Actual source code: ex11.c
petsc-3.12.4 2020-02-04
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      2: static char help[] = "Solves a linear system in parallel with KSP.\n\n";

      4: /*T
      5:    Concepts: KSP^solving a Helmholtz equation
      6:    Concepts: complex numbers;
      7:    Concepts: Helmholtz equation
      8:    Processors: n
      9: T*/

     13: /*
     14:    Description: Solves a complex linear system in parallel with KSP.

     16:    The model problem:
     17:       Solve Helmholtz equation on the unit square: (0,1) x (0,1)
     18:           -delta u - sigma1*u + i*sigma2*u = f,
     19:            where delta = Laplace operator
     20:       Dirichlet b.c.'s on all sides
     21:       Use the 2-D, five-point finite difference stencil.

     23:    Compiling the code:
     24:       This code uses the complex numbers version of PETSc, so configure
     25:       must be run to enable this
     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>

     38: int main(int argc,char **args)
     39: {
     40:   Vec            x,b,u;      /* approx solution, RHS, exact solution */
     41:   Mat            A;            /* linear system matrix */
     42:   KSP            ksp;         /* linear solver context */
     43:   PetscReal      norm;         /* norm of solution error */
     44:   PetscInt       dim,i,j,Ii,J,Istart,Iend,n = 6,its,use_random;
     46:   PetscScalar    v,none = -1.0,sigma2,pfive = 0.5,*xa;
     47:   PetscRandom    rctx;
     48:   PetscReal      h2,sigma1 = 100.0;
     49:   PetscBool      flg = PETSC_FALSE;

     51:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
     52:   PetscOptionsGetReal(NULL,NULL,"-sigma1",&sigma1,NULL);
     53:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     54:   dim  = n*n;

     56:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     57:          Compute the matrix and right-hand-side vector that define
     58:          the linear system, Ax = b.
     59:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     60:   /*
     61:      Create parallel matrix, specifying only its global dimensions.
     62:      When using MatCreate(), the matrix format can be specified at
     63:      runtime. Also, the parallel partitioning of the matrix is
     64:      determined by PETSc at runtime.
     65:   */
     66:   MatCreate(PETSC_COMM_WORLD,&A);
     67:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim);
     68:   MatSetFromOptions(A);
     69:   MatSetUp(A);

     71:   /*
     72:      Currently, all PETSc parallel matrix formats are partitioned by
     73:      contiguous chunks of rows across the processors.  Determine which
     74:      rows of the matrix are locally owned.
     75:   */
     76:   MatGetOwnershipRange(A,&Istart,&Iend);

     78:   /*
     79:      Set matrix elements in parallel.
     80:       - Each processor needs to insert only elements that it owns
     81:         locally (but any non-local elements will be sent to the
     82:         appropriate processor during matrix assembly).
     83:       - Always specify global rows and columns of matrix entries.
     84:   */

     86:   PetscOptionsGetBool(NULL,NULL,"-norandom",&flg,NULL);
     87:   if (flg) use_random = 0;
     88:   else use_random = 1;
     89:   if (use_random) {
     90:     PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
     91:     PetscRandomSetFromOptions(rctx);
     92:     PetscRandomSetInterval(rctx,0.0,PETSC_i);
     93:   } else {
     94:     sigma2 = 10.0*PETSC_i;
     95:   }
     96:   h2 = 1.0/((n+1)*(n+1));
     97:   for (Ii=Istart; Ii<Iend; Ii++) {
     98:     v = -1.0; i = Ii/n; j = Ii - i*n;
     99:     if (i>0) {
    100:       J = Ii-n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);
    101:     }
    102:     if (i<n-1) {
    103:       J = Ii+n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);
    104:     }
    105:     if (j>0) {
    106:       J = Ii-1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);
    107:     }
    108:     if (j<n-1) {
    109:       J = Ii+1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);
    110:     }
    111:     if (use_random) {PetscRandomGetValue(rctx,&sigma2);}
    112:     v    = 4.0 - sigma1*h2 + sigma2*h2;
    113:     MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);
    114:   }
    115:   if (use_random) {PetscRandomDestroy(&rctx);}

    117:   /*
    118:      Assemble matrix, using the 2-step process:
    119:        MatAssemblyBegin(), MatAssemblyEnd()
    120:      Computations can be done while messages are in transition
    121:      by placing code between these two statements.
    122:   */
    123:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    124:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

    126:   /*
    127:      Create parallel vectors.
    128:       - When using VecCreate(), VecSetSizes() and VecSetFromOptions(),
    129:       we specify only the vector's global
    130:         dimension; the parallel partitioning is determined at runtime.
    131:       - Note: We form 1 vector from scratch and then duplicate as needed.
    132:   */
    133:   VecCreate(PETSC_COMM_WORLD,&u);
    134:   VecSetSizes(u,PETSC_DECIDE,dim);
    135:   VecSetFromOptions(u);
    136:   VecDuplicate(u,&b);
    137:   VecDuplicate(b,&x);

    139:   /*
    140:      Set exact solution; then compute right-hand-side vector.
    141:   */

    143:   if (use_random) {
    144:     PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
    145:     PetscRandomSetFromOptions(rctx);
    146:     VecSetRandom(u,rctx);
    147:   } else {
    148:     VecSet(u,pfive);
    149:   }
    150:   MatMult(A,u,b);

    152:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    153:                 Create the linear solver and set various options
    154:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    156:   /*
    157:      Create linear solver context
    158:   */
    159:   KSPCreate(PETSC_COMM_WORLD,&ksp);

    161:   /*
    162:      Set operators. Here the matrix that defines the linear system
    163:      also serves as the preconditioning matrix.
    164:   */
    165:   KSPSetOperators(ksp,A,A);

    167:   /*
    168:     Set runtime options, e.g.,
    169:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
    170:   */
    171:   KSPSetFromOptions(ksp);

    173:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    174:                       Solve the linear system
    175:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    177:   KSPSolve(ksp,b,x);

    179:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    180:                       Check solution and clean up
    181:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    183:   /*
    184:       Print the first 3 entries of x; this demonstrates extraction of the
    185:       real and imaginary components of the complex vector, x.
    186:   */
    187:   flg  = PETSC_FALSE;
    188:   PetscOptionsGetBool(NULL,NULL,"-print_x3",&flg,NULL);
    189:   if (flg) {
    190:     VecGetArray(x,&xa);
    191:     PetscPrintf(PETSC_COMM_WORLD,"The first three entries of x are:\n");
    192:     for (i=0; i<3; i++) {
    193:       PetscPrintf(PETSC_COMM_WORLD,"x[%D] = %g + %g i\n",i,(double)PetscRealPart(xa[i]),(double)PetscImaginaryPart(xa[i]));
    194:     }
    195:     VecRestoreArray(x,&xa);
    196:   }

    198:   /*
    199:      Check the error
    200:   */
    201:   VecAXPY(x,none,u);
    202:   VecNorm(x,NORM_2,&norm);
    203:   KSPGetIterationNumber(ksp,&its);
    204:   if (norm < 1.e-12) {
    205:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error < 1.e-12 iterations %D\n",its);
    206:   } else {
    207:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);
    208:   }

    210:   /*
    211:      Free work space.  All PETSc objects should be destroyed when they
    212:      are no longer needed.
    213:   */
    214:   KSPDestroy(&ksp);
    215:   if (use_random) {PetscRandomDestroy(&rctx);}
    216:   VecDestroy(&u); VecDestroy(&x);
    217:   VecDestroy(&b); MatDestroy(&A);
    218:   PetscFinalize();
    219:   return ierr;
    220: }

    223: /*TEST

    225:    build:
    226:       requires: complex

    228:    test:
    229:       args: -n 6 -norandom -pc_type none -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

    231:    testset:
    232:       suffix: deflation
    233:       args: -n 6 -norandom -pc_type deflation -ksp_monitor_short
    234:       test:
    235:       test:
    236:         requires: superlu_dist
    237:         nsize: 3
    238:         args: -pc_deflation_compute_space {{db2 aggregation}}

    240:       test:
    241:         suffix: pc_deflation_init_only-0
    242:         requires: superlu_dist
    243:         nsize: 4
    244:         args: -ksp_type fgmres -pc_deflation_compute_space db4 -pc_deflation_compute_space_size 2 -pc_deflation_levels 2 -deflation_ksp_max_it 10
    245:         #TODO remove suffix and next test when this works
    246:         #args: -pc_deflation_init_only {{0 1}separate output}
    247:         args: -pc_deflation_init_only 0

    249:       test:
    250:         suffix: pc_deflation_init_only-1
    251:         requires: superlu_dist
    252:         nsize: 4
    253:         args: -ksp_type fgmres -pc_deflation_compute_space db4 -pc_deflation_compute_space_size 2 -pc_deflation_levels 2 -deflation_ksp_max_it 10
    254:         args: -pc_deflation_init_only 1

    256: TEST*/