Actual source code: ex46.c
petsc-3.13.6 2020-09-29
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      2: static char help[] = "Solves a linear system in parallel with KSP and DM.\n\
      3: Compare this to ex2 which solves the same problem without a DM.\n\n";

      5: /*T
      6:    Concepts: KSP^basic parallel example;
      7:    Concepts: KSP^Laplacian, 2d
      8:    Concepts: DM^using distributed arrays;
      9:    Concepts: Laplacian, 2d
     10:    Processors: n
     11: T*/

     15: /*
     16:   Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
     17:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
     18:   automatically includes:
     19:      petscsys.h       - base PETSc routines   petscvec.h - vectors
     20:      petscmat.h - matrices
     21:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     22:      petscviewer.h - viewers               petscpc.h  - preconditioners
     23: */
     24:  #include <petscdm.h>
     25:  #include <petscdmda.h>
     26:  #include <petscksp.h>

     28: int main(int argc,char **argv)
     29: {
     30:   DM             da;            /* distributed array */
     31:   Vec            x,b,u;         /* approx solution, RHS, exact solution */
     32:   Mat            A;             /* linear system matrix */
     33:   KSP            ksp;           /* linear solver context */
     34:   PetscRandom    rctx;          /* random number generator context */
     35:   PetscReal      norm;          /* norm of solution error */
     36:   PetscInt       i,j,its;
     38:   PetscBool      flg = PETSC_FALSE;
     39:   PetscLogStage  stage;
     40:   DMDALocalInfo  info;

     42:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
     43:   /*
     44:      Create distributed array to handle parallel distribution.
     45:      The problem size will default to 8 by 7, but this can be
     46:      changed using -da_grid_x M -da_grid_y N
     47:   */
     48:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,8,7,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
     49:   DMSetFromOptions(da);
     50:   DMSetUp(da);

     52:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     53:          Compute the matrix and right-hand-side vector that define
     54:          the linear system, Ax = b.
     55:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     56:   /*
     57:      Create parallel matrix preallocated according to the DMDA, format AIJ by default.
     58:      To use symmetric storage, run with -dm_mat_type sbaij -mat_ignore_lower_triangular
     59:   */
     60:   DMCreateMatrix(da,&A);

     62:   /*
     63:      Set matrix elements for the 2-D, five-point stencil in parallel.
     64:       - Each processor needs to insert only elements that it owns
     65:         locally (but any non-local elements will be sent to the
     66:         appropriate processor during matrix assembly).
     67:       - Rows and columns are specified by the stencil
     68:       - Entries are normalized for a domain [0,1]x[0,1]
     69:    */
     70:   PetscLogStageRegister("Assembly", &stage);
     71:   PetscLogStagePush(stage);
     72:   DMDAGetLocalInfo(da,&info);
     73:   for (j=info.ys; j<info.ys+info.ym; j++) {
     74:     for (i=info.xs; i<info.xs+info.xm; i++) {
     75:       PetscReal   hx  = 1./info.mx,hy = 1./info.my;
     76:       MatStencil  row = {0},col[5] = {{0}};
     77:       PetscScalar v[5];
     78:       PetscInt    ncols = 0;
     79:       row.j        = j; row.i = i;
     80:       col[ncols].j = j; col[ncols].i = i; v[ncols++] = 2*(hx/hy + hy/hx);
     81:       /* boundaries */
     82:       if (i>0)         {col[ncols].j = j;   col[ncols].i = i-1; v[ncols++] = -hy/hx;}
     83:       if (i<info.mx-1) {col[ncols].j = j;   col[ncols].i = i+1; v[ncols++] = -hy/hx;}
     84:       if (j>0)         {col[ncols].j = j-1; col[ncols].i = i;   v[ncols++] = -hx/hy;}
     85:       if (j<info.my-1) {col[ncols].j = j+1; col[ncols].i = i;   v[ncols++] = -hx/hy;}
     86:       MatSetValuesStencil(A,1,&row,ncols,col,v,INSERT_VALUES);
     87:     }
     88:   }

     90:   /*
     91:      Assemble matrix, using the 2-step process:
     92:        MatAssemblyBegin(), MatAssemblyEnd()
     93:      Computations can be done while messages are in transition
     94:      by placing code between these two statements.
     95:   */
     96:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     97:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
     98:   PetscLogStagePop();

    100:   /*
    101:      Create parallel vectors compatible with the DMDA.
    102:   */
    103:   DMCreateGlobalVector(da,&u);
    104:   VecDuplicate(u,&b);
    105:   VecDuplicate(u,&x);

    107:   /*
    108:      Set exact solution; then compute right-hand-side vector.
    109:      By default we use an exact solution of a vector with all
    110:      elements of 1.0;  Alternatively, using the runtime option
    111:      -random_sol forms a solution vector with random components.
    112:   */
    113:   PetscOptionsGetBool(NULL,NULL,"-random_exact_sol",&flg,NULL);
    114:   if (flg) {
    115:     PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
    116:     PetscRandomSetFromOptions(rctx);
    117:     VecSetRandom(u,rctx);
    118:     PetscRandomDestroy(&rctx);
    119:   } else {
    120:     VecSet(u,1.);
    121:   }
    122:   MatMult(A,u,b);

    124:   /*
    125:      View the exact solution vector if desired
    126:   */
    127:   flg  = PETSC_FALSE;
    128:   PetscOptionsGetBool(NULL,NULL,"-view_exact_sol",&flg,NULL);
    129:   if (flg) {VecView(u,PETSC_VIEWER_STDOUT_WORLD);}

    131:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    132:                 Create the linear solver and set various options
    133:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    135:   /*
    136:      Create linear solver context
    137:   */
    138:   KSPCreate(PETSC_COMM_WORLD,&ksp);

    140:   /*
    141:      Set operators. Here the matrix that defines the linear system
    142:      also serves as the preconditioning matrix.
    143:   */
    144:   KSPSetOperators(ksp,A,A);

    146:   /*
    147:     Set runtime options, e.g.,
    148:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
    149:     These options will override those specified above as long as
    150:     KSPSetFromOptions() is called _after_ any other customization
    151:     routines.
    152:   */
    153:   KSPSetFromOptions(ksp);

    155:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    156:                       Solve the linear system
    157:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    159:   KSPSolve(ksp,b,x);

    161:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    162:                       Check solution and clean up
    163:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    165:   /*
    166:      Check the error
    167:   */
    168:   VecAXPY(x,-1.,u);
    169:   VecNorm(x,NORM_2,&norm);
    170:   KSPGetIterationNumber(ksp,&its);

    172:   /*
    173:      Print convergence information.  PetscPrintf() produces a single
    174:      print statement from all processes that share a communicator.
    175:      An alternative is PetscFPrintf(), which prints to a file.
    176:   */
    177:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);

    179:   /*
    180:      Free work space.  All PETSc objects should be destroyed when they
    181:      are no longer needed.
    182:   */
    183:   KSPDestroy(&ksp);
    184:   VecDestroy(&u);
    185:   VecDestroy(&x);
    186:   VecDestroy(&b);
    187:   MatDestroy(&A);
    188:   DMDestroy(&da);

    190:   /*
    191:      Always call PetscFinalize() before exiting a program.  This routine
    192:        - finalizes the PETSc libraries as well as MPI
    193:        - provides summary and diagnostic information if certain runtime
    194:          options are chosen (e.g., -log_view).
    195:   */
    196:   PetscFinalize();
    197:   return ierr;
    198: }

    201: /*TEST

    203:    testset:
    204:       requires: cuda
    205:       args: -dm_mat_type aijcusparse -dm_vec_type cuda -random_exact_sol
    206:       output_file: output/ex46_aijcusparse.out

    208:       test:
    209:         suffix: aijcusparse
    210:         args: -use_gpu_aware_mpi 0
    211:       test:
    212:         suffix: aijcusparse_mpi_gpu_aware

    214:    testset:
    215:       requires: cuda
    216:       args: -dm_mat_type aijcusparse -dm_vec_type cuda -random_exact_sol -pc_type ilu -pc_factor_mat_solver_type cusparse
    217:       output_file: output/ex46_aijcusparse_2.out
    218:       test:
    219:         suffix: aijcusparse_2
    220:         args: -use_gpu_aware_mpi 0
    221:       test:
    222:         suffix: aijcusparse_2_mpi_gpu_aware

    225: TEST*/