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"; 6 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*/ 13 14 /* 15 16 This example models the partial differential equation 17 18 - Div((1 + ||GRAD T||^2)^(1/2) (GRAD T)) = 0. 19 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 22 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. 26 27 */ 28 29 #include <petscsnes.h> 30 #include <petscdm.h> 31 #include <petscdmda.h> 32 33 extern PetscErrorCode FormFunctionLocal(DMDALocalInfo*,PetscScalar**,PetscScalar**,void*); 34 35 int main(int argc,char **argv) 36 { 37 SNES snes; 38 PetscErrorCode ierr; 39 PetscInt its,lits; 40 PetscReal litspit; 41 DM da; 42 43 ierr = PetscInitialize(&argc,&argv,NULL,help);if (ierr) return ierr; 44 /* 45 Set the DMDA (grid structure) for the grids. 46 */ 47 ierr = DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,5,5,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da);CHKERRQ(ierr); 48 ierr = DMSetFromOptions(da);CHKERRQ(ierr); 49 ierr = DMSetUp(da);CHKERRQ(ierr); 50 ierr = DMDASNESSetFunctionLocal(da,INSERT_VALUES,(PetscErrorCode (*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,NULL);CHKERRQ(ierr); 51 ierr = SNESCreate(PETSC_COMM_WORLD,&snes);CHKERRQ(ierr); 52 ierr = SNESSetDM(snes,da);CHKERRQ(ierr); 53 ierr = DMDestroy(&da);CHKERRQ(ierr); 54 55 ierr = SNESSetFromOptions(snes);CHKERRQ(ierr); 56 57 ierr = SNESSolve(snes,0,0);CHKERRQ(ierr); 58 ierr = SNESGetIterationNumber(snes,&its);CHKERRQ(ierr); 59 ierr = SNESGetLinearSolveIterations(snes,&lits);CHKERRQ(ierr); 60 litspit = ((PetscReal)lits)/((PetscReal)its); 61 ierr = PetscPrintf(PETSC_COMM_WORLD,"Number of SNES iterations = %D\n",its);CHKERRQ(ierr); 62 ierr = PetscPrintf(PETSC_COMM_WORLD,"Number of Linear iterations = %D\n",lits);CHKERRQ(ierr); 63 ierr = PetscPrintf(PETSC_COMM_WORLD,"Average Linear its / SNES = %e\n",(double)litspit);CHKERRQ(ierr); 64 65 ierr = SNESDestroy(&snes);CHKERRQ(ierr); 66 ierr = PetscFinalize(); 67 return ierr; 68 } 69 70 PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,PetscScalar **t,PetscScalar **f,void *ptr) 71 { 72 PetscInt i,j; 73 PetscScalar hx,hy; 74 PetscScalar gradup,graddown,gradleft,gradright,gradx,grady; 75 PetscScalar coeffup,coeffdown,coeffleft,coeffright; 76 77 PetscFunctionBeginUser; 78 hx = 1.0/(PetscReal)(info->mx-1); hy = 1.0/(PetscReal)(info->my-1); 79 80 /* Evaluate function */ 81 for (j=info->ys; j<info->ys+info->ym; j++) { 82 for (i=info->xs; i<info->xs+info->xm; i++) { 83 84 if (i == 0 || i == info->mx-1 || j == 0 || j == info->my-1) { 85 f[j][i] = t[j][i] - (1.0 - (2.0*hx*(PetscReal)i - 1.0)*(2.0*hx*(PetscReal)i - 1.0)); 86 } else { 87 88 gradup = (t[j+1][i] - t[j][i])/hy; 89 graddown = (t[j][i] - t[j-1][i])/hy; 90 gradright = (t[j][i+1] - t[j][i])/hx; 91 gradleft = (t[j][i] - t[j][i-1])/hx; 92 93 gradx = .5*(t[j][i+1] - t[j][i-1])/hx; 94 grady = .5*(t[j+1][i] - t[j-1][i])/hy; 95 96 coeffup = 1.0/PetscSqrtScalar(1.0 + gradup*gradup + gradx*gradx); 97 coeffdown = 1.0/PetscSqrtScalar(1.0 + graddown*graddown + gradx*gradx); 98 99 coeffleft = 1.0/PetscSqrtScalar(1.0 + gradleft*gradleft + grady*grady); 100 coeffright = 1.0/PetscSqrtScalar(1.0 + gradright*gradright + grady*grady); 101 102 f[j][i] = (coeffup*gradup - coeffdown*graddown)*hx + (coeffright*gradright - coeffleft*gradleft)*hy; 103 } 104 105 } 106 } 107 PetscFunctionReturn(0); 108 } 109 110 /*TEST 111 112 test: 113 args: -pc_type mg -da_refine 1 -ksp_type fgmres 114 115 test: 116 suffix: 2 117 nsize: 2 118 args: -pc_type mg -da_refine 1 -ksp_type fgmres 119 120 TEST*/ 121