Actual source code: ex24.c

  1: /*$Id: ex24.c,v 1.25 2001/08/07 03:04:16 balay Exp $*/

  3: static char help[] = "Solves PDE optimization problem of ex22.c with AD for adjoint.\n\n";

 5:  #include petscda.h
 6:  #include petscpf.h
 7:  #include petscmg.h
 8:  #include petscsnes.h

 10: /*

 12:               Minimize F(w,u) such that G(w,u) = 0

 14:          L(w,u,lambda) = F(w,u) + lambda^T G(w,u)

 16:        w - design variables (what we change to get an optimal solution)
 17:        u - state variables (i.e. the PDE solution)
 18:        lambda - the Lagrange multipliers

 20:             U = (w u lambda)

 22:        fu, fw, flambda contain the gradient of L(w,u,lambda)

 24:             FU = (fw fu flambda)

 26:        In this example the PDE is 
 27:                              Uxx - u^2 = 2, 
 28:                             u(0) = w(0), thus this is the free parameter
 29:                             u(1) = 0
 30:        the function we wish to minimize is 
 31:                             \integral u^{2}

 33:        The exact solution for u is given by u(x) = x*x - 1.25*x + .25

 35:        Use the usual centered finite differences.

 37:        Note we treat the problem as non-linear though it happens to be linear

 39:        The lambda and u are NOT interlaced.

 41:           We optionally provide a preconditioner on each level from the operator

 43:               (1   0   0)
 44:               (0   J   0)
 45:               (0   0   J')

 47:   
 48: */


 51: extern int FormFunction(SNES,Vec,Vec,void*);
 52: extern int PDEFormFunctionLocal(DALocalInfo*,PetscScalar*,PetscScalar*,PassiveScalar*);

 54: typedef struct {
 55:   Mat        J;           /* Jacobian of PDE system */
 56:   KSP       ksp;        /* Solver for that Jacobian */
 57: } AppCtx;

 61: int myPCApply(DMMG dmmg,Vec x,Vec y)
 62: {
 63:   Vec          xu,xlambda,yu,ylambda;
 64:   PetscScalar  *xw,*yw;
 65:   int          ierr;
 66:   VecPack      packer = (VecPack)dmmg->dm;
 67:   AppCtx       *appctx = (AppCtx*)dmmg->user;

 70:   VecPackGetAccess(packer,x,&xw,&xu,&xlambda);
 71:   VecPackGetAccess(packer,y,&yw,&yu,&ylambda);
 72:   if (yw && xw) {
 73:     yw[0] = xw[0];
 74:   }
 75:   KSPSetRhs(appctx->ksp,xu);
 76:   KSPSetSolution(appctx->ksp,yu);
 77:   KSPSolve(appctx->ksp);

 79:   KSPSetRhs(appctx->ksp,xlambda);
 80:   KSPSetSolution(appctx->ksp,ylambda);
 81:   KSPSolveTranspose(appctx->ksp);
 82:   /*  VecCopy(xu,yu);
 83:       VecCopy(xlambda,ylambda); */
 84:   VecPackRestoreAccess(packer,x,&xw,&xu,&xlambda);
 85:   VecPackRestoreAccess(packer,y,&yw,&yu,&ylambda);
 86:   return(0);
 87: }

 91: int myPCView(DMMG dmmg,PetscViewer v)
 92: {
 93:   int     ierr;
 94:   AppCtx  *appctx = (AppCtx*)dmmg->user;

 97:   KSPView(appctx->ksp,v);
 98:   return(0);
 99: }

103: int main(int argc,char **argv)
104: {
105:   int        ierr,nlevels,i,j;
106:   DA         da;
107:   DMMG       *dmmg;
108:   VecPack    packer;
109:   AppCtx     *appctx;
110:   ISColoring iscoloring;
111:   PetscTruth bdp;

113:   PetscInitialize(&argc,&argv,PETSC_NULL,help);

115:   /* Hardwire several options; can be changed at command line */
116:   PetscOptionsSetValue("-dmmg_grid_sequence",PETSC_NULL);
117:   PetscOptionsSetValue("-ksp_type","fgmres");
118:   PetscOptionsSetValue("-ksp_max_it","5");
119:   PetscOptionsSetValue("-pc_mg_type","full");
120:   PetscOptionsSetValue("-mg_coarse_ksp_type","gmres");
121:   PetscOptionsSetValue("-mg_levels_ksp_type","gmres");
122:   PetscOptionsSetValue("-mg_coarse_ksp_max_it","6");
123:   PetscOptionsSetValue("-mg_levels_ksp_max_it","3");
124:   PetscOptionsSetValue("-snes_mf_type","wp");
125:   PetscOptionsSetValue("-snes_mf_compute_norma","no");
126:   PetscOptionsSetValue("-snes_mf_compute_normu","no");
127:   PetscOptionsSetValue("-snes_ls","basic");
128:   PetscOptionsSetValue("-dmmg_jacobian_mf_fd",0);
129:   /* PetscOptionsSetValue("-snes_ls","basicnonorms"); */
130:   PetscOptionsInsert(&argc,&argv,PETSC_NULL);

132:   /* create VecPack object to manage composite vector */
133:   VecPackCreate(PETSC_COMM_WORLD,&packer);
134:   VecPackAddArray(packer,1);
135:   DACreate1d(PETSC_COMM_WORLD,DA_NONPERIODIC,-5,1,1,PETSC_NULL,&da);
136:   VecPackAddDA(packer,da);
137:   VecPackAddDA(packer,da);
138:   DADestroy(da);

140:   /* create nonlinear multi-level solver */
141:   DMMGCreate(PETSC_COMM_WORLD,2,PETSC_NULL,&dmmg);
142:   DMMGSetDM(dmmg,(DM)packer);
143:   VecPackDestroy(packer);

145:   /* Create Jacobian of PDE function for each level */
146:   nlevels = DMMGGetLevels(dmmg);
147:   for (i=0; i<nlevels; i++) {
148:     packer = (VecPack)dmmg[i]->dm;
149:     VecPackGetEntries(packer,PETSC_NULL,&da,PETSC_NULL);
150:     PetscNew(AppCtx,&appctx);
151:     DAGetColoring(da,IS_COLORING_GHOSTED,&iscoloring);
152:     DAGetMatrix(da,MATAIJ,&appctx->J);
153:     MatSetColoring(appctx->J,iscoloring);
154:     ISColoringDestroy(iscoloring);
155:     DASetLocalFunction(da,(DALocalFunction1)PDEFormFunctionLocal);
156:     DASetLocalAdicFunction(da,ad_PDEFormFunctionLocal);
157:     dmmg[i]->user = (void*)appctx;
158:   }

160:   DMMGSetSNES(dmmg,FormFunction,PETSC_NULL);

162:   PetscOptionsHasName(PETSC_NULL,"-bdp",&bdp);
163:   if (bdp) {
164:     for (i=0; i<nlevels; i++) {
165:       KSP  ksp;
166:       PC   pc,mpc;

168:       appctx = (AppCtx*) dmmg[i]->user;
169:       KSPCreate(PETSC_COMM_WORLD,&appctx->ksp);
170:       KSPSetOptionsPrefix(appctx->ksp,"bdp_");
171:       KSPSetFromOptions(appctx->ksp);

173:       SNESGetKSP(dmmg[i]->snes,&ksp);
174:       KSPGetPC(ksp,&pc);
175:       for (j=0; j<=i; j++) {
176:         MGGetSmoother(pc,j,&ksp);
177:         KSPGetPC(ksp,&mpc);
178:         PCSetType(mpc,PCSHELL);
179:         PCShellSetApply(mpc,(int (*)(void*,Vec,Vec))myPCApply,dmmg[j]);
180:         PCShellSetView(mpc,(int (*)(void*,PetscViewer))myPCView);
181:       }
182:     }
183:   }

185:   DMMGSolve(dmmg);

187:   /* VecView(DMMGGetx(dmmg),PETSC_VIEWER_SOCKET_WORLD); */
188:   for (i=0; i<nlevels; i++) {
189:     appctx = (AppCtx*)dmmg[i]->user;
190:     MatDestroy(appctx->J);
191:     if (appctx->ksp) {KSPDestroy(appctx->ksp);}
192:     PetscFree(appctx);
193:   }
194:   DMMGDestroy(dmmg);

196:   PetscFinalize();
197:   return 0;
198: }
199: 
200: /*
201:      Enforces the PDE on the grid
202:      This local function acts on the ghosted version of U (accessed via DAGetLocalVector())
203:      BUT the global, nonghosted version of FU

205:      Process adiC(36): PDEFormFunctionLocal
206: */
209: int PDEFormFunctionLocal(DALocalInfo *info,PetscScalar *u,PetscScalar *fu,PassiveScalar *w)
210: {
211:   int          xs = info->xs,xm = info->xm,i,mx = info->mx;
212:   PetscScalar  d,h;

214:   d    = mx-1.0;
215:   h    = 1.0/d;

217:   for (i=xs; i<xs+xm; i++) {
218:     if      (i == 0)    fu[i]   = 2.0*d*(u[i] - w[0]) + h*u[i]*u[i];
219:     else if (i == mx-1) fu[i]   = 2.0*d*u[i] + h*u[i]*u[i];
220:     else                fu[i]   = -(d*(u[i+1] - 2.0*u[i] + u[i-1]) - 2.0*h) + h*u[i]*u[i];
221:   }

223:   PetscLogFlops(9*mx);
224:   return 0;
225: }

227: /*
228:       Evaluates FU = Gradiant(L(w,u,lambda))

230:       This is the function that is usually passed to the SNESSetJacobian() or DMMGSetSNES() and
231:     defines the nonlinear set of equations that are to be solved.

233:      This local function acts on the ghosted version of U (accessed via VecPackGetLocalVectors() and
234:    VecPackScatter()) BUT the global, nonghosted version of FU (via VecPackAccess()).

236:      This function uses PDEFormFunction() to enforce the PDE constraint equations and its adjoint
237:    for the Lagrange multiplier equations

239: */
242: int FormFunction(SNES snes,Vec U,Vec FU,void* dummy)
243: {
244:   DMMG         dmmg = (DMMG)dummy;
245:   int          ierr,xs,xm,i,N,nredundant;
246:   PetscScalar  *u,*w,*fw,*fu,*lambda,*flambda,d,h,h2;
247:   Vec          vu,vlambda,vfu,vflambda,vglambda;
248:   DA           da;
249:   VecPack      packer = (VecPack)dmmg->dm;
250:   AppCtx       *appctx = (AppCtx*)dmmg->user;
251:   PetscTruth   skipadic;

254:   PetscOptionsHasName(0,"-skipadic",&skipadic);

256:   VecPackGetEntries(packer,&nredundant,&da,PETSC_IGNORE);
257:   DAGetCorners(da,&xs,PETSC_NULL,PETSC_NULL,&xm,PETSC_NULL,PETSC_NULL);
258:   DAGetInfo(da,0,&N,0,0,0,0,0,0,0,0,0);
259:   d    = (N-1.0);
260:   h    = 1.0/d;
261:   h2   = 2.0*h;

263:   VecPackGetLocalVectors(packer,&w,&vu,&vlambda);
264:   VecPackScatter(packer,U,w,vu,vlambda);
265:   VecPackGetAccess(packer,FU,&fw,&vfu,&vflambda);
266:   VecPackGetAccess(packer,U,0,0,&vglambda);

268:   /* G() */
269:   DAFormFunction1(da,vu,vfu,w);
270:   if (!skipadic) {
271:     /* lambda^T G_u() */
272:     DAComputeJacobian1WithAdic(da,vu,appctx->J,w);
273:     if (appctx->ksp) {
274:       KSPSetOperators(appctx->ksp,appctx->J,appctx->J,SAME_NONZERO_PATTERN);
275:     }
276:     MatMultTranspose(appctx->J,vglambda,vflambda);
277:   }

279:   DAVecGetArray(da,vu,&u);
280:   DAVecGetArray(da,vfu,&fu);
281:   DAVecGetArray(da,vlambda,&lambda);
282:   DAVecGetArray(da,vflambda,&flambda);

284:   /* L_w */
285:   if (xs == 0) { /* only first processor computes this */
286:     fw[0] = -2.*d*lambda[0];
287:   }

289:   /* lambda^T G_u() */
290:   if (skipadic) {
291:     for (i=xs; i<xs+xm; i++) {
292:       if      (i == 0)   flambda[0]   = 2.*d*lambda[0]   - d*lambda[1] + h2*lambda[0]*u[0];
293:       else if (i == 1)   flambda[1]   = 2.*d*lambda[1]   - d*lambda[2] + h2*lambda[1]*u[1];
294:       else if (i == N-1) flambda[N-1] = 2.*d*lambda[N-1] - d*lambda[N-2] + h2*lambda[N-1]*u[N-1];
295:       else if (i == N-2) flambda[N-2] = 2.*d*lambda[N-2] - d*lambda[N-3] + h2*lambda[N-2]*u[N-2];
296:       else               flambda[i]   = - d*(lambda[i+1] - 2.0*lambda[i] + lambda[i-1]) + h2*lambda[i]*u[i];
297:     }
298:   }

300:   /* F_u */
301:   for (i=xs; i<xs+xm; i++) {
302:     if      (i == 0)   flambda[0]   +=    h*u[0];
303:     else if (i == 1)   flambda[1]   +=    h2*u[1];
304:     else if (i == N-1) flambda[N-1] +=    h*u[N-1];
305:     else if (i == N-2) flambda[N-2] +=    h2*u[N-2];
306:     else               flambda[i]   +=    h2*u[i];
307:   }

309:   DAVecRestoreArray(da,vu,&u);
310:   DAVecRestoreArray(da,vfu,&fu);
311:   DAVecRestoreArray(da,vlambda,&lambda);
312:   DAVecRestoreArray(da,vflambda,&flambda);

314:   VecPackRestoreLocalVectors(packer,&w,&vu,&vlambda);
315:   VecPackRestoreAccess(packer,FU,&fw,&vfu,&vflambda);
316:   VecPackRestoreAccess(packer,U,0,0,&vglambda);

318:   PetscLogFlops(9*N);
319:   return(0);
320: }