Actual source code: ex8.c

      2: static char help[] = "Illustrates use of the preconditioner ASM.\n\
      3: The Additive Schwarz Method for solving a linear system in parallel with KSP.  The\n\
      4: code indicates the procedure for setting user-defined subdomains.  Input\n\
      5: parameters include:\n\
      6:   -user_set_subdomain_solvers:  User explicitly sets subdomain solvers\n\
      7:   -user_set_subdomains:  Activate user-defined subdomains\n\n";

      9: /*
     10:    Note:  This example focuses on setting the subdomains for the ASM
     11:    preconditioner for a problem on a 2D rectangular grid.  See ex1.c
     12:    and ex2.c for more detailed comments on the basic usage of KSP
     13:    (including working with matrices and vectors).

     15:    The ASM preconditioner is fully parallel, but currently the routine
     16:    PCASMCreateSubdomains2D(), which is used in this example to demonstrate
     17:    user-defined subdomains (activated via -user_set_subdomains), is
     18:    uniprocessor only.

     20:    This matrix in this linear system arises from the discretized Laplacian,
     21:    and thus is not very interesting in terms of experimenting with variants
     22:    of the ASM preconditioner.
     23: */

     25: /*T
     26:    Concepts: KSP^Additive Schwarz Method (ASM) with user-defined subdomains
     27:    Processors: n
     28: T*/

     32: /*
     33:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
     34:   automatically includes:
     35:      petscsys.h       - base PETSc routines   petscvec.h - vectors
     36:      petscmat.h - matrices
     37:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     38:      petscviewer.h - viewers               petscpc.h  - preconditioners
     39: */
     40: #include <petscksp.h>

     42: int main(int argc,char **args)
     43: {
     44:   Vec            x,b,u;                 /* approx solution, RHS, exact solution */
     45:   Mat            A;                       /* linear system matrix */
     46:   KSP            ksp;                    /* linear solver context */
     47:   PC             pc;                      /* PC context */
     48:   IS             *is,*is_local;           /* array of index sets that define the subdomains */
     49:   PetscInt       overlap = 1;             /* width of subdomain overlap */
     50:   PetscInt       Nsub;                    /* number of subdomains */
     51:   PetscInt       m = 15,n = 17;          /* mesh dimensions in x- and y- directions */
     52:   PetscInt       M = 2,N = 1;            /* number of subdomains in x- and y- directions */
     53:   PetscInt       i,j,Ii,J,Istart,Iend;
     55:   PetscMPIInt    size;
     56:   PetscBool      flg;
     57:   PetscBool      user_subdomains = PETSC_FALSE;
     58:   PetscScalar    v, one = 1.0;
     59:   PetscReal      e;

     61:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
     62:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
     63:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
     64:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     65:   PetscOptionsGetInt(NULL,NULL,"-Mdomains",&M,NULL);
     66:   PetscOptionsGetInt(NULL,NULL,"-Ndomains",&N,NULL);
     67:   PetscOptionsGetInt(NULL,NULL,"-overlap",&overlap,NULL);
     68:   PetscOptionsGetBool(NULL,NULL,"-user_set_subdomains",&user_subdomains,NULL);

     70:   /* -------------------------------------------------------------------
     71:          Compute the matrix and right-hand-side vector that define
     72:          the linear system, Ax = b.
     73:      ------------------------------------------------------------------- */

     75:   /*
     76:      Assemble the matrix for the five point stencil, YET AGAIN
     77:   */
     78:   MatCreate(PETSC_COMM_WORLD,&A);
     79:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
     80:   MatSetFromOptions(A);
     81:   MatSetUp(A);
     82:   MatGetOwnershipRange(A,&Istart,&Iend);
     83:   for (Ii=Istart; Ii<Iend; Ii++) {
     84:     v = -1.0; i = Ii/n; j = Ii - i*n;
     85:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
     86:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
     87:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
     88:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
     89:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
     90:   }
     91:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     92:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

     94:   /*
     95:      Create and set vectors
     96:   */
     97:   VecCreate(PETSC_COMM_WORLD,&b);
     98:   VecSetSizes(b,PETSC_DECIDE,m*n);
     99:   VecSetFromOptions(b);
    100:   VecDuplicate(b,&u);
    101:   VecDuplicate(b,&x);
    102:   VecSet(u,one);
    103:   MatMult(A,u,b);

    105:   /*
    106:      Create linear solver context
    107:   */
    108:   KSPCreate(PETSC_COMM_WORLD,&ksp);

    110:   /*
    111:      Set operators. Here the matrix that defines the linear system
    112:      also serves as the preconditioning matrix.
    113:   */
    114:   KSPSetOperators(ksp,A,A);

    116:   /*
    117:      Set the default preconditioner for this program to be ASM
    118:   */
    119:   KSPGetPC(ksp,&pc);
    120:   PCSetType(pc,PCASM);

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

    126:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    127:        Basic method, should be sufficient for the needs of many users.
    128:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    130:      Set the overlap, using the default PETSc decomposition via
    131:          PCASMSetOverlap(pc,overlap);
    132:      Could instead use the option -pc_asm_overlap <ovl>

    134:      Set the total number of blocks via -pc_asm_blocks <blks>
    135:      Note:  The ASM default is to use 1 block per processor.  To
    136:      experiment on a single processor with various overlaps, you
    137:      must specify use of multiple blocks!
    138:   */

    140:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    141:        More advanced method, setting user-defined subdomains
    142:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    144:      Firstly, create index sets that define the subdomains.  The utility
    145:      routine PCASMCreateSubdomains2D() is a simple example (that currently
    146:      supports 1 processor only!).  More generally, the user should write
    147:      a custom routine for a particular problem geometry.

    149:      Then call either PCASMSetLocalSubdomains() or PCASMSetTotalSubdomains()
    150:      to set the subdomains for the ASM preconditioner.
    151:   */

    153:   if (!user_subdomains) { /* basic version */
    154:     PCASMSetOverlap(pc,overlap);
    155:   } else { /* advanced version */
    156:     if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"PCASMCreateSubdomains2D() is currently a uniprocessor routine only!");
    157:     PCASMCreateSubdomains2D(m,n,M,N,1,overlap,&Nsub,&is,&is_local);
    158:     PCASMSetLocalSubdomains(pc,Nsub,is,is_local);
    159:     flg  = PETSC_FALSE;
    160:     PetscOptionsGetBool(NULL,NULL,"-subdomain_view",&flg,NULL);
    161:     if (flg) {
    162:       PetscPrintf(PETSC_COMM_SELF,"Nmesh points: %D x %D; subdomain partition: %D x %D; overlap: %D; Nsub: %D\n",m,n,M,N,overlap,Nsub);
    163:       PetscPrintf(PETSC_COMM_SELF,"IS:\n");
    164:       for (i=0; i<Nsub; i++) {
    165:         PetscPrintf(PETSC_COMM_SELF,"  IS[%D]\n",i);
    166:         ISView(is[i],PETSC_VIEWER_STDOUT_SELF);
    167:       }
    168:       PetscPrintf(PETSC_COMM_SELF,"IS_local:\n");
    169:       for (i=0; i<Nsub; i++) {
    170:         PetscPrintf(PETSC_COMM_SELF,"  IS_local[%D]\n",i);
    171:         ISView(is_local[i],PETSC_VIEWER_STDOUT_SELF);
    172:       }
    173:     }
    174:   }

    176:   /* -------------------------------------------------------------------
    177:                 Set the linear solvers for the subblocks
    178:      ------------------------------------------------------------------- */

    180:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    181:        Basic method, should be sufficient for the needs of most users.
    182:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    184:      By default, the ASM preconditioner uses the same solver on each
    185:      block of the problem.  To set the same solver options on all blocks,
    186:      use the prefix -sub before the usual PC and KSP options, e.g.,
    187:           -sub_pc_type <pc> -sub_ksp_type <ksp> -sub_ksp_rtol 1.e-4

    189:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    190:         Advanced method, setting different solvers for various blocks.
    191:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    193:      Note that each block's KSP context is completely independent of
    194:      the others, and the full range of uniprocessor KSP options is
    195:      available for each block.

    197:      - Use PCASMGetSubKSP() to extract the array of KSP contexts for
    198:        the local blocks.
    199:      - See ex7.c for a simple example of setting different linear solvers
    200:        for the individual blocks for the block Jacobi method (which is
    201:        equivalent to the ASM method with zero overlap).
    202:   */

    204:   flg  = PETSC_FALSE;
    205:   PetscOptionsGetBool(NULL,NULL,"-user_set_subdomain_solvers",&flg,NULL);
    206:   if (flg) {
    207:     KSP       *subksp;        /* array of KSP contexts for local subblocks */
    208:     PetscInt  nlocal,first;   /* number of local subblocks, first local subblock */
    209:     PC        subpc;          /* PC context for subblock */
    210:     PetscBool isasm;

    212:     PetscPrintf(PETSC_COMM_WORLD,"User explicitly sets subdomain solvers.\n");

    214:     /*
    215:        Set runtime options
    216:     */
    217:     KSPSetFromOptions(ksp);

    219:     /*
    220:        Flag an error if PCTYPE is changed from the runtime options
    221:      */
    222:     PetscObjectTypeCompare((PetscObject)pc,PCASM,&isasm);
    223:     if (!isasm) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Cannot Change the PCTYPE when manually changing the subdomain solver settings");

    225:     /*
    226:        Call KSPSetUp() to set the block Jacobi data structures (including
    227:        creation of an internal KSP context for each block).

    229:        Note: KSPSetUp() MUST be called before PCASMGetSubKSP().
    230:     */
    231:     KSPSetUp(ksp);

    233:     /*
    234:        Extract the array of KSP contexts for the local blocks
    235:     */
    236:     PCASMGetSubKSP(pc,&nlocal,&first,&subksp);

    238:     /*
    239:        Loop over the local blocks, setting various KSP options
    240:        for each block.
    241:     */
    242:     for (i=0; i<nlocal; i++) {
    243:       KSPGetPC(subksp[i],&subpc);
    244:       PCSetType(subpc,PCILU);
    245:       KSPSetType(subksp[i],KSPGMRES);
    246:       KSPSetTolerances(subksp[i],1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
    247:     }
    248:   } else {
    249:     /*
    250:        Set runtime options
    251:     */
    252:     KSPSetFromOptions(ksp);
    253:   }

    255:   /* -------------------------------------------------------------------
    256:                       Solve the linear system
    257:      ------------------------------------------------------------------- */

    259:   KSPSolve(ksp,b,x);

    261:   /* -------------------------------------------------------------------
    262:                       Compare result to the exact solution
    263:      ------------------------------------------------------------------- */
    264:   VecAXPY(x,-1.0,u);
    265:   VecNorm(x,NORM_INFINITY, &e);

    267:   flg  = PETSC_FALSE;
    268:   PetscOptionsGetBool(NULL,NULL,"-print_error",&flg,NULL);
    269:   if (flg) {
    270:     PetscPrintf(PETSC_COMM_WORLD, "Infinity norm of the error: %g\n",(double) e);
    271:   }

    273:   /*
    274:      Free work space.  All PETSc objects should be destroyed when they
    275:      are no longer needed.
    276:   */

    278:   if (user_subdomains) {
    279:     for (i=0; i<Nsub; i++) {
    280:       ISDestroy(&is[i]);
    281:       ISDestroy(&is_local[i]);
    282:     }
    283:     PetscFree(is);
    284:     PetscFree(is_local);
    285:   }
    286:   KSPDestroy(&ksp);
    287:   VecDestroy(&u);
    288:   VecDestroy(&x);
    289:   VecDestroy(&b);
    290:   MatDestroy(&A);
    291:   PetscFinalize();
    292:   return ierr;
    293: }

    296: /*TEST

    298:    test:
    299:       suffix: 1
    300:       args: -print_error

    302: TEST*/