Actual source code: ex11.c

      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*/

     11: /*
     12:    Description: Solves a complex linear system in parallel with KSP.

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

     21:    Compiling the code:
     22:       This code uses the complex numbers version of PETSc, so configure
     23:       must be run to enable this
     24: */

     26: /*
     27:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
     28:   automatically includes:
     29:      petsc.h       - base PETSc routines   petscvec.h - vectors
     30:      petscsys.h    - system routines       petscmat.h - matrices
     31:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
     32:      petscviewer.h - viewers               petscpc.h  - preconditioners
     33: */
     34:  #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,I,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:   PetscTruth     flg;

     51:   PetscInitialize(&argc,&args,(char *)0,help);
     52: #if !defined(PETSC_USE_COMPLEX)
     53:   SETERRQ(1,"This example requires complex numbers");
     54: #endif

     56:   PetscOptionsGetReal(PETSC_NULL,"-sigma1",&sigma1,PETSC_NULL);
     57:   PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
     58:   dim = n*n;

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

     74:   /*
     75:      Currently, all PETSc parallel matrix formats are partitioned by
     76:      contiguous chunks of rows across the processors.  Determine which
     77:      rows of the matrix are locally owned.
     78:   */
     79:   MatGetOwnershipRange(A,&Istart,&Iend);

     81:   /*
     82:      Set matrix elements in parallel.
     83:       - Each processor needs to insert only elements that it owns
     84:         locally (but any non-local elements will be sent to the
     85:         appropriate processor during matrix assembly).
     86:       - Always specify global rows and columns of matrix entries.
     87:   */

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

    114:   /*
    115:      Assemble matrix, using the 2-step process:
    116:        MatAssemblyBegin(), MatAssemblyEnd()
    117:      Computations can be done while messages are in transition
    118:      by placing code between these two statements.
    119:   */
    120:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    121:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

    123:   /*
    124:      Create parallel vectors.
    125:       - When using VecCreate(), VecSetSizes() and VecSetFromOptions(),
    126:       we specify only the vector's global
    127:         dimension; the parallel partitioning is determined at runtime.
    128:       - Note: We form 1 vector from scratch and then duplicate as needed.
    129:   */
    130:   VecCreate(PETSC_COMM_WORLD,&u);
    131:   VecSetSizes(u,PETSC_DECIDE,dim);
    132:   VecSetFromOptions(u);
    133:   VecDuplicate(u,&b);
    134:   VecDuplicate(b,&x);

    136:   /*
    137:      Set exact solution; then compute right-hand-side vector.
    138:   */
    139:
    140:   if (use_random) {
    141:     PetscRandomCreate(PETSC_COMM_WORLD,RANDOM_DEFAULT,&rctx);
    142:     VecSetRandom(u,rctx);
    143:   } else {
    144:     VecSet(u,pfive);
    145:   }
    146:   MatMult(A,u,b);

    148:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    149:                 Create the linear solver and set various options
    150:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    152:   /*
    153:      Create linear solver context
    154:   */
    155:   KSPCreate(PETSC_COMM_WORLD,&ksp);

    157:   /*
    158:      Set operators. Here the matrix that defines the linear system
    159:      also serves as the preconditioning matrix.
    160:   */
    161:   KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);

    163:   /*
    164:     Set runtime options, e.g.,
    165:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
    166:   */
    167:   KSPSetFromOptions(ksp);

    169:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    170:                       Solve the linear system
    171:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    173:   KSPSolve(ksp,b,x);

    175:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    176:                       Check solution and clean up
    177:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    179:   /*
    180:       Print the first 3 entries of x; this demonstrates extraction of the
    181:       real and imaginary components of the complex vector, x.
    182:   */
    183:   PetscOptionsHasName(PETSC_NULL,"-print_x3",&flg);
    184:   if (flg) {
    185:     VecGetArray(x,&xa);
    186:     PetscPrintf(PETSC_COMM_WORLD,"The first three entries of x are:\n");
    187:     for (i=0; i<3; i++){
    188:       PetscPrintf(PETSC_COMM_WORLD,"x[%D] = %g + %g i\n",i,PetscRealPart(xa[i]),PetscImaginaryPart(xa[i]));
    189:   }
    190:     VecRestoreArray(x,&xa);
    191:   }

    193:   /*
    194:      Check the error
    195:   */
    196:   VecAXPY(x,none,u);
    197:   VecNorm(x,NORM_2,&norm);
    198:   KSPGetIterationNumber(ksp,&its);
    199:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A iterations %D\n",norm,its);

    201:   /*
    202:      Free work space.  All PETSc objects should be destroyed when they
    203:      are no longer needed.
    204:   */
    205:   KSPDestroy(ksp);
    206:   if (use_random) {PetscRandomDestroy(rctx);}
    207:   VecDestroy(u); VecDestroy(x);
    208:   VecDestroy(b); MatDestroy(A);
    209:   PetscFinalize();
    210:   return 0;
    211: }