Date: 2022-08-02T03:14:47+00:00

Actual source code: ex64.c

      1: /*
      2:  *
      3:  *  Created on: Aug 10, 2015
      4:  *      Author: Fande Kong  <fdkong.jd@gmail.com>
      5:  */

      7: static char help[] = "Illustrates use of the preconditioner GASM.\n \
      8:    using hierarchical partitioning and MatIncreaseOverlapSplit \
      9:         -pc_gasm_total_subdomains\n \
     10:         -pc_gasm_print_subdomains\n \n";

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

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

     23:    This matrix in this linear system arises from the discretized Laplacian,
     24:    and thus is not very interesting in terms of experimenting with variants
     25:    of the GASM preconditioner.
     26: */

     28: /*
     29:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
     30:   automatically includes:
     31:      petscsys.h    - base PETSc routines   petscvec.h - vectors
     32:      petscmat.h    - matrices
     33:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     34:      petscviewer.h - viewers               petscpc.h  - preconditioners
     35: */
     36: #include <petscksp.h>
     37: #include <petscmat.h>

     39: int main(int argc,char **args)
     40: {
     41:   Vec            x,b,u;                  /* approx solution, RHS, exact solution */
     42:   Mat            A,perA;                      /* linear system matrix */
     43:   KSP            ksp;                    /* linear solver context */
     44:   PC             pc;                     /* PC context */
     45:   PetscInt       overlap;                /* width of subdomain overlap */
     46:   PetscInt       m,n;                    /* mesh dimensions in x- and y- directions */
     47:   PetscInt       M,N;                    /* number of subdomains in x- and y- directions */
     48:   PetscInt       i,j,Ii,J,Istart,Iend;
     50:   PetscMPIInt    size;
     51:   PetscBool      flg;
     52:   PetscBool       user_set_subdomains;
     53:   PetscScalar     v, one = 1.0;
     54:   MatPartitioning part;
     55:   IS              coarseparts,fineparts;
     56:   IS              is,isn,isrows;
     57:   MPI_Comm        comm;
     58:   PetscReal       e;

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

     78:   /* -------------------------------------------------------------------
     79:          Compute the matrix and right-hand-side vector that define
     80:          the linear system, Ax = b.
     81:      ------------------------------------------------------------------- */

     83:   /*
     84:      Assemble the matrix for the five point stencil, YET AGAIN
     85:   */
     86:   MatCreate(comm,&A);
     87:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
     88:   MatSetFromOptions(A);
     89:   MatSetUp(A);
     90:   MatGetOwnershipRange(A,&Istart,&Iend);
     91:   for (Ii=Istart; Ii<Iend; Ii++) {
     92:     v = -1.0; i = Ii/n; j = Ii - i*n;
     93:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
     94:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
     95:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
     96:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
     97:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
     98:   }
     99:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    100:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

    102:   /*
    103:     Partition the graph of the matrix
    104:   */
    105:   MatPartitioningCreate(comm,&part);
    106:   MatPartitioningSetAdjacency(part,A);
    107:   MatPartitioningSetType(part,MATPARTITIONINGHIERARCH);
    108:   MatPartitioningHierarchicalSetNcoarseparts(part,2);
    109:   MatPartitioningHierarchicalSetNfineparts(part,2);
    110:   MatPartitioningSetFromOptions(part);
    111:   /* get new processor owner number of each vertex */
    112:   MatPartitioningApply(part,&is);
    113:   /* get coarse parts according to which we rearrange the matrix */
    114:   MatPartitioningHierarchicalGetCoarseparts(part,&coarseparts);
    115:   /* fine parts are used with coarse parts */
    116:   MatPartitioningHierarchicalGetFineparts(part,&fineparts);
    117:   /* get new global number of each old global number */
    118:   ISPartitioningToNumbering(is,&isn);
    119:   ISBuildTwoSided(is,NULL,&isrows);
    120:   MatCreateSubMatrix(A,isrows,isrows,MAT_INITIAL_MATRIX,&perA);
    121:   MatCreateVecs(perA,&b,NULL);
    122:   VecSetFromOptions(b);
    123:   VecDuplicate(b,&u);
    124:   VecDuplicate(b,&x);
    125:   VecSet(u,one);
    126:   MatMult(perA,u,b);
    127:   KSPCreate(comm,&ksp);
    128:   /*
    129:      Set operators. Here the matrix that defines the linear system
    130:      also serves as the preconditioning matrix.
    131:   */
    132:   KSPSetOperators(ksp,perA,perA);

    134:   /*
    135:      Set the default preconditioner for this program to be GASM
    136:   */
    137:   KSPGetPC(ksp,&pc);
    138:   PCSetType(pc,PCGASM);
    139:   KSPSetFromOptions(ksp);
    140:   /* -------------------------------------------------------------------
    141:                       Solve the linear system
    142:      ------------------------------------------------------------------- */

    144:   KSPSolve(ksp,b,x);
    145:   /* -------------------------------------------------------------------
    146:                       Compare result to the exact solution
    147:      ------------------------------------------------------------------- */
    148:   VecAXPY(x,-1.0,u);
    149:   VecNorm(x,NORM_INFINITY, &e);

    151:   flg  = PETSC_FALSE;
    152:   PetscOptionsGetBool(NULL,NULL,"-print_error",&flg,NULL);
    153:   if (flg) {
    154:     PetscPrintf(PETSC_COMM_WORLD, "Infinity norm of the error: %g\n", (double)e);
    155:   }
    156:   /*
    157:      Free work space.  All PETSc objects should be destroyed when they
    158:      are no longer needed.
    159:   */
    160:   KSPDestroy(&ksp);
    161:   VecDestroy(&u);
    162:   VecDestroy(&x);
    163:   VecDestroy(&b);
    164:   MatDestroy(&A);
    165:   MatDestroy(&perA);
    166:   ISDestroy(&is);
    167:   ISDestroy(&coarseparts);
    168:   ISDestroy(&fineparts);
    169:   ISDestroy(&isrows);
    170:   ISDestroy(&isn);
    171:   MatPartitioningDestroy(&part);
    172:   PetscFinalize();
    173:   return 0;
    174: }

    176: /*TEST

    178:    test:
    179:       nsize: 4
    180:       requires: superlu_dist parmetis
    181:       args: -ksp_monitor -pc_gasm_overlap 1 -sub_pc_type lu -sub_pc_factor_mat_solver_type superlu_dist -pc_gasm_total_subdomains 2

    183: TEST*/