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 /* 8 9 This example models the partial differential equation 10 11 - Div((1 + ||GRAD T||^2)^(1/2) (GRAD T)) = 0. 12 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 15 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. 19 20 */ 21 22 #include <petscsnes.h> 23 #include <petscdm.h> 24 #include <petscdmda.h> 25 26 extern PetscErrorCode FormFunctionLocal(DMDALocalInfo*,PetscScalar**,PetscScalar**,void*); 27 28 int main(int argc,char **argv) 29 { 30 SNES snes; 31 PetscInt its,lits; 32 PetscReal litspit; 33 DM da; 34 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)); 47 48 PetscCall(SNESSetFromOptions(snes)); 49 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)); 57 58 PetscCall(SNESDestroy(&snes)); 59 PetscCall(PetscFinalize()); 60 return 0; 61 } 62 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; 69 70 PetscFunctionBeginUser; 71 hx = 1.0/(PetscReal)(info->mx-1); hy = 1.0/(PetscReal)(info->my-1); 72 73 /* Evaluate function */ 74 for (j=info->ys; j<info->ys+info->ym; j++) { 75 for (i=info->xs; i<info->xs+info->xm; i++) { 76 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 81 gradup = (t[j+1][i] - t[j][i])/hy; 82 graddown = (t[j][i] - t[j-1][i])/hy; 83 gradright = (t[j][i+1] - t[j][i])/hx; 84 gradleft = (t[j][i] - t[j][i-1])/hx; 85 86 gradx = .5*(t[j][i+1] - t[j][i-1])/hx; 87 grady = .5*(t[j+1][i] - t[j-1][i])/hy; 88 89 coeffup = 1.0/PetscSqrtScalar(1.0 + gradup*gradup + gradx*gradx); 90 coeffdown = 1.0/PetscSqrtScalar(1.0 + graddown*graddown + gradx*gradx); 91 92 coeffleft = 1.0/PetscSqrtScalar(1.0 + gradleft*gradleft + grady*grady); 93 coeffright = 1.0/PetscSqrtScalar(1.0 + gradright*gradright + grady*grady); 94 95 f[j][i] = (coeffup*gradup - coeffdown*graddown)*hx + (coeffright*gradright - coeffleft*gradleft)*hy; 96 } 97 98 } 99 } 100 PetscFunctionReturn(0); 101 } 102 103 /*TEST 104 105 test: 106 args: -pc_type mg -da_refine 1 -ksp_type fgmres 107 108 test: 109 suffix: 2 110 nsize: 2 111 args: -pc_type mg -da_refine 1 -ksp_type fgmres 112 113 test: 114 suffix: 3 115 nsize: 2 116 args: -pc_type mg -da_refine 1 -ksp_type fgmres -snes_type newtontrdc -snes_trdc_use_cauchy false 117 118 test: 119 suffix: 4 120 nsize: 2 121 args: -pc_type mg -da_refine 1 -ksp_type fgmres -snes_type newtontrdc 122 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" 123 124 TEST*/ 125