Actual source code: ex23.c
2: static char help[] = "Solves PDE problem from ex22.c\n\n";
4: #include petscda.h
5: #include petscpf.h
6: #include petscsnes.h
7: #include petscdmmg.h
9: /*
11: In this example the PDE is
12: Uxx + U^2 = 2,
13: u(0) = .25
14: u(1) = 0
16: The exact solution for u is given by u(x) = x*x - 1.25*x + .25
18: Use the usual centered finite differences.
21: See ex22.c for a design optimization problem
23: */
25: typedef struct {
26: PetscViewer u_viewer;
27: PetscViewer fu_viewer;
28: } UserCtx;
35: int main(int argc,char **argv)
36: {
38: UserCtx user;
39: DA da;
40: DMMG *dmmg;
42: PetscInitialize(&argc,&argv,PETSC_NULL,help);
44: /* Hardwire several options; can be changed at command line */
45: PetscOptionsSetValue("-dmmg_grid_sequence",PETSC_NULL);
46: PetscOptionsSetValue("-ksp_type","fgmres");
47: PetscOptionsSetValue("-ksp_max_it","5");
48: PetscOptionsSetValue("-pc_mg_type","full");
49: PetscOptionsSetValue("-mg_coarse_ksp_type","gmres");
50: PetscOptionsSetValue("-mg_levels_ksp_type","gmres");
51: PetscOptionsSetValue("-mg_coarse_ksp_max_it","3");
52: PetscOptionsSetValue("-mg_levels_ksp_max_it","3");
53: /* PetscOptionsSetValue("-snes_mf_type","wp"); */
54: /* PetscOptionsSetValue("-snes_mf_compute_norma","no"); */
55: /* PetscOptionsSetValue("-snes_mf_compute_normu","no"); */
56: PetscOptionsSetValue("-snes_ls","basic");
57: /* PetscOptionsSetValue("-dmmg_jacobian_mf_fd",0); */
58: /* PetscOptionsSetValue("-snes_ls","basicnonorms"); */
59: PetscOptionsInsert(&argc,&argv,PETSC_NULL);
60:
61: /* Create a global vector from a da arrays */
62: DACreate1d(PETSC_COMM_WORLD,DA_NONPERIODIC,-5,1,1,PETSC_NULL,&da);
64: /* create graphics windows */
65: PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"u - state variables",-1,-1,-1,-1,&user.u_viewer);
66: PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"fu - discretization of function",-1,-1,-1,-1,&user.fu_viewer);
68: /* create nonlinear multi-level solver */
69: DMMGCreate(PETSC_COMM_WORLD,2,&user,&dmmg);
70: DMMGSetDM(dmmg,(DM)da);
71: DMMGSetSNES(dmmg,FormFunction,PETSC_NULL);
72: DMMGSetSNESLocali(dmmg,FormFunctionLocali,0,0);
73: DMMGSolve(dmmg);
74: DMMGDestroy(dmmg);
76: DADestroy(da);
77: PetscViewerDestroy(user.u_viewer);
78: PetscViewerDestroy(user.fu_viewer);
80: PetscFinalize();
81: return 0;
82: }
83:
84: /*
85: This local function acts on the ghosted version of U (accessed via DAGetLocalVector())
86: BUT the global, nonghosted version of FU
88: */
89: PetscErrorCode FormFunction(SNES snes,Vec U,Vec FU,void* dummy)
90: {
91: DMMG dmmg = (DMMG)dummy;
93: PetscInt xs,xm,i,N;
94: PetscScalar *u,*fu,d,h;
95: Vec vu;
96: DA da = (DA) dmmg->dm;
99: DAGetLocalVector(da,&vu);
100: DAGlobalToLocalBegin(da,U,INSERT_VALUES,vu);
101: DAGlobalToLocalEnd(da,U,INSERT_VALUES,vu);
103: DAGetCorners(da,&xs,PETSC_NULL,PETSC_NULL,&xm,PETSC_NULL,PETSC_NULL);
104: DAGetInfo(da,0,&N,0,0,0,0,0,0,0,0,0);
105: DAVecGetArray(da,vu,&u);
106: DAVecGetArray(da,FU,&fu);
107: d = N-1.0;
108: h = 1.0/d;
110: for (i=xs; i<xs+xm; i++) {
111: if (i == 0) fu[0] = 2.0*d*(u[0] - .25) + h*u[0]*u[0];
112: else if (i == N-1) fu[N-1] = 2.0*d*u[N-1] + h*u[N-1]*u[N-1];
113: else fu[i] = -(d*(u[i+1] - 2.0*u[i] + u[i-1]) - 2.0*h) + h*u[i]*u[i];
114: }
116: DAVecRestoreArray(da,vu,&u);
117: DAVecRestoreArray(da,FU,&fu);
118: DARestoreLocalVector(da,&vu);
119: PetscLogFlops(9*N);
120: return(0);
121: }
123: PetscErrorCode FormFunctionLocali(DALocalInfo *info,MatStencil *pt,PetscScalar *u,PetscScalar *fu,void* dummy)
124: {
125: PetscInt i,N = info->mx;
126: PetscScalar d,h;
129: d = N-1.0;
130: h = 1.0/d;
132: i = pt->i;
133: if (i == 0) *fu = 2.0*d*(u[0] - .25) + h*u[0]*u[0];
134: else if (i == N-1) *fu = 2.0*d*u[N-1] + h*u[N-1]*u[N-1];
135: else *fu = -(d*(u[i+1] - 2.0*u[i] + u[i-1]) - 2.0*h) + h*u[i]*u[i];
137: return(0);
138: }