Date: 2022-08-02T03:14:46+00:00

Actual source code: ex11.c

      2: static char help[] = "Solves a linear system in parallel with KSP.\n\n";

      4: /*
      5:    Description: Solves a complex linear system in parallel with KSP.

      7:    The model problem:
      8:       Solve Helmholtz equation on the unit square: (0,1) x (0,1)
      9:           -delta u - sigma1*u + i*sigma2*u = f,
     10:            where delta = Laplace operator
     11:       Dirichlet b.c.'s on all sides
     12:       Use the 2-D, five-point finite difference stencil.

     14:    Compiling the code:
     15:       This code uses the complex numbers version of PETSc, so configure
     16:       must be run to enable this
     17: */

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

     29: int main(int argc,char **args)
     30: {
     31:   Vec            x,b,u;      /* approx solution, RHS, exact solution */
     32:   Mat            A;            /* linear system matrix */
     33:   KSP            ksp;         /* linear solver context */
     34:   PetscReal      norm;         /* norm of solution error */
     35:   PetscInt       dim,i,j,Ii,J,Istart,Iend,n = 6,its,use_random;
     36:   PetscScalar    v,none = -1.0,sigma2,pfive = 0.5,*xa;
     37:   PetscRandom    rctx;
     38:   PetscReal      h2,sigma1 = 100.0;
     39:   PetscBool      flg = PETSC_FALSE;

     41:   PetscInitialize(&argc,&args,(char*)0,help);
     42:   PetscOptionsGetReal(NULL,NULL,"-sigma1",&sigma1,NULL);
     43:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     44:   dim  = n*n;

     46:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     47:          Compute the matrix and right-hand-side vector that define
     48:          the linear system, Ax = b.
     49:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     50:   /*
     51:      Create parallel matrix, specifying only its global dimensions.
     52:      When using MatCreate(), the matrix format can be specified at
     53:      runtime. Also, the parallel partitioning of the matrix is
     54:      determined by PETSc at runtime.
     55:   */
     56:   MatCreate(PETSC_COMM_WORLD,&A);
     57:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim);
     58:   MatSetFromOptions(A);
     59:   MatSetUp(A);

     61:   /*
     62:      Currently, all PETSc parallel matrix formats are partitioned by
     63:      contiguous chunks of rows across the processors.  Determine which
     64:      rows of the matrix are locally owned.
     65:   */
     66:   MatGetOwnershipRange(A,&Istart,&Iend);

     68:   /*
     69:      Set matrix elements in parallel.
     70:       - Each processor needs to insert only elements that it owns
     71:         locally (but any non-local elements will be sent to the
     72:         appropriate processor during matrix assembly).
     73:       - Always specify global rows and columns of matrix entries.
     74:   */

     76:   PetscOptionsGetBool(NULL,NULL,"-norandom",&flg,NULL);
     77:   if (flg) use_random = 0;
     78:   else use_random = 1;
     79:   if (use_random) {
     80:     PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
     81:     PetscRandomSetFromOptions(rctx);
     82:     PetscRandomSetInterval(rctx,0.0,PETSC_i);
     83:   } else {
     84:     sigma2 = 10.0*PETSC_i;
     85:   }
     86:   h2 = 1.0/((n+1)*(n+1));
     87:   for (Ii=Istart; Ii<Iend; Ii++) {
     88:     v = -1.0; i = Ii/n; j = Ii - i*n;
     89:     if (i>0) {
     90:       J = Ii-n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);
     91:     }
     92:     if (i<n-1) {
     93:       J = Ii+n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);
     94:     }
     95:     if (j>0) {
     96:       J = Ii-1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);
     97:     }
     98:     if (j<n-1) {
     99:       J = Ii+1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);
    100:     }
    101:     if (use_random) PetscRandomGetValue(rctx,&sigma2);
    102:     v    = 4.0 - sigma1*h2 + sigma2*h2;
    103:     MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);
    104:   }
    105:   if (use_random) PetscRandomDestroy(&rctx);

    107:   /*
    108:      Assemble matrix, using the 2-step process:
    109:        MatAssemblyBegin(), MatAssemblyEnd()
    110:      Computations can be done while messages are in transition
    111:      by placing code between these two statements.
    112:   */
    113:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    114:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

    116:   /*
    117:      Create parallel vectors.
    118:       - When using VecCreate(), VecSetSizes() and VecSetFromOptions(),
    119:       we specify only the vector's global
    120:         dimension; the parallel partitioning is determined at runtime.
    121:       - Note: We form 1 vector from scratch and then duplicate as needed.
    122:   */
    123:   VecCreate(PETSC_COMM_WORLD,&u);
    124:   VecSetSizes(u,PETSC_DECIDE,dim);
    125:   VecSetFromOptions(u);
    126:   VecDuplicate(u,&b);
    127:   VecDuplicate(b,&x);

    129:   /*
    130:      Set exact solution; then compute right-hand-side vector.
    131:   */

    133:   if (use_random) {
    134:     PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
    135:     PetscRandomSetFromOptions(rctx);
    136:     VecSetRandom(u,rctx);
    137:   } else {
    138:     VecSet(u,pfive);
    139:   }
    140:   MatMult(A,u,b);

    142:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    143:                 Create the linear solver and set various options
    144:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    146:   /*
    147:      Create linear solver context
    148:   */
    149:   KSPCreate(PETSC_COMM_WORLD,&ksp);

    151:   /*
    152:      Set operators. Here the matrix that defines the linear system
    153:      also serves as the preconditioning matrix.
    154:   */
    155:   KSPSetOperators(ksp,A,A);

    157:   /*
    158:     Set runtime options, e.g.,
    159:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
    160:   */
    161:   KSPSetFromOptions(ksp);

    163:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    164:                       Solve the linear system
    165:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    167:   KSPSolve(ksp,b,x);

    169:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    170:                       Check solution and clean up
    171:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    173:   /*
    174:       Print the first 3 entries of x; this demonstrates extraction of the
    175:       real and imaginary components of the complex vector, x.
    176:   */
    177:   flg  = PETSC_FALSE;
    178:   PetscOptionsGetBool(NULL,NULL,"-print_x3",&flg,NULL);
    179:   if (flg) {
    180:     VecGetArray(x,&xa);
    181:     PetscPrintf(PETSC_COMM_WORLD,"The first three entries of x are:\n");
    182:     for (i=0; i<3; i++) {
    183:       PetscPrintf(PETSC_COMM_WORLD,"x[%D] = %g + %g i\n",i,(double)PetscRealPart(xa[i]),(double)PetscImaginaryPart(xa[i]));
    184:     }
    185:     VecRestoreArray(x,&xa);
    186:   }

    188:   /*
    189:      Check the error
    190:   */
    191:   VecAXPY(x,none,u);
    192:   VecNorm(x,NORM_2,&norm);
    193:   KSPGetIterationNumber(ksp,&its);
    194:   if (norm < 1.e-12) {
    195:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error < 1.e-12 iterations %D\n",its);
    196:   } else {
    197:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);
    198:   }

    200:   /*
    201:      Free work space.  All PETSc objects should be destroyed when they
    202:      are no longer needed.
    203:   */
    204:   KSPDestroy(&ksp);
    205:   if (use_random) PetscRandomDestroy(&rctx);
    206:   VecDestroy(&u)); PetscCall(VecDestroy(&x);
    207:   VecDestroy(&b)); PetscCall(MatDestroy(&A);
    208:   PetscFinalize();
    209:   return 0;
    210: }

    212: /*TEST

    214:    build:
    215:       requires: complex

    217:    test:
    218:       args: -n 6 -norandom -pc_type none -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    220:    testset:
    221:       suffix: deflation
    222:       args: -norandom -pc_type deflation -ksp_monitor_short
    223:       requires: superlu_dist

    225:       test:
    226:         nsize: 6

    228:       test:
    229:         nsize: 3
    230:         args: -pc_deflation_compute_space {{db2 aggregation}}

    232:       test:
    233:         suffix: pc_deflation_init_only-0
    234:         nsize: 4
    235:         args: -ksp_type fgmres -pc_deflation_compute_space db4 -pc_deflation_compute_space_size 2 -pc_deflation_levels 2 -deflation_ksp_max_it 10
    236:         #TODO remove suffix and next test when this works
    237:         #args: -pc_deflation_init_only {{0 1}separate output}
    238:         args: -pc_deflation_init_only 0

    240:       test:
    241:         suffix: pc_deflation_init_only-1
    242:         nsize: 4
    243:         args: -ksp_type fgmres -pc_deflation_compute_space db4 -pc_deflation_compute_space_size 2 -pc_deflation_levels 2 -deflation_ksp_max_it 10
    244:         args: -pc_deflation_init_only 1

    246: TEST*/