Date: 2021-03-03T22:27:33+00:00

Actual source code: ex62.c
petsc-3.14.5 2021-03-03
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      1: static char help[] = "Illustrates use of PCGASM.\n\
      2: The Generalized Additive Schwarz Method for solving a linear system in parallel with KSP.  The\n\
      3: code indicates the procedure for setting user-defined subdomains.\n\
      4: See section 'ex62' below for command-line options.\n\
      5: Without -user_set_subdomains, the general PCGASM options are meaningful:\n\
      6:   -pc_gasm_total_subdomains\n\
      7:   -pc_gasm_print_subdomains\n\
      8: \n";

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

     16:    The GASM preconditioner is fully parallel.  The user-space routine
     17:    CreateSubdomains2D that computes the domain decomposition is also parallel
     18:    and attempts to generate both subdomains straddling processors and multiple
     19:    domains per processor.

     22:    This matrix in this linear system arises from the discretized Laplacian,
     23:    and thus is not very interesting in terms of experimenting with variants
     24:    of the GASM preconditioner.
     25: */

     27: /*T
     28:    Concepts: KSP^Additive Schwarz Method (GASM) with user-defined subdomains
     29:    Processors: n
     30: T*/

     34: /*
     35:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
     36:   automatically includes:
     37:      petscsys.h    - base PETSc routines   petscvec.h - vectors
     38:      petscmat.h    - matrices
     39:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     40:      petscviewer.h - viewers               petscpc.h  - preconditioners
     41: */
     42: #include <petscksp.h>

     44: PetscErrorCode AssembleMatrix(Mat,PetscInt m,PetscInt n);

     46: int main(int argc,char **args)
     47: {
     48:   Vec            x,b,u;                  /* approx solution, RHS, exact solution */
     49:   Mat            A;                      /* linear system matrix */
     50:   KSP            ksp;                    /* linear solver context */
     51:   PC             pc;                     /* PC context */
     52:   IS             *inneris,*outeris;      /* array of index sets that define the subdomains */
     53:   PetscInt       overlap;                /* width of subdomain overlap */
     54:   PetscInt       Nsub;                   /* number of subdomains */
     55:   PetscInt       m,n;                    /* mesh dimensions in x- and y- directions */
     56:   PetscInt       M,N;                    /* number of subdomains in x- and y- directions */
     58:   PetscMPIInt    size;
     59:   PetscBool      flg=PETSC_FALSE;
     60:   PetscBool      user_set_subdomains=PETSC_FALSE;
     61:   PetscReal      one,e;

     63:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
     64:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
     65:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"ex62","PCGASM");
     66:   m = 15;
     67:   PetscOptionsInt("-M", "Number of mesh points in the x-direction","PCGASMCreateSubdomains2D",m,&m,NULL);
     68:   n = 17;
     69:   PetscOptionsInt("-N","Number of mesh points in the y-direction","PCGASMCreateSubdomains2D",n,&n,NULL);
     70:   user_set_subdomains = PETSC_FALSE;
     71:   PetscOptionsBool("-user_set_subdomains","Use the user-specified 2D tiling of mesh by subdomains","PCGASMCreateSubdomains2D",user_set_subdomains,&user_set_subdomains,NULL);
     72:   M = 2;
     73:   PetscOptionsInt("-Mdomains","Number of subdomain tiles in the x-direction","PCGASMSetSubdomains2D",M,&M,NULL);
     74:   N = 1;
     75:   PetscOptionsInt("-Ndomains","Number of subdomain tiles in the y-direction","PCGASMSetSubdomains2D",N,&N,NULL);
     76:   overlap = 1;
     77:   PetscOptionsInt("-overlap","Size of tile overlap.","PCGASMSetSubdomains2D",overlap,&overlap,NULL);
     78:   PetscOptionsEnd();

     80:   /* -------------------------------------------------------------------
     81:          Compute the matrix and right-hand-side vector that define
     82:          the linear system, Ax = b.
     83:      ------------------------------------------------------------------- */

     85:   /*
     86:      Assemble the matrix for the five point stencil, YET AGAIN
     87:   */
     88:   MatCreate(PETSC_COMM_WORLD,&A);
     89:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
     90:   MatSetFromOptions(A);
     91:   MatSetUp(A);
     92:   MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);
     93:   MatSetOption(A, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE);
     94:   AssembleMatrix(A,m,n);

     96:   /*
     97:      Create and set vectors
     98:   */
     99:   VecCreate(PETSC_COMM_WORLD,&b);
    100:   VecSetSizes(b,PETSC_DECIDE,m*n);
    101:   VecSetFromOptions(b);
    102:   VecDuplicate(b,&u);
    103:   VecDuplicate(b,&x);
    104:   one  = 1.0;
    105:   VecSet(u,one);
    106:   MatMult(A,u,b);

    108:   /*
    109:      Create linear solver context
    110:   */
    111:   KSPCreate(PETSC_COMM_WORLD,&ksp);

    113:   /*
    114:      Set operators. Here the matrix that defines the linear system
    115:      also serves as the preconditioning matrix.
    116:   */
    117:   KSPSetOperators(ksp,A,A);

    119:   /*
    120:      Set the default preconditioner for this program to be GASM
    121:   */
    122:   KSPGetPC(ksp,&pc);
    123:   PCSetType(pc,PCGASM);

    125:   /* -------------------------------------------------------------------
    126:                   Define the problem decomposition
    127:      ------------------------------------------------------------------- */

    129:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    130:        Basic method, should be sufficient for the needs of many users.
    131:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    133:      Set the overlap, using the default PETSc decomposition via
    134:          PCGASMSetOverlap(pc,overlap);
    135:      Could instead use the option -pc_gasm_overlap <ovl>

    137:      Set the total number of blocks via -pc_gasm_blocks <blks>
    138:      Note:  The GASM default is to use 1 block per processor.  To
    139:      experiment on a single processor with various overlaps, you
    140:      must specify use of multiple blocks!
    141:   */

    143:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    144:        More advanced method, setting user-defined subdomains
    145:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    147:      Firstly, create index sets that define the subdomains.  The utility
    148:      routine PCGASMCreateSubdomains2D() is a simple example, which partitions
    149:      the 2D grid into MxN subdomains with an optional overlap.
    150:      More generally, the user should write a custom routine for a particular
    151:      problem geometry.

    153:      Then call PCGASMSetLocalSubdomains() with resulting index sets
    154:      to set the subdomains for the GASM preconditioner.
    155:   */

    157:   if (user_set_subdomains) { /* user-control version */
    158:     PCGASMCreateSubdomains2D(pc, m,n,M,N,1,overlap,&Nsub,&inneris,&outeris);
    159:     PCGASMSetSubdomains(pc,Nsub,inneris,outeris);
    160:     PCGASMDestroySubdomains(Nsub,&inneris,&outeris);
    161:     flg  = PETSC_FALSE;
    162:     PetscOptionsGetBool(NULL,NULL,"-subdomain_view",&flg,NULL);
    163:     if (flg) {
    164:       PetscInt i;
    165:       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);
    166:       PetscPrintf(PETSC_COMM_SELF,"Outer IS:\n");
    167:       for (i=0; i<Nsub; i++) {
    168:         PetscPrintf(PETSC_COMM_SELF,"  outer IS[%D]\n",i);
    169:         ISView(outeris[i],PETSC_VIEWER_STDOUT_SELF);
    170:       }
    171:       PetscPrintf(PETSC_COMM_SELF,"Inner IS:\n");
    172:       for (i=0; i<Nsub; i++) {
    173:         PetscPrintf(PETSC_COMM_SELF,"  inner IS[%D]\n",i);
    174:         ISView(inneris[i],PETSC_VIEWER_STDOUT_SELF);
    175:       }
    176:     }
    177:   } else { /* basic setup */
    178:     KSPSetFromOptions(ksp);
    179:   }

    181:   /* -------------------------------------------------------------------
    182:                 Set the linear solvers for the subblocks
    183:      ------------------------------------------------------------------- */

    185:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    186:        Basic method, should be sufficient for the needs of most users.
    187:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

    194:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    195:         Advanced method, setting different solvers for various blocks.
    196:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

    202:      - Use PCGASMGetSubKSP() to extract the array of KSP contexts for
    203:        the local blocks.
    204:      - See ex7.c for a simple example of setting different linear solvers
    205:        for the individual blocks for the block Jacobi method (which is
    206:        equivalent to the GASM method with zero overlap).
    207:   */

    209:   flg  = PETSC_FALSE;
    210:   PetscOptionsGetBool(NULL,NULL,"-user_set_subdomain_solvers",&flg,NULL);
    211:   if (flg) {
    212:     KSP       *subksp;        /* array of KSP contexts for local subblocks */
    213:     PetscInt  i,nlocal,first;   /* number of local subblocks, first local subblock */
    214:     PC        subpc;          /* PC context for subblock */
    215:     PetscBool isasm;

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

    219:     /*
    220:        Set runtime options
    221:     */
    222:     KSPSetFromOptions(ksp);

    224:     /*
    225:        Flag an error if PCTYPE is changed from the runtime options
    226:      */
    227:     PetscObjectTypeCompare((PetscObject)pc,PCGASM,&isasm);
    228:     if (!isasm) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Cannot Change the PCTYPE when manually changing the subdomain solver settings");

    230:     /*
    231:        Call KSPSetUp() to set the block Jacobi data structures (including
    232:        creation of an internal KSP context for each block).

    234:        Note: KSPSetUp() MUST be called before PCGASMGetSubKSP().
    235:     */
    236:     KSPSetUp(ksp);

    238:     /*
    239:        Extract the array of KSP contexts for the local blocks
    240:     */
    241:     PCGASMGetSubKSP(pc,&nlocal,&first,&subksp);

    243:     /*
    244:        Loop over the local blocks, setting various KSP options
    245:        for each block.
    246:     */
    247:     for (i=0; i<nlocal; i++) {
    248:       KSPGetPC(subksp[i],&subpc);
    249:       PCSetType(subpc,PCILU);
    250:       KSPSetType(subksp[i],KSPGMRES);
    251:       KSPSetTolerances(subksp[i],1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
    252:     }
    253:   } else {
    254:     /*
    255:        Set runtime options
    256:     */
    257:     KSPSetFromOptions(ksp);
    258:   }

    260:   /* -------------------------------------------------------------------
    261:                       Solve the linear system
    262:      ------------------------------------------------------------------- */

    264:   KSPSolve(ksp,b,x);

    266:   /* -------------------------------------------------------------------
    267:         Assemble the matrix again to test repeated setup and solves.
    268:      ------------------------------------------------------------------- */

    270:   AssembleMatrix(A,m,n);
    271:   KSPSolve(ksp,b,x);

    273:   /* -------------------------------------------------------------------
    274:                       Compare result to the exact solution
    275:      ------------------------------------------------------------------- */
    276:   VecAXPY(x,-1.0,u);
    277:   VecNorm(x,NORM_INFINITY, &e);

    279:   flg  = PETSC_FALSE;
    280:   PetscOptionsGetBool(NULL,NULL,"-print_error",&flg,NULL);
    281:   if (flg) {
    282:     PetscPrintf(PETSC_COMM_WORLD, "Infinity norm of the error: %g\n", (double)e);
    283:   }

    285:   /*
    286:      Free work space.  All PETSc objects should be destroyed when they
    287:      are no longer needed.
    288:   */

    290:   KSPDestroy(&ksp);
    291:   VecDestroy(&u);
    292:   VecDestroy(&x);
    293:   VecDestroy(&b);
    294:   MatDestroy(&A);
    295:   PetscFinalize();
    296:   return ierr;
    297: }

    299: PetscErrorCode AssembleMatrix(Mat A,PetscInt m,PetscInt n)
    300: {
    302:   PetscInt       i,j,Ii,J,Istart,Iend;
    303:   PetscScalar    v;

    306:   MatGetOwnershipRange(A,&Istart,&Iend);
    307:   for (Ii=Istart; Ii<Iend; Ii++) {
    308:     v = -1.0; i = Ii/n; j = Ii - i*n;
    309:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
    310:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
    311:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
    312:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
    313:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
    314:   }
    315:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    316:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

    318:   return(0);
    319: }

    322: /*TEST

    324:    test:
    325:       suffix: 2D_1
    326:       args: -M 7 -N 9 -user_set_subdomains -Mdomains 1 -Ndomains 3 -overlap 1 -print_error -pc_gasm_print_subdomains

    328:    test:
    329:       suffix: 2D_2
    330:       nsize: 2
    331:       args: -M 7 -N 9 -user_set_subdomains -Mdomains 1 -Ndomains 3 -overlap 1 -print_error -pc_gasm_print_subdomains

    333:    test:
    334:       suffix: 2D_3
    335:       nsize: 3
    336:       args: -M 7 -N 9 -user_set_subdomains -Mdomains 1 -Ndomains 3 -overlap 1 -print_error -pc_gasm_print_subdomains

    338:    test:
    339:       suffix: hp
    340:       nsize: 4
    341:       requires: superlu_dist
    342:       args: -M 7 -N 9 -pc_gasm_overlap 1 -sub_pc_type lu -sub_pc_factor_mat_solver_type superlu_dist -ksp_monitor -print_error -pc_gasm_total_subdomains 2 -pc_gasm_use_hierachical_partitioning 1
    343:       output_file: output/ex62.out
    344:       TODO: bug, triggers New nonzero at (0,15) caused a malloc in MatCreateSubMatrices_MPIAIJ_SingleIS_Local

    346:    test:
    347:       suffix: superlu_dist_1
    348:       requires: superlu_dist
    349:       args: -M 7 -N 9 -print_error -pc_gasm_total_subdomains 1 -pc_gasm_print_subdomains -sub_pc_type lu -sub_pc_factor_mat_solver_type superlu_dist

    351:    test:
    352:       suffix: superlu_dist_2
    353:       nsize: 2
    354:       requires: superlu_dist
    355:       args: -M 7 -N 9 -print_error -pc_gasm_total_subdomains 1 -pc_gasm_print_subdomains -sub_pc_type lu -sub_pc_factor_mat_solver_type superlu_dist

    357:    test:
    358:       suffix: superlu_dist_3
    359:       nsize: 3
    360:       requires: superlu_dist
    361:       args: -M 7 -N 9 -print_error -pc_gasm_total_subdomains 2 -pc_gasm_print_subdomains -sub_pc_type lu -sub_pc_factor_mat_solver_type superlu_dist

    363:    test:
    364:       suffix: superlu_dist_4
    365:       nsize: 4
    366:       requires: superlu_dist
    367:       args: -M 7 -N 9 -print_error -pc_gasm_total_subdomains 2 -pc_gasm_print_subdomains -sub_pc_type lu -sub_pc_factor_mat_solver_type superlu_dist

    369: TEST*/