Actual source code: ex46.c
petsc-3.15.0 2021-03-30
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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: #if defined(PETSC_USE_LOG)
     40:   PetscLogStage  stage;
     41: #endif
     42:   DMDALocalInfo  info;

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

     54:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     55:          Compute the matrix and right-hand-side vector that define
     56:          the linear system, Ax = b.
     57:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     58:   /*
     59:      Create parallel matrix preallocated according to the DMDA, format AIJ by default.
     60:      To use symmetric storage, run with -dm_mat_type sbaij -mat_ignore_lower_triangular
     61:   */
     62:   DMCreateMatrix(da,&A);

     64:   /*
     65:      Set matrix elements for the 2-D, five-point stencil in parallel.
     66:       - Each processor needs to insert only elements that it owns
     67:         locally (but any non-local elements will be sent to the
     68:         appropriate processor during matrix assembly).
     69:       - Rows and columns are specified by the stencil
     70:       - Entries are normalized for a domain [0,1]x[0,1]
     71:    */
     72:   PetscLogStageRegister("Assembly", &stage);
     73:   PetscLogStagePush(stage);
     74:   DMDAGetLocalInfo(da,&info);
     75:   for (j=info.ys; j<info.ys+info.ym; j++) {
     76:     for (i=info.xs; i<info.xs+info.xm; i++) {
     77:       PetscReal   hx  = 1./info.mx,hy = 1./info.my;
     78:       MatStencil  row = {0},col[5] = {{0}};
     79:       PetscScalar v[5];
     80:       PetscInt    ncols = 0;
     81:       row.j        = j; row.i = i;
     82:       col[ncols].j = j; col[ncols].i = i; v[ncols++] = 2*(hx/hy + hy/hx);
     83:       /* boundaries */
     84:       if (i>0)         {col[ncols].j = j;   col[ncols].i = i-1; v[ncols++] = -hy/hx;}
     85:       if (i<info.mx-1) {col[ncols].j = j;   col[ncols].i = i+1; v[ncols++] = -hy/hx;}
     86:       if (j>0)         {col[ncols].j = j-1; col[ncols].i = i;   v[ncols++] = -hx/hy;}
     87:       if (j<info.my-1) {col[ncols].j = j+1; col[ncols].i = i;   v[ncols++] = -hx/hy;}
     88:       MatSetValuesStencil(A,1,&row,ncols,col,v,INSERT_VALUES);
     89:     }
     90:   }

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

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

    109:   /*
    110:      Set exact solution; then compute right-hand-side vector.
    111:      By default we use an exact solution of a vector with all
    112:      elements of 1.0;  Alternatively, using the runtime option
    113:      -random_sol forms a solution vector with random components.
    114:   */
    115:   PetscOptionsGetBool(NULL,NULL,"-random_exact_sol",&flg,NULL);
    116:   if (flg) {
    117:     PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
    118:     PetscRandomSetFromOptions(rctx);
    119:     VecSetRandom(u,rctx);
    120:     PetscRandomDestroy(&rctx);
    121:   } else {
    122:     VecSet(u,1.);
    123:   }
    124:   MatMult(A,u,b);

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

    133:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    134:                 Create the linear solver and set various options
    135:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    137:   /*
    138:      Create linear solver context
    139:   */
    140:   KSPCreate(PETSC_COMM_WORLD,&ksp);

    142:   /*
    143:      Set operators. Here the matrix that defines the linear system
    144:      also serves as the preconditioning matrix.
    145:   */
    146:   KSPSetOperators(ksp,A,A);

    148:   /*
    149:     Set runtime options, e.g.,
    150:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
    151:     These options will override those specified above as long as
    152:     KSPSetFromOptions() is called _after_ any other customization
    153:     routines.
    154:   */
    155:   KSPSetFromOptions(ksp);

    157:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    158:                       Solve the linear system
    159:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    161:   KSPSolve(ksp,b,x);

    163:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    164:                       Check solution and clean up
    165:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

    174:   /*
    175:      Print convergence information.  PetscPrintf() produces a single
    176:      print statement from all processes that share a communicator.
    177:      An alternative is PetscFPrintf(), which prints to a file.
    178:   */
    179:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);

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

    192:   /*
    193:      Always call PetscFinalize() before exiting a program.  This routine
    194:        - finalizes the PETSc libraries as well as MPI
    195:        - provides summary and diagnostic information if certain runtime
    196:          options are chosen (e.g., -log_view).
    197:   */
    198:   PetscFinalize();
    199:   return ierr;
    200: }

    203: /*TEST

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

    210:       test:
    211:         suffix: aijcusparse
    212:         args: -use_gpu_aware_mpi 0
    213:       test:
    214:         suffix: aijcusparse_mpi_gpu_aware

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

    227: TEST*/