Date: 2022-08-02T03:14:46+00:00

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: /*
     26:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
     27:   automatically includes:
     28:      petscsys.h       - base PETSc routines   petscvec.h - vectors
     29:      petscmat.h - matrices
     30:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     31:      petscviewer.h - viewers               petscpc.h  - preconditioners
     32: */
     33: #include <petscksp.h>

     35: int main(int argc,char **args)
     36: {
     37:   Vec            x,b,u;                 /* approx solution, RHS, exact solution */
     38:   Mat            A;                       /* linear system matrix */
     39:   KSP            ksp;                    /* linear solver context */
     40:   PC             pc;                      /* PC context */
     41:   IS             *is,*is_local;           /* array of index sets that define the subdomains */
     42:   PetscInt       overlap = 1;             /* width of subdomain overlap */
     43:   PetscInt       Nsub;                    /* number of subdomains */
     44:   PetscInt       m = 15,n = 17;          /* mesh dimensions in x- and y- directions */
     45:   PetscInt       M = 2,N = 1;            /* number of subdomains in x- and y- directions */
     46:   PetscInt       i,j,Ii,J,Istart,Iend;
     47:   PetscMPIInt    size;
     48:   PetscBool      flg;
     49:   PetscBool      user_subdomains = PETSC_FALSE;
     50:   PetscScalar    v, one = 1.0;
     51:   PetscReal      e;

     53:   PetscInitialize(&argc,&args,(char*)0,help);
     54:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
     55:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
     56:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     57:   PetscOptionsGetInt(NULL,NULL,"-Mdomains",&M,NULL);
     58:   PetscOptionsGetInt(NULL,NULL,"-Ndomains",&N,NULL);
     59:   PetscOptionsGetInt(NULL,NULL,"-overlap",&overlap,NULL);
     60:   PetscOptionsGetBool(NULL,NULL,"-user_set_subdomains",&user_subdomains,NULL);

     62:   /* -------------------------------------------------------------------
     63:          Compute the matrix and right-hand-side vector that define
     64:          the linear system, Ax = b.
     65:      ------------------------------------------------------------------- */

     67:   /*
     68:      Assemble the matrix for the five point stencil, YET AGAIN
     69:   */
     70:   MatCreate(PETSC_COMM_WORLD,&A);
     71:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
     72:   MatSetFromOptions(A);
     73:   MatSetUp(A);
     74:   MatGetOwnershipRange(A,&Istart,&Iend);
     75:   for (Ii=Istart; Ii<Iend; Ii++) {
     76:     v = -1.0; i = Ii/n; j = Ii - i*n;
     77:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
     78:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
     79:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
     80:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
     81:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
     82:   }
     83:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     84:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

     86:   /*
     87:      Create and set vectors
     88:   */
     89:   MatCreateVecs(A,&u,&b);
     90:   VecDuplicate(u,&x);
     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 the default preconditioner for this program to be ASM
    107:   */
    108:   KSPGetPC(ksp,&pc);
    109:   PCSetType(pc,PCASM);

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

    115:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    116:        Basic method, should be sufficient for the needs of many users.
    117:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

    123:      Set the total number of blocks via -pc_asm_blocks <blks>
    124:      Note:  The ASM default is to use 1 block per processor.  To
    125:      experiment on a single processor with various overlaps, you
    126:      must specify use of multiple blocks!
    127:   */

    129:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    130:        More advanced method, setting user-defined subdomains
    131:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

    138:      Then call either PCASMSetLocalSubdomains() or PCASMSetTotalSubdomains()
    139:      to set the subdomains for the ASM preconditioner.
    140:   */

    142:   if (!user_subdomains) { /* basic version */
    143:     PCASMSetOverlap(pc,overlap);
    144:   } else { /* advanced version */
    146:     PCASMCreateSubdomains2D(m,n,M,N,1,overlap,&Nsub,&is,&is_local);
    147:     PCASMSetLocalSubdomains(pc,Nsub,is,is_local);
    148:     flg  = PETSC_FALSE;
    149:     PetscOptionsGetBool(NULL,NULL,"-subdomain_view",&flg,NULL);
    150:     if (flg) {
    151:       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);
    152:       PetscPrintf(PETSC_COMM_SELF,"IS:\n");
    153:       for (i=0; i<Nsub; i++) {
    154:         PetscPrintf(PETSC_COMM_SELF,"  IS[%D]\n",i);
    155:         ISView(is[i],PETSC_VIEWER_STDOUT_SELF);
    156:       }
    157:       PetscPrintf(PETSC_COMM_SELF,"IS_local:\n");
    158:       for (i=0; i<Nsub; i++) {
    159:         PetscPrintf(PETSC_COMM_SELF,"  IS_local[%D]\n",i);
    160:         ISView(is_local[i],PETSC_VIEWER_STDOUT_SELF);
    161:       }
    162:     }
    163:   }

    165:   /* -------------------------------------------------------------------
    166:                 Set the linear solvers for the subblocks
    167:      ------------------------------------------------------------------- */

    169:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    170:        Basic method, should be sufficient for the needs of most users.
    171:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

    178:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    179:         Advanced method, setting different solvers for various blocks.
    180:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

    186:      - Use PCASMGetSubKSP() to extract the array of KSP contexts for
    187:        the local blocks.
    188:      - See ex7.c for a simple example of setting different linear solvers
    189:        for the individual blocks for the block Jacobi method (which is
    190:        equivalent to the ASM method with zero overlap).
    191:   */

    193:   flg  = PETSC_FALSE;
    194:   PetscOptionsGetBool(NULL,NULL,"-user_set_subdomain_solvers",&flg,NULL);
    195:   if (flg) {
    196:     KSP       *subksp;        /* array of KSP contexts for local subblocks */
    197:     PetscInt  nlocal,first;   /* number of local subblocks, first local subblock */
    198:     PC        subpc;          /* PC context for subblock */
    199:     PetscBool isasm;

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

    203:     /*
    204:        Set runtime options
    205:     */
    206:     KSPSetFromOptions(ksp);

    208:     /*
    209:        Flag an error if PCTYPE is changed from the runtime options
    210:      */
    211:     PetscObjectTypeCompare((PetscObject)pc,PCASM,&isasm);

    214:     /*
    215:        Call KSPSetUp() to set the block Jacobi data structures (including
    216:        creation of an internal KSP context for each block).

    218:        Note: KSPSetUp() MUST be called before PCASMGetSubKSP().
    219:     */
    220:     KSPSetUp(ksp);

    222:     /*
    223:        Extract the array of KSP contexts for the local blocks
    224:     */
    225:     PCASMGetSubKSP(pc,&nlocal,&first,&subksp);

    227:     /*
    228:        Loop over the local blocks, setting various KSP options
    229:        for each block.
    230:     */
    231:     for (i=0; i<nlocal; i++) {
    232:       KSPGetPC(subksp[i],&subpc);
    233:       PCSetType(subpc,PCILU);
    234:       KSPSetType(subksp[i],KSPGMRES);
    235:       KSPSetTolerances(subksp[i],1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
    236:     }
    237:   } else {
    238:     /*
    239:        Set runtime options
    240:     */
    241:     KSPSetFromOptions(ksp);
    242:   }

    244:   /* -------------------------------------------------------------------
    245:                       Solve the linear system
    246:      ------------------------------------------------------------------- */

    248:   KSPSolve(ksp,b,x);

    250:   /* -------------------------------------------------------------------
    251:                       Compare result to the exact solution
    252:      ------------------------------------------------------------------- */
    253:   VecAXPY(x,-1.0,u);
    254:   VecNorm(x,NORM_INFINITY, &e);

    256:   flg  = PETSC_FALSE;
    257:   PetscOptionsGetBool(NULL,NULL,"-print_error",&flg,NULL);
    258:   if (flg) {
    259:     PetscPrintf(PETSC_COMM_WORLD, "Infinity norm of the error: %g\n",(double) e);
    260:   }

    262:   /*
    263:      Free work space.  All PETSc objects should be destroyed when they
    264:      are no longer needed.
    265:   */

    267:   if (user_subdomains) {
    268:     for (i=0; i<Nsub; i++) {
    269:       ISDestroy(&is[i]);
    270:       ISDestroy(&is_local[i]);
    271:     }
    272:     PetscFree(is);
    273:     PetscFree(is_local);
    274:   }
    275:   KSPDestroy(&ksp);
    276:   VecDestroy(&u);
    277:   VecDestroy(&x);
    278:   VecDestroy(&b);
    279:   MatDestroy(&A);
    280:   PetscFinalize();
    281:   return 0;
    282: }

    284: /*TEST

    286:    test:
    287:       suffix: 1
    288:       args: -print_error

    290: TEST*/