Actual source code: ex22.c
1: /*$Id: ex22.c,v 1.23 2001/08/07 21:31:17 bsmith Exp $*/
3: static char help[] = "Solves PDE optimization problem.nn";
5: #include petscda.h
6: #include petscpf.h
7: #include petscsnes.h
9: /*
11: w - design variables (what we change to get an optimal solution)
12: u - state variables (i.e. the PDE solution)
13: lambda - the Lagrange multipliers
15: U = (w u lambda)
17: fu, fw, flambda contain the gradient of L(w,u,lambda)
19: FU = (fw fu flambda)
21: In this example the PDE is
22: Uxx = 2,
23: u(0) = w(0), thus this is the free parameter
24: u(1) = 0
25: the function we wish to minimize is
26: integral u^{2}
28: The exact solution for u is given by u(x) = x*x - 1.25*x + .25
30: Use the usual centered finite differences.
32: Note we treat the problem as non-linear though it happens to be linear
34: See ex21.c for the same code, but that does NOT interlaces the u and the lambda
36: The vectors u_lambda and fu_lambda contain the u and the lambda interlaced
37: */
39: typedef struct {
40: PetscViewer u_lambda_viewer;
41: PetscViewer fu_lambda_viewer;
42: } UserCtx;
44: extern int FormFunction(SNES,Vec,Vec,void*);
45: extern int Monitor(SNES,int,PetscReal,void*);
48: int main(int argc,char **argv)
49: {
50: int ierr;
51: UserCtx user;
52: DA da;
53: DMMG *dmmg;
54: VecPack packer;
56: PetscInitialize(&argc,&argv,PETSC_NULL,help);
58: /* Hardwire several options; can be changed at command line */
59: PetscOptionsSetValue("-dmmg_grid_sequence",PETSC_NULL);
60: PetscOptionsSetValue("-ksp_type","fgmres");
61: PetscOptionsSetValue("-ksp_max_it","5");
62: PetscOptionsSetValue("-pc_mg_type","full");
63: PetscOptionsSetValue("-mg_coarse_ksp_type","gmres");
64: PetscOptionsSetValue("-mg_levels_ksp_type","gmres");
65: PetscOptionsSetValue("-mg_coarse_ksp_max_it","6");
66: PetscOptionsSetValue("-mg_levels_ksp_max_it","3");
67: PetscOptionsSetValue("-snes_mf_type","wp");
68: PetscOptionsSetValue("-snes_mf_compute_norma","no");
69: PetscOptionsSetValue("-snes_mf_compute_normu","no");
70: PetscOptionsSetValue("-snes_ls","basic");
71: PetscOptionsSetValue("-dmmg_jacobian_mf_fd",0);
72: /* PetscOptionsSetValue("-snes_ls","basicnonorms"); */
73: PetscOptionsInsert(&argc,&argv,PETSC_NULL);
75: /* Create a global vector that includes a single redundant array and two da arrays */
76: VecPackCreate(PETSC_COMM_WORLD,&packer);
77: VecPackAddArray(packer,1);
78: DACreate1d(PETSC_COMM_WORLD,DA_NONPERIODIC,-5,2,1,PETSC_NULL,&da);
79: VecPackAddDA(packer,da);
81: /* create graphics windows */
82: PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"u_lambda - state variables and Lagrange multipliers",-1,-1,-1,-1,&user.u_lambda_viewer);
83: PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"fu_lambda - derivate w.r.t. state variables and Lagrange multipliers",-1,-1,-1,-1,&user.fu_lambda_viewer);
85: /* create nonlinear multi-level solver */
86: DMMGCreate(PETSC_COMM_WORLD,2,&user,&dmmg);
87: DMMGSetDM(dmmg,(DM)packer);
88: DMMGSetSNES(dmmg,FormFunction,PETSC_NULL);
89: /*
90: for (i=0; i<DMMGGetLevels(dmmg); i++) {
91: SNESSetMonitor(dmmg[i]->snes,Monitor,dmmg[i],0);
92: }*/
93: DMMGSolve(dmmg);
94: DMMGDestroy(dmmg);
96: DADestroy(da);
97: VecPackDestroy(packer);
98: PetscViewerDestroy(user.u_lambda_viewer);
99: PetscViewerDestroy(user.fu_lambda_viewer);
101: PetscFinalize();
102: return 0;
103: }
105: typedef struct {
106: PetscScalar u;
107: PetscScalar lambda;
108: } ULambda;
109:
110: /*
111: Evaluates FU = Gradiant(L(w,u,lambda))
113: This local function acts on the ghosted version of U (accessed via VecPackGetLocalVectors() and
114: VecPackScatter()) BUT the global, nonghosted version of FU (via VecPackGetAccess()).
116: */
117: int FormFunction(SNES snes,Vec U,Vec FU,void* dummy)
118: {
119: DMMG dmmg = (DMMG)dummy;
120: int ierr,xs,xm,i,N,nredundant;
121: ULambda *u_lambda,*fu_lambda;
122: PetscScalar d,h,*w,*fw;
123: Vec vu_lambda,vfu_lambda;
124: DA da;
125: VecPack packer = (VecPack)dmmg->dm;
128: VecPackGetEntries(packer,&nredundant,&da);
129: VecPackGetLocalVectors(packer,&w,&vu_lambda);
130: VecPackScatter(packer,U,w,vu_lambda);
131: VecPackGetAccess(packer,FU,&fw,&vfu_lambda);
133: DAGetCorners(da,&xs,PETSC_NULL,PETSC_NULL,&xm,PETSC_NULL,PETSC_NULL);
134: DAGetInfo(da,0,&N,0,0,0,0,0,0,0,0,0);
135: DAVecGetArray(da,vu_lambda,(void**)&u_lambda);
136: DAVecGetArray(da,vfu_lambda,(void**)&fu_lambda);
137: d = N-1.0;
138: h = 1.0/d;
140: /* derivative of L() w.r.t. w */
141: if (xs == 0) { /* only first processor computes this */
142: fw[0] = -2.0*d*u_lambda[0].lambda;
143: }
145: /* derivative of L() w.r.t. u */
146: for (i=xs; i<xs+xm; i++) {
147: if (i == 0) fu_lambda[0].lambda = h*u_lambda[0].u + 2.*d*u_lambda[0].lambda - d*u_lambda[1].lambda;
148: else if (i == 1) fu_lambda[1].lambda = 2.*h*u_lambda[1].u + 2.*d*u_lambda[1].lambda - d*u_lambda[2].lambda;
149: else if (i == N-1) fu_lambda[N-1].lambda = h*u_lambda[N-1].u + 2.*d*u_lambda[N-1].lambda - d*u_lambda[N-2].lambda;
150: else if (i == N-2) fu_lambda[N-2].lambda = 2.*h*u_lambda[N-2].u + 2.*d*u_lambda[N-2].lambda - d*u_lambda[N-3].lambda;
151: else fu_lambda[i].lambda = 2.*h*u_lambda[i].u - d*(u_lambda[i+1].lambda - 2.0*u_lambda[i].lambda + u_lambda[i-1].lambda);
152: }
154: /* derivative of L() w.r.t. lambda */
155: for (i=xs; i<xs+xm; i++) {
156: if (i == 0) fu_lambda[0].u = 2.0*d*(u_lambda[0].u - w[0]);
157: else if (i == N-1) fu_lambda[N-1].u = 2.0*d*u_lambda[N-1].u;
158: else fu_lambda[i].u = -(d*(u_lambda[i+1].u - 2.0*u_lambda[i].u + u_lambda[i-1].u) - 2.0*h);
159: }
161: DAVecRestoreArray(da,vu_lambda,(void**)&u_lambda);
162: DAVecRestoreArray(da,vfu_lambda,(void**)&fu_lambda);
163: VecPackRestoreLocalVectors(packer,&w,&vu_lambda);
164: VecPackRestoreAccess(packer,FU,&fw,&vfu_lambda);
165: PetscLogFlops(13*N);
166: return(0);
167: }
169: /*
170: Computes the exact solution
171: */
172: int u_solution(void *dummy,int n,PetscScalar *x,PetscScalar *u)
173: {
174: int i;
176: for (i=0; i<n; i++) {
177: u[2*i] = x[i]*x[i] - 1.25*x[i] + .25;
178: }
179: return(0);
180: }
182: int ExactSolution(VecPack packer,Vec U)
183: {
184: PF pf;
185: Vec x;
186: Vec u_global;
187: PetscScalar *w;
188: DA da;
189: int m,ierr;
192: VecPackGetEntries(packer,&m,&da);
194: PFCreate(PETSC_COMM_WORLD,1,1,&pf);
195: PFSetType(pf,PFQUICK,(void*)u_solution);
196: DAGetCoordinates(da,&x);
197: if (!x) {
198: DASetUniformCoordinates(da,0.0,1.0,0.0,1.0,0.0,1.0);
199: DAGetCoordinates(da,&x);
200: }
201: VecPackGetAccess(packer,U,&w,&u_global,0);
202: if (w) w[0] = .25;
203: PFApplyVec(pf,x,u_global);
204: PFDestroy(pf);
205: VecPackRestoreAccess(packer,U,&w,&u_global,0);
206: return(0);
207: }
210: int Monitor(SNES snes,int its,PetscReal rnorm,void *dummy)
211: {
212: DMMG dmmg = (DMMG)dummy;
213: UserCtx *user = (UserCtx*)dmmg->user;
214: int ierr,m,N;
215: PetscScalar mone = -1.0,*w,*dw;
216: Vec u_lambda,U,F,Uexact;
217: VecPack packer = (VecPack)dmmg->dm;
218: PetscReal norm;
219: DA da;
222: SNESGetSolution(snes,&U);
223: VecPackGetAccess(packer,U,&w,&u_lambda);
224: VecView(u_lambda,user->u_lambda_viewer);
225: VecPackRestoreAccess(packer,U,&w,&u_lambda);
227: SNESGetFunction(snes,&F,0,0);
228: VecPackGetAccess(packer,F,&w,&u_lambda);
229: /* VecView(u_lambda,user->fu_lambda_viewer); */
230: VecPackRestoreAccess(packer,U,&w,&u_lambda);
232: VecPackGetEntries(packer,&m,&da);
233: DAGetInfo(da,0,&N,0,0,0,0,0,0,0,0,0);
234: VecDuplicate(U,&Uexact);
235: ExactSolution(packer,Uexact);
236: VecAXPY(&mone,U,Uexact);
237: VecPackGetAccess(packer,Uexact,&dw,&u_lambda);
238: VecStrideNorm(u_lambda,0,NORM_2,&norm);
239: norm = norm/sqrt(N-1.);
240: if (dw) PetscPrintf(dmmg->comm,"Norm of error %g Error at x = 0 %gn",norm,PetscRealPart(dw[0]));
241: VecView(u_lambda,user->fu_lambda_viewer);
242: VecPackRestoreAccess(packer,Uexact,&dw,&u_lambda);
243: VecDestroy(Uexact);
244: return(0);
245: }