Actual source code: ex25.c

      1: static const char help[] = "Minimum surface problem in 2D.\n\
      2: Uses 2-dimensional distributed arrays.\n\
      3: \n\
      4:   Solves the linear systems via multilevel methods \n\
      5: \n\n";

      7: /*

      9:     This example models the partial differential equation

     11:          - Div((1 + ||GRAD T||^2)^(1/2) (GRAD T)) = 0.

     13:     in the unit square, which is uniformly discretized in each of x and
     14:     y in this simple encoding.  The degrees of freedom are vertex centered

     16:     A finite difference approximation with the usual 5-point stencil
     17:     is used to discretize the boundary value problem to obtain a
     18:     nonlinear system of equations.

     20: */

     22: #include <petscsnes.h>
     23: #include <petscdm.h>
     24: #include <petscdmda.h>

     26: extern PetscErrorCode FormFunctionLocal(DMDALocalInfo *, PetscScalar **, PetscScalar **, void *);

     28: int main(int argc, char **argv)
     29: {
     30:   SNES      snes;
     31:   PetscInt  its, lits;
     32:   PetscReal litspit;
     33:   DM        da;

     35:   PetscFunctionBeginUser;
     36:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
     37:   /*
     38:       Set the DMDA (grid structure) for the grids.
     39:   */
     40:   PetscCall(DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DMDA_STENCIL_STAR, 5, 5, PETSC_DECIDE, PETSC_DECIDE, 1, 1, 0, 0, &da));
     41:   PetscCall(DMSetFromOptions(da));
     42:   PetscCall(DMSetUp(da));
     43:   PetscCall(DMDASNESSetFunctionLocal(da, INSERT_VALUES, (PetscErrorCode (*)(DMDALocalInfo *, void *, void *, void *))FormFunctionLocal, NULL));
     44:   PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes));
     45:   PetscCall(SNESSetDM(snes, da));
     46:   PetscCall(DMDestroy(&da));

     48:   PetscCall(SNESSetFromOptions(snes));

     50:   PetscCall(SNESSolve(snes, 0, 0));
     51:   PetscCall(SNESGetIterationNumber(snes, &its));
     52:   PetscCall(SNESGetLinearSolveIterations(snes, &lits));
     53:   litspit = ((PetscReal)lits) / ((PetscReal)its);
     54:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Number of SNES iterations = %" PetscInt_FMT "\n", its));
     55:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Number of Linear iterations = %" PetscInt_FMT "\n", lits));
     56:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Average Linear its / SNES = %e\n", (double)litspit));

     58:   PetscCall(SNESDestroy(&snes));
     59:   PetscCall(PetscFinalize());
     60:   return 0;
     61: }

     63: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info, PetscScalar **t, PetscScalar **f, void *ptr)
     64: {
     65:   PetscInt    i, j;
     66:   PetscScalar hx, hy;
     67:   PetscScalar gradup, graddown, gradleft, gradright, gradx, grady;
     68:   PetscScalar coeffup, coeffdown, coeffleft, coeffright;

     70:   PetscFunctionBeginUser;
     71:   hx = 1.0 / (PetscReal)(info->mx - 1);
     72:   hy = 1.0 / (PetscReal)(info->my - 1);

     74:   /* Evaluate function */
     75:   for (j = info->ys; j < info->ys + info->ym; j++) {
     76:     for (i = info->xs; i < info->xs + info->xm; i++) {
     77:       if (i == 0 || i == info->mx - 1 || j == 0 || j == info->my - 1) {
     78:         f[j][i] = t[j][i] - (1.0 - (2.0 * hx * (PetscReal)i - 1.0) * (2.0 * hx * (PetscReal)i - 1.0));
     79:       } else {
     80:         gradup    = (t[j + 1][i] - t[j][i]) / hy;
     81:         graddown  = (t[j][i] - t[j - 1][i]) / hy;
     82:         gradright = (t[j][i + 1] - t[j][i]) / hx;
     83:         gradleft  = (t[j][i] - t[j][i - 1]) / hx;

     85:         gradx = .5 * (t[j][i + 1] - t[j][i - 1]) / hx;
     86:         grady = .5 * (t[j + 1][i] - t[j - 1][i]) / hy;

     88:         coeffup   = 1.0 / PetscSqrtScalar(1.0 + gradup * gradup + gradx * gradx);
     89:         coeffdown = 1.0 / PetscSqrtScalar(1.0 + graddown * graddown + gradx * gradx);

     91:         coeffleft  = 1.0 / PetscSqrtScalar(1.0 + gradleft * gradleft + grady * grady);
     92:         coeffright = 1.0 / PetscSqrtScalar(1.0 + gradright * gradright + grady * grady);

     94:         f[j][i] = (coeffup * gradup - coeffdown * graddown) * hx + (coeffright * gradright - coeffleft * gradleft) * hy;
     95:       }
     96:     }
     97:   }
     98:   PetscFunctionReturn(PETSC_SUCCESS);
     99: }

    101: /*TEST

    103:    test:
    104:       args: -pc_type mg -da_refine 1 -ksp_type fgmres

    106:    test:
    107:       suffix: 2
    108:       nsize: 2
    109:       args: -pc_type mg -da_refine 1 -ksp_type fgmres

    111:    test:
    112:       suffix: 3
    113:       nsize: 2
    114:       args: -pc_type mg -da_refine 1 -ksp_type fgmres -snes_type newtontrdc -snes_trdc_use_cauchy false

    116:    test:
    117:       suffix: 4
    118:       nsize: 2
    119:       args: -pc_type mg -da_refine 1 -ksp_type fgmres -snes_type newtontrdc
    120:       filter: sed -e "s/SNES iterations = 1[0-3]/SNES iterations = 13/g" |sed -e "s/Linear iterations = 2[7-9]/Linear iterations = 29/g" |sed -e "s/Linear iterations = 3[0-1]/Linear iterations = 29/g"

    122: TEST*/