short -mat_type aijcusparse -sub_pc_factor_mat_solver_type cusparse -vec_type cuda

    299: TEST*/