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: /*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.

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

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

 27: */

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

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

 35: int main(int argc,char **argv)
 36: {
 37:   SNES           snes;
 38:   PetscInt       its,lits;
 39:   PetscReal      litspit;
 40:   DM             da;

 42:   PetscInitialize(&argc,&argv,NULL,help);
 43:   /*
 44:       Set the DMDA (grid structure) for the grids.
 45:   */
 46:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,5,5,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da);
 47:   DMSetFromOptions(da);
 48:   DMSetUp(da);
 49:   DMDASNESSetFunctionLocal(da,INSERT_VALUES,(PetscErrorCode (*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,NULL);
 50:   SNESCreate(PETSC_COMM_WORLD,&snes);
 51:   SNESSetDM(snes,da);
 52:   DMDestroy(&da);

 54:   SNESSetFromOptions(snes);

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

 64:   SNESDestroy(&snes);
 65:   PetscFinalize();
 66:   return 0;
 67: }

 69: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,PetscScalar **t,PetscScalar **f,void *ptr)
 70: {
 71:   PetscInt    i,j;
 72:   PetscScalar hx,hy;
 73:   PetscScalar gradup,graddown,gradleft,gradright,gradx,grady;
 74:   PetscScalar coeffup,coeffdown,coeffleft,coeffright;

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

 79:   /* Evaluate function */
 80:   for (j=info->ys; j<info->ys+info->ym; j++) {
 81:     for (i=info->xs; i<info->xs+info->xm; i++) {

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

 87:         gradup    = (t[j+1][i] - t[j][i])/hy;
 88:         graddown  = (t[j][i] - t[j-1][i])/hy;
 89:         gradright = (t[j][i+1] - t[j][i])/hx;
 90:         gradleft  = (t[j][i] - t[j][i-1])/hx;

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

 95:         coeffup   = 1.0/PetscSqrtScalar(1.0 + gradup*gradup + gradx*gradx);
 96:         coeffdown = 1.0/PetscSqrtScalar(1.0 + graddown*graddown + gradx*gradx);

 98:         coeffleft  = 1.0/PetscSqrtScalar(1.0 + gradleft*gradleft + grady*grady);
 99:         coeffright = 1.0/PetscSqrtScalar(1.0 + gradright*gradright + grady*grady);

101:         f[j][i] = (coeffup*gradup - coeffdown*graddown)*hx + (coeffright*gradright - coeffleft*gradleft)*hy;
102:       }

104:     }
105:   }
106:   return 0;
107: }

109: /*TEST

111:    test:
112:       args: -pc_type mg -da_refine 1 -ksp_type fgmres

114:    test:
115:       suffix: 2
116:       nsize: 2
117:       args: -pc_type mg -da_refine 1 -ksp_type fgmres

119:    test:
120:       suffix: 3
121:       nsize: 2
122:       args: -pc_type mg -da_refine 1 -ksp_type fgmres -snes_type newtontrdc -snes_trdc_use_cauchy false

124:    test:
125:       suffix: 4
126:       nsize: 2
127:       args: -pc_type mg -da_refine 1 -ksp_type fgmres -snes_type newtontrdc
128:       filter: sed -e "s/SNES iterations = 1[1-3]/SNES iterations = 13/g" |sed -e "s/Linear iterations = 2[8-9]/Linear iterations = 29/g" |sed -e "s/Linear iterations = 3[0-1]/Linear iterations = 29/g"

130: TEST*/