Date: 2013-07-02T14:50:07+00:00

Actual source code: ex25.c
petsc-3.4.2 2013-07-02

      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: /*T
      8:    Concepts: SNES^solving a system of nonlinear equations
      9:    Concepts: DMDA^using distributed arrays
     10:    Concepts: multigrid;
     11:    Processors: n
     12: T*/

     14: /*

     16:     This example models the partial differential equation

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

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

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

     28: */

     30: #include <petscsnes.h>
     31: #include <petscdmda.h>

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

     37: int main(int argc,char **argv)
     38: {
     39:   SNES           snes;
     41:   PetscInt       its,lits;
     42:   PetscReal      litspit;
     43:   DM             da;

     45:   PetscInitialize(&argc,&argv,NULL,help);

     47:   /*
     48:       Set the DMDA (grid structure) for the grids.
     49:   */
     50:   DMDACreate2d(PETSC_COMM_WORLD, DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_NONE,DMDA_STENCIL_STAR,-5,-5,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da);
     51:   DMDASNESSetFunctionLocal(da,INSERT_VALUES,(PetscErrorCode (*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,NULL);
     52:   SNESCreate(PETSC_COMM_WORLD,&snes);
     53:   SNESSetDM(snes,da);
     54:   DMDestroy(&da);

     56:   SNESSetFromOptions(snes);

     58:   SNESSolve(snes,0,0);
     59:   SNESGetIterationNumber(snes,&its);
     60:   SNESGetLinearSolveIterations(snes,&lits);
     61:   litspit = ((PetscReal)lits)/((PetscReal)its);
     62:   PetscPrintf(PETSC_COMM_WORLD,"Number of SNES iterations = %D\n",its);
     63:   PetscPrintf(PETSC_COMM_WORLD,"Number of Linear iterations = %D\n",lits);
     64:   PetscPrintf(PETSC_COMM_WORLD,"Average Linear its / SNES = %e\n",litspit);

     66:   SNESDestroy(&snes);
     67:   PetscFinalize();

     69:   return 0;
     70: }

     74: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,PetscScalar **t,PetscScalar **f,void *ptr)
     75: {
     76:   PetscInt    i,j;
     77:   PetscScalar hx,hy;
     78:   PetscScalar gradup,graddown,gradleft,gradright,gradx,grady;
     79:   PetscScalar coeffup,coeffdown,coeffleft,coeffright;

     82:   hx = 1.0/(PetscReal)(info->mx-1);  hy    = 1.0/(PetscReal)(info->my-1);

     84:   /* Evaluate function */
     85:   for (j=info->ys; j<info->ys+info->ym; j++) {
     86:     for (i=info->xs; i<info->xs+info->xm; i++) {

     88:       if (i == 0 || i == info->mx-1 || j == 0 || j == info->my-1) {
     89:         f[j][i] = t[j][i] - (1.0 - (2.0*hx*(PetscReal)i - 1.0)*(2.0*hx*(PetscReal)i - 1.0));
     90:       } else {

     92:         gradup    = (t[j+1][i] - t[j][i])/hy;
     93:         graddown  = (t[j][i] - t[j-1][i])/hy;
     94:         gradright = (t[j][i+1] - t[j][i])/hx;
     95:         gradleft  = (t[j][i] - t[j][i-1])/hx;

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

    100:         coeffup   = 1.0/PetscSqrtScalar(1.0 + gradup*gradup + gradx*gradx);
    101:         coeffdown = 1.0/PetscSqrtScalar(1.0 + graddown*graddown + gradx*gradx);

    103:         coeffleft  = 1.0/PetscSqrtScalar(1.0 + gradleft*gradleft + grady*grady);
    104:         coeffright = 1.0/PetscSqrtScalar(1.0 + gradright*gradright + grady*grady);

    106:         f[j][i] = (coeffup*gradup - coeffdown*graddown)*hx + (coeffright*gradright - coeffleft*gradleft)*hy;
    107:       }

    109:     }
    110:   }
    111:   return(0);
    112: }