Actual source code: ex24.c

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

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

  9: /*

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

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

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

 19:             U = (w u lambda)

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

 23:             FU = (fw fu flambda)

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

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

 34:        Use the usual centered finite differences.

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

 38:        The lambda and u are NOT interlaced.

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

 42:               (1   0   0)
 43:               (0   J   0)
 44:               (0   0   J')

 46:   
 47: */



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

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

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

 76:   KSPSolveTranspose(appctx->ksp,xlambda,ylambda);
 77:   /*  VecCopy(xu,yu);
 78:       VecCopy(xlambda,ylambda); */
 79:   VecPackRestoreAccess(packer,x,&xw,&xu,&xlambda);
 80:   VecPackRestoreAccess(packer,y,&yw,&yu,&ylambda);
 81:   return(0);
 82: }

 86: PetscErrorCode myPCView(DMMG dmmg,PetscViewer v)
 87: {
 89:   AppCtx         *appctx = (AppCtx*)dmmg->user;

 92:   KSPView(appctx->ksp,v);
 93:   return(0);
 94: }

 98: int main(int argc,char **argv)
 99: {
101:   PetscInt       nlevels,i,j;
102:   DA             da;
103:   DMMG           *dmmg;
104:   VecPack        packer;
105:   AppCtx         *appctx;
106:   ISColoring     iscoloring;
107:   PetscTruth     bdp;

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

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

128:   /* create VecPack object to manage composite vector */
129:   VecPackCreate(PETSC_COMM_WORLD,&packer);
130:   VecPackAddArray(packer,1);
131:   DACreate1d(PETSC_COMM_WORLD,DA_NONPERIODIC,-5,1,1,PETSC_NULL,&da);
132:   VecPackAddDA(packer,da);
133:   VecPackAddDA(packer,da);
134:   DADestroy(da);

136:   /* create nonlinear multi-level solver */
137:   DMMGCreate(PETSC_COMM_WORLD,2,PETSC_NULL,&dmmg);
138:   DMMGSetDM(dmmg,(DM)packer);
139:   VecPackDestroy(packer);

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

156:   DMMGSetSNES(dmmg,FormFunction,PETSC_NULL);

158:   PetscOptionsHasName(PETSC_NULL,"-bdp",&bdp);
159:   if (bdp) {
160:     for (i=0; i<nlevels; i++) {
161:       KSP  ksp;
162:       PC   pc,mpc;

164:       appctx = (AppCtx*) dmmg[i]->user;
165:       KSPCreate(PETSC_COMM_WORLD,&appctx->ksp);
166:       KSPSetOptionsPrefix(appctx->ksp,"bdp_");
167:       KSPSetFromOptions(appctx->ksp);

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

181:   DMMGSolve(dmmg);

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

192:   PetscFinalize();
193:   return 0;
194: }
195: 
196: /*
197:      Enforces the PDE on the grid
198:      This local function acts on the ghosted version of U (accessed via DAGetLocalVector())
199:      BUT the global, nonghosted version of FU

201:      Process adiC(36): PDEFormFunctionLocal
202: */
205: PetscErrorCode PDEFormFunctionLocal(DALocalInfo *info,PetscScalar *u,PetscScalar *fu,PassiveScalar *w)
206: {
207:   PetscInt     xs = info->xs,xm = info->xm,i,mx = info->mx;
208:   PetscScalar  d,h;

210:   d    = mx-1.0;
211:   h    = 1.0/d;

213:   for (i=xs; i<xs+xm; i++) {
214:     if      (i == 0)    fu[i]   = 2.0*d*(u[i] - w[0]) + h*u[i]*u[i];
215:     else if (i == mx-1) fu[i]   = 2.0*d*u[i] + h*u[i]*u[i];
216:     else                fu[i]   = -(d*(u[i+1] - 2.0*u[i] + u[i-1]) - 2.0*h) + h*u[i]*u[i];
217:   }

219:   PetscLogFlops(9*mx);
220:   return 0;
221: }

223: /*
224:       Evaluates FU = Gradiant(L(w,u,lambda))

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

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

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

235: */
238: PetscErrorCode FormFunction(SNES snes,Vec U,Vec FU,void* dummy)
239: {
240:   DMMG           dmmg = (DMMG)dummy;
242:   PetscInt       xs,xm,i,N,nredundant;
243:   PetscScalar    *u,*w,*fw,*fu,*lambda,*flambda,d,h,h2;
244:   Vec            vu,vlambda,vfu,vflambda,vglambda;
245:   DA             da;
246:   VecPack        packer = (VecPack)dmmg->dm;
247:   AppCtx         *appctx = (AppCtx*)dmmg->user;
248:   PetscTruth     skipadic;

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

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

260:   VecPackGetLocalVectors(packer,&w,&vu,&vlambda);
261:   VecPackScatter(packer,U,w,vu,vlambda);
262:   VecPackGetAccess(packer,FU,&fw,&vfu,&vflambda);
263:   VecPackGetAccess(packer,U,0,0,&vglambda);

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

276:   DAVecGetArray(da,vu,&u);
277:   DAVecGetArray(da,vfu,&fu);
278:   DAVecGetArray(da,vlambda,&lambda);
279:   DAVecGetArray(da,vflambda,&flambda);

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

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

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

306:   DAVecRestoreArray(da,vu,&u);
307:   DAVecRestoreArray(da,vfu,&fu);
308:   DAVecRestoreArray(da,vlambda,&lambda);
309:   DAVecRestoreArray(da,vflambda,&flambda);

311:   VecPackRestoreLocalVectors(packer,&w,&vu,&vlambda);
312:   VecPackRestoreAccess(packer,FU,&fw,&vfu,&vflambda);
313:   VecPackRestoreAccess(packer,U,0,0,&vglambda);

315:   PetscLogFlops(9*N);
316:   return(0);
317: }