Date: 2022-03-04T17:39:12+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: /*T
     26:    Concepts: KSP^Additive Schwarz Method (ASM) with user-defined subdomains
     27:    Processors: n
     28: T*/

     30: /*
     31:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
     32:   automatically includes:
     33:      petscsys.h       - base PETSc routines   petscvec.h - vectors
     34:      petscmat.h - matrices
     35:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     36:      petscviewer.h - viewers               petscpc.h  - preconditioners
     37: */
     38: #include <petscksp.h>

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

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

     68:   /* -------------------------------------------------------------------
     69:          Compute the matrix and right-hand-side vector that define
     70:          the linear system, Ax = b.
     71:      ------------------------------------------------------------------- */

     73:   /*
     74:      Assemble the matrix for the five point stencil, YET AGAIN
     75:   */
     76:   MatCreate(PETSC_COMM_WORLD,&A);
     77:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
     78:   MatSetFromOptions(A);
     79:   MatSetUp(A);
     80:   MatGetOwnershipRange(A,&Istart,&Iend);
     81:   for (Ii=Istart; Ii<Iend; Ii++) {
     82:     v = -1.0; i = Ii/n; j = Ii - i*n;
     83:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
     84:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
     85:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
     86:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
     87:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
     88:   }
     89:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     90:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

     92:   /*
     93:      Create and set vectors
     94:   */
     95:   MatCreateVecs(A,&u,&b);
     96:   VecDuplicate(u,&x);
     97:   VecSet(u,one);
     98:   MatMult(A,u,b);

    100:   /*
    101:      Create linear solver context
    102:   */
    103:   KSPCreate(PETSC_COMM_WORLD,&ksp);

    105:   /*
    106:      Set operators. Here the matrix that defines the linear system
    107:      also serves as the preconditioning matrix.
    108:   */
    109:   KSPSetOperators(ksp,A,A);

    111:   /*
    112:      Set the default preconditioner for this program to be ASM
    113:   */
    114:   KSPGetPC(ksp,&pc);
    115:   PCSetType(pc,PCASM);

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

    121:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    122:        Basic method, should be sufficient for the needs of many users.
    123:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

    129:      Set the total number of blocks via -pc_asm_blocks <blks>
    130:      Note:  The ASM default is to use 1 block per processor.  To
    131:      experiment on a single processor with various overlaps, you
    132:      must specify use of multiple blocks!
    133:   */

    135:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    136:        More advanced method, setting user-defined subdomains
    137:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

    144:      Then call either PCASMSetLocalSubdomains() or PCASMSetTotalSubdomains()
    145:      to set the subdomains for the ASM preconditioner.
    146:   */

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

    171:   /* -------------------------------------------------------------------
    172:                 Set the linear solvers for the subblocks
    173:      ------------------------------------------------------------------- */

    175:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    176:        Basic method, should be sufficient for the needs of most users.
    177:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

    184:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    185:         Advanced method, setting different solvers for various blocks.
    186:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

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

    199:   flg  = PETSC_FALSE;
    200:   PetscOptionsGetBool(NULL,NULL,"-user_set_subdomain_solvers",&flg,NULL);
    201:   if (flg) {
    202:     KSP       *subksp;        /* array of KSP contexts for local subblocks */
    203:     PetscInt  nlocal,first;   /* number of local subblocks, first local subblock */
    204:     PC        subpc;          /* PC context for subblock */
    205:     PetscBool isasm;

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

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

    214:     /*
    215:        Flag an error if PCTYPE is changed from the runtime options
    216:      */
    217:     PetscObjectTypeCompare((PetscObject)pc,PCASM,&isasm);
    218:     if (!isasm) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Cannot Change the PCTYPE when manually changing the subdomain solver settings");

    220:     /*
    221:        Call KSPSetUp() to set the block Jacobi data structures (including
    222:        creation of an internal KSP context for each block).

    224:        Note: KSPSetUp() MUST be called before PCASMGetSubKSP().
    225:     */
    226:     KSPSetUp(ksp);

    228:     /*
    229:        Extract the array of KSP contexts for the local blocks
    230:     */
    231:     PCASMGetSubKSP(pc,&nlocal,&first,&subksp);

    233:     /*
    234:        Loop over the local blocks, setting various KSP options
    235:        for each block.
    236:     */
    237:     for (i=0; i<nlocal; i++) {
    238:       KSPGetPC(subksp[i],&subpc);
    239:       PCSetType(subpc,PCILU);
    240:       KSPSetType(subksp[i],KSPGMRES);
    241:       KSPSetTolerances(subksp[i],1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
    242:     }
    243:   } else {
    244:     /*
    245:        Set runtime options
    246:     */
    247:     KSPSetFromOptions(ksp);
    248:   }

    250:   /* -------------------------------------------------------------------
    251:                       Solve the linear system
    252:      ------------------------------------------------------------------- */

    254:   KSPSolve(ksp,b,x);

    256:   /* -------------------------------------------------------------------
    257:                       Compare result to the exact solution
    258:      ------------------------------------------------------------------- */
    259:   VecAXPY(x,-1.0,u);
    260:   VecNorm(x,NORM_INFINITY, &e);

    262:   flg  = PETSC_FALSE;
    263:   PetscOptionsGetBool(NULL,NULL,"-print_error",&flg,NULL);
    264:   if (flg) {
    265:     PetscPrintf(PETSC_COMM_WORLD, "Infinity norm of the error: %g\n",(double) e);
    266:   }

    268:   /*
    269:      Free work space.  All PETSc objects should be destroyed when they
    270:      are no longer needed.
    271:   */

    273:   if (user_subdomains) {
    274:     for (i=0; i<Nsub; i++) {
    275:       ISDestroy(&is[i]);
    276:       ISDestroy(&is_local[i]);
    277:     }
    278:     PetscFree(is);
    279:     PetscFree(is_local);
    280:   }
    281:   KSPDestroy(&ksp);
    282:   VecDestroy(&u);
    283:   VecDestroy(&x);
    284:   VecDestroy(&b);
    285:   MatDestroy(&A);
    286:   PetscFinalize();
    287:   return ierr;
    288: }

    290: /*TEST

    292:    test:
    293:       suffix: 1
    294:       args: -print_error

    296: TEST*/