Actual source code: ex25.c

petsc-master 2018-04-21
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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

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 <petscdm.h>
32:  #include <petscdmda.h>

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

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

44:   PetscInitialize(&argc,&argv,NULL,help);if (ierr) return ierr;
45:   /*
46:       Set the DMDA (grid structure) for the grids.
47:   */
48:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,5,5,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da);
49:   DMSetFromOptions(da);
50:   DMSetUp(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",(double)litspit);

66:   SNESDestroy(&snes);
67:   PetscFinalize();
68:   return ierr;
69: }

71: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,PetscScalar **t,PetscScalar **f,void *ptr)
72: {
73:   PetscInt    i,j;
74:   PetscScalar hx,hy;
76:   PetscScalar coeffup,coeffdown,coeffleft,coeffright;

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

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

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

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

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

104:       }

106:     }
107:   }
108:   return(0);
109: }

112: /*TEST

114:    test:
115:       args: -pc_type mg -da_refine 1 -ksp_type fgmres

117:    test:
118:       suffix: 2
119:       nsize: 2
120:       args: -pc_type mg -da_refine 1 -ksp_type fgmres

122: TEST*/