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: #undef __FUNCT__
50: int main(int argc,char **argv)
51: {
52: int ierr;
53: UserCtx user;
54: DA da;
55: DMMG *dmmg;
56: VecPack packer;
58: PetscInitialize(&argc,&argv,PETSC_NULL,help);
60: /* Hardwire several options; can be changed at command line */
61: PetscOptionsSetValue("-dmmg_grid_sequence",PETSC_NULL);
62: PetscOptionsSetValue("-ksp_type","fgmres");
63: PetscOptionsSetValue("-ksp_max_it","5");
64: PetscOptionsSetValue("-pc_mg_type","full");
65: PetscOptionsSetValue("-mg_coarse_ksp_type","gmres");
66: PetscOptionsSetValue("-mg_levels_ksp_type","gmres");
67: PetscOptionsSetValue("-mg_coarse_ksp_max_it","6");
68: PetscOptionsSetValue("-mg_levels_ksp_max_it","3");
69: PetscOptionsSetValue("-snes_mf_type","wp");
70: PetscOptionsSetValue("-snes_mf_compute_norma","no");
71: PetscOptionsSetValue("-snes_mf_compute_normu","no");
72: PetscOptionsSetValue("-snes_ls","basic");
73: PetscOptionsSetValue("-dmmg_jacobian_mf_fd",0);
74: /* PetscOptionsSetValue("-snes_ls","basicnonorms"); */
75: PetscOptionsInsert(&argc,&argv,PETSC_NULL);
77: /* Create a global vector that includes a single redundant array and two da arrays */
78: VecPackCreate(PETSC_COMM_WORLD,&packer);
79: VecPackAddArray(packer,1);
80: DACreate1d(PETSC_COMM_WORLD,DA_NONPERIODIC,-5,2,1,PETSC_NULL,&da);
81: VecPackAddDA(packer,da);
83: /* create graphics windows */
84: PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"u_lambda - state variables and Lagrange multipliers",-1,-1,-1,-1,&user.u_lambda_viewer);
85: PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"fu_lambda - derivate w.r.t. state variables and Lagrange multipliers",-1,-1,-1,-1,&user.fu_lambda_viewer);
87: /* create nonlinear multi-level solver */
88: DMMGCreate(PETSC_COMM_WORLD,2,&user,&dmmg);
89: DMMGSetDM(dmmg,(DM)packer);
90: DMMGSetSNES(dmmg,FormFunction,PETSC_NULL);
91: /*
92: for (i=0; i<DMMGGetLevels(dmmg); i++) {
93: SNESSetMonitor(dmmg[i]->snes,Monitor,dmmg[i],0);
94: }*/
95: DMMGSolve(dmmg);
96: DMMGDestroy(dmmg);
98: DADestroy(da);
99: VecPackDestroy(packer);
100: PetscViewerDestroy(user.u_lambda_viewer);
101: PetscViewerDestroy(user.fu_lambda_viewer);
103: PetscFinalize();
104: return 0;
105: }
107: typedef struct {
108: PetscScalar u;
109: PetscScalar lambda;
110: } ULambda;
111:
112: /*
113: Evaluates FU = Gradiant(L(w,u,lambda))
115: This local function acts on the ghosted version of U (accessed via VecPackGetLocalVectors() and
116: VecPackScatter()) BUT the global, nonghosted version of FU (via VecPackGetAccess()).
118: */
119: int FormFunction(SNES snes,Vec U,Vec FU,void* dummy)
120: {
121: DMMG dmmg = (DMMG)dummy;
122: int ierr,xs,xm,i,N,nredundant;
123: ULambda *u_lambda,*fu_lambda;
124: PetscScalar d,h,*w,*fw;
125: Vec vu_lambda,vfu_lambda;
126: DA da;
127: VecPack packer = (VecPack)dmmg->dm;
130: VecPackGetEntries(packer,&nredundant,&da);
131: VecPackGetLocalVectors(packer,&w,&vu_lambda);
132: VecPackScatter(packer,U,w,vu_lambda);
133: VecPackGetAccess(packer,FU,&fw,&vfu_lambda);
135: DAGetCorners(da,&xs,PETSC_NULL,PETSC_NULL,&xm,PETSC_NULL,PETSC_NULL);
136: DAGetInfo(da,0,&N,0,0,0,0,0,0,0,0,0);
137: DAVecGetArray(da,vu_lambda,(void**)&u_lambda);
138: DAVecGetArray(da,vfu_lambda,(void**)&fu_lambda);
139: d = N-1.0;
140: h = 1.0/d;
142: /* derivative of L() w.r.t. w */
143: if (xs == 0) { /* only first processor computes this */
144: fw[0] = -2.0*d*u_lambda[0].lambda;
145: }
147: /* derivative of L() w.r.t. u */
148: for (i=xs; i<xs+xm; i++) {
149: if (i == 0) fu_lambda[0].lambda = h*u_lambda[0].u + 2.*d*u_lambda[0].lambda - d*u_lambda[1].lambda;
150: 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;
151: 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;
152: 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;
153: 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);
154: }
156: /* derivative of L() w.r.t. lambda */
157: for (i=xs; i<xs+xm; i++) {
158: if (i == 0) fu_lambda[0].u = 2.0*d*(u_lambda[0].u - w[0]);
159: else if (i == N-1) fu_lambda[N-1].u = 2.0*d*u_lambda[N-1].u;
160: 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);
161: }
163: DAVecRestoreArray(da,vu_lambda,(void**)&u_lambda);
164: DAVecRestoreArray(da,vfu_lambda,(void**)&fu_lambda);
165: VecPackRestoreLocalVectors(packer,&w,&vu_lambda);
166: VecPackRestoreAccess(packer,FU,&fw,&vfu_lambda);
167: PetscLogFlops(13*N);
168: return(0);
169: }
171: /*
172: Computes the exact solution
173: */
174: int u_solution(void *dummy,int n,PetscScalar *x,PetscScalar *u)
175: {
176: int i;
178: for (i=0; i<n; i++) {
179: u[2*i] = x[i]*x[i] - 1.25*x[i] + .25;
180: }
181: return(0);
182: }
184: int ExactSolution(VecPack packer,Vec U)
185: {
186: PF pf;
187: Vec x;
188: Vec u_global;
189: PetscScalar *w;
190: DA da;
191: int m,ierr;
194: VecPackGetEntries(packer,&m,&da);
196: PFCreate(PETSC_COMM_WORLD,1,1,&pf);
197: PFSetType(pf,PFQUICK,(void*)u_solution);
198: DAGetCoordinates(da,&x);
199: if (!x) {
200: DASetUniformCoordinates(da,0.0,1.0,0.0,1.0,0.0,1.0);
201: DAGetCoordinates(da,&x);
202: }
203: VecPackGetAccess(packer,U,&w,&u_global,0);
204: if (w) w[0] = .25;
205: PFApplyVec(pf,x,u_global);
206: PFDestroy(pf);
207: VecPackRestoreAccess(packer,U,&w,&u_global,0);
208: return(0);
209: }
212: int Monitor(SNES snes,int its,PetscReal rnorm,void *dummy)
213: {
214: DMMG dmmg = (DMMG)dummy;
215: UserCtx *user = (UserCtx*)dmmg->user;
216: int ierr,m,N;
217: PetscScalar mone = -1.0,*w,*dw;
218: Vec u_lambda,U,F,Uexact;
219: VecPack packer = (VecPack)dmmg->dm;
220: PetscReal norm;
221: DA da;
224: SNESGetSolution(snes,&U);
225: VecPackGetAccess(packer,U,&w,&u_lambda);
226: VecView(u_lambda,user->u_lambda_viewer);
227: VecPackRestoreAccess(packer,U,&w,&u_lambda);
229: SNESGetFunction(snes,&F,0,0);
230: VecPackGetAccess(packer,F,&w,&u_lambda);
231: /* VecView(u_lambda,user->fu_lambda_viewer); */
232: VecPackRestoreAccess(packer,U,&w,&u_lambda);
234: VecPackGetEntries(packer,&m,&da);
235: DAGetInfo(da,0,&N,0,0,0,0,0,0,0,0,0);
236: VecDuplicate(U,&Uexact);
237: ExactSolution(packer,Uexact);
238: VecAXPY(&mone,U,Uexact);
239: VecPackGetAccess(packer,Uexact,&dw,&u_lambda);
240: VecStrideNorm(u_lambda,0,NORM_2,&norm);
241: norm = norm/sqrt(N-1.);
242: if (dw) PetscPrintf(dmmg->comm,"Norm of error %g Error at x = 0 %gn",norm,PetscRealPart(dw[0]));
243: VecView(u_lambda,user->fu_lambda_viewer);
244: VecPackRestoreAccess(packer,Uexact,&dw,&u_lambda);
245: VecDestroy(Uexact);
246: return(0);
247: }