Actual source code: hyperbolic.c

  1: #include <petsctao.h>

  3: /*T
  4:    Concepts: TAO^Solving a system of nonlinear equations, nonlinear least squares
  5:    Routines: TaoCreate();
  6:    Routines: TaoSetType();
  7:    Routines: TaoSetInitialVector();
  8:    Routines: TaoSetObjectiveRoutine();
  9:    Routines: TaoSetGradientRoutine();
 10:    Routines: TaoSetConstraintsRoutine();
 11:    Routines: TaoSetJacobianStateRoutine();
 12:    Routines: TaoSetJacobianDesignRoutine();
 13:    Routines: TaoSetStateDesignIS();
 14:    Routines: TaoSetFromOptions();
 15:    Routines: TaoSolve();
 16:    Routines: TaoDestroy();
 17:    Processors: 1
 18: T*/

 20: typedef struct {
 21:   PetscInt n; /*  Number of variables */
 22:   PetscInt m; /*  Number of constraints */
 23:   PetscInt mx; /*  grid points in each direction */
 24:   PetscInt nt; /*  Number of time steps */
 25:   PetscInt ndata; /*  Number of data points per sample */
 26:   IS       s_is;
 27:   IS       d_is;
 28:   VecScatter state_scatter;
 29:   VecScatter design_scatter;
 30:   VecScatter *uxi_scatter,*uyi_scatter,*ux_scatter,*uy_scatter,*ui_scatter;
 31:   VecScatter *yi_scatter;

 33:   Mat       Js,Jd,JsBlockPrec,JsInv,JsBlock;
 34:   PetscBool jformed,c_formed;

 36:   PetscReal alpha; /*  Regularization parameter */
 37:   PetscReal gamma;
 38:   PetscReal ht; /*  Time step */
 39:   PetscReal T; /*  Final time */
 40:   Mat Q,QT;
 41:   Mat L,LT;
 42:   Mat Div,Divwork,Divxy[2];
 43:   Mat Grad,Gradxy[2];
 44:   Mat M;
 45:   Mat *C,*Cwork;
 46:   /* Mat Hs,Hd,Hsd; */
 47:   Vec q;
 48:   Vec ur; /*  reference */

 50:   Vec d;
 51:   Vec dwork;

 53:   Vec y; /*  state variables */
 54:   Vec ywork;
 55:   Vec ytrue;
 56:   Vec *yi,*yiwork,*ziwork;
 57:   Vec *uxi,*uyi,*uxiwork,*uyiwork,*ui,*uiwork;

 59:   Vec u; /*  design variables */
 60:   Vec uwork,vwork;
 61:   Vec utrue;

 63:   Vec js_diag;

 65:   Vec c; /*  constraint vector */
 66:   Vec cwork;

 68:   Vec lwork;

 70:   KSP      solver;
 71:   PC       prec;
 72:   PetscInt block_index;

 74:   PetscInt ksp_its;
 75:   PetscInt ksp_its_initial;
 76: } AppCtx;

 78: PetscErrorCode FormFunction(Tao, Vec, PetscReal*, void*);
 79: PetscErrorCode FormGradient(Tao, Vec, Vec, void*);
 80: PetscErrorCode FormFunctionGradient(Tao, Vec, PetscReal*, Vec, void*);
 81: PetscErrorCode FormJacobianState(Tao, Vec, Mat, Mat, Mat, void*);
 82: PetscErrorCode FormJacobianDesign(Tao, Vec, Mat,void*);
 83: PetscErrorCode FormConstraints(Tao, Vec, Vec, void*);
 84: PetscErrorCode FormHessian(Tao, Vec, Mat, Mat, void*);
 85: PetscErrorCode Gather(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat);
 86: PetscErrorCode Scatter(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat);
 87: PetscErrorCode HyperbolicInitialize(AppCtx *user);
 88: PetscErrorCode HyperbolicDestroy(AppCtx *user);
 89: PetscErrorCode HyperbolicMonitor(Tao, void*);

 91: PetscErrorCode StateMatMult(Mat,Vec,Vec);
 92: PetscErrorCode StateMatBlockMult(Mat,Vec,Vec);
 93: PetscErrorCode StateMatBlockMultTranspose(Mat,Vec,Vec);
 94: PetscErrorCode StateMatMultTranspose(Mat,Vec,Vec);
 95: PetscErrorCode StateMatGetDiagonal(Mat,Vec);
 96: PetscErrorCode StateMatDuplicate(Mat,MatDuplicateOption,Mat*);
 97: PetscErrorCode StateMatInvMult(Mat,Vec,Vec);
 98: PetscErrorCode StateMatInvTransposeMult(Mat,Vec,Vec);
 99: PetscErrorCode StateMatBlockPrecMult(PC,Vec,Vec);

101: PetscErrorCode DesignMatMult(Mat,Vec,Vec);
102: PetscErrorCode DesignMatMultTranspose(Mat,Vec,Vec);

104: PetscErrorCode Scatter_yi(Vec,Vec*,VecScatter*,PetscInt); /*  y to y1,y2,...,y_nt */
105: PetscErrorCode Gather_yi(Vec,Vec*,VecScatter*,PetscInt);
106: PetscErrorCode Scatter_uxi_uyi(Vec,Vec*,VecScatter*,Vec*,VecScatter*,PetscInt); /*  u to ux_1,uy_1,ux_2,uy_2,...,u */
107: PetscErrorCode Gather_uxi_uyi(Vec,Vec*,VecScatter*,Vec*,VecScatter*,PetscInt);

109: static  char help[]="";

111: int main(int argc, char **argv)
112: {
113:   PetscErrorCode     ierr;
114:   Vec                x,x0;
115:   Tao                tao;
116:   AppCtx             user;
117:   IS                 is_allstate,is_alldesign;
118:   PetscInt           lo,hi,hi2,lo2,ksp_old;
119:   PetscInt           ntests = 1;
120:   PetscInt           i;
121: #if defined(PETSC_USE_LOG)
122:   PetscLogStage      stages[1];
123: #endif

125:   PetscInitialize(&argc, &argv, (char*)0,help);if (ierr) return ierr;
126:   user.mx = 32;
127:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"hyperbolic example",NULL);
128:   PetscOptionsInt("-mx","Number of grid points in each direction","",user.mx,&user.mx,NULL);
129:   user.nt = 16;
130:   PetscOptionsInt("-nt","Number of time steps","",user.nt,&user.nt,NULL);
131:   user.ndata = 64;
132:   PetscOptionsInt("-ndata","Numbers of data points per sample","",user.ndata,&user.ndata,NULL);
133:   user.alpha = 10.0;
134:   PetscOptionsReal("-alpha","Regularization parameter","",user.alpha,&user.alpha,NULL);
135:   user.T = 1.0/32.0;
136:   PetscOptionsReal("-Tfinal","Final time","",user.T,&user.T,NULL);
137:   PetscOptionsInt("-ntests","Number of times to repeat TaoSolve","",ntests,&ntests,NULL);
138:   PetscOptionsEnd();

140:   user.m = user.mx*user.mx*user.nt; /*  number of constraints */
141:   user.n = user.mx*user.mx*3*user.nt; /*  number of variables */
142:   user.ht = user.T/user.nt; /*  Time step */
143:   user.gamma = user.T*user.ht / (user.mx*user.mx);

145:   VecCreate(PETSC_COMM_WORLD,&user.u);
146:   VecCreate(PETSC_COMM_WORLD,&user.y);
147:   VecCreate(PETSC_COMM_WORLD,&user.c);
148:   VecSetSizes(user.u,PETSC_DECIDE,user.n-user.m);
149:   VecSetSizes(user.y,PETSC_DECIDE,user.m);
150:   VecSetSizes(user.c,PETSC_DECIDE,user.m);
151:   VecSetFromOptions(user.u);
152:   VecSetFromOptions(user.y);
153:   VecSetFromOptions(user.c);

155:   /* Create scatters for reduced spaces.
156:      If the state vector y and design vector u are partitioned as
157:      [y_1; y_2; ...; y_np] and [u_1; u_2; ...; u_np] (with np = # of processors),
158:      then the solution vector x is organized as
159:      [y_1; u_1; y_2; u_2; ...; y_np; u_np].
160:      The index sets user.s_is and user.d_is correspond to the indices of the
161:      state and design variables owned by the current processor.
162:   */
163:   VecCreate(PETSC_COMM_WORLD,&x);

165:   VecGetOwnershipRange(user.y,&lo,&hi);
166:   VecGetOwnershipRange(user.u,&lo2,&hi2);

168:   ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_allstate);
169:   ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+lo2,1,&user.s_is);

171:   ISCreateStride(PETSC_COMM_SELF,hi2-lo2,lo2,1,&is_alldesign);
172:   ISCreateStride(PETSC_COMM_SELF,hi2-lo2,hi+lo2,1,&user.d_is);

174:   VecSetSizes(x,hi-lo+hi2-lo2,user.n);
175:   VecSetFromOptions(x);

177:   VecScatterCreate(x,user.s_is,user.y,is_allstate,&user.state_scatter);
178:   VecScatterCreate(x,user.d_is,user.u,is_alldesign,&user.design_scatter);
179:   ISDestroy(&is_alldesign);
180:   ISDestroy(&is_allstate);

182:   /* Create TAO solver and set desired solution method */
183:   TaoCreate(PETSC_COMM_WORLD,&tao);
184:   TaoSetType(tao,TAOLCL);

186:   /* Set up initial vectors and matrices */
187:   HyperbolicInitialize(&user);

189:   Gather(x,user.y,user.state_scatter,user.u,user.design_scatter);
190:   VecDuplicate(x,&x0);
191:   VecCopy(x,x0);

193:   /* Set solution vector with an initial guess */
194:   TaoSetInitialVector(tao,x);
195:   TaoSetObjectiveRoutine(tao, FormFunction, (void *)&user);
196:   TaoSetGradientRoutine(tao, FormGradient, (void *)&user);
197:   TaoSetConstraintsRoutine(tao, user.c, FormConstraints, (void *)&user);
198:   TaoSetJacobianStateRoutine(tao, user.Js, user.Js, user.JsInv, FormJacobianState, (void *)&user);
199:   TaoSetJacobianDesignRoutine(tao, user.Jd, FormJacobianDesign, (void *)&user);
200:   TaoSetFromOptions(tao);
201:   TaoSetStateDesignIS(tao,user.s_is,user.d_is);

203:   /* SOLVE THE APPLICATION */
204:   PetscLogStageRegister("Trials",&stages[0]);
205:   PetscLogStagePush(stages[0]);
206:   user.ksp_its_initial = user.ksp_its;
207:   ksp_old = user.ksp_its;
208:   for (i=0; i<ntests; i++) {
209:     TaoSolve(tao);
210:     PetscPrintf(PETSC_COMM_WORLD,"KSP Iterations = %D\n",user.ksp_its-ksp_old);
211:     VecCopy(x0,x);
212:     TaoSetInitialVector(tao,x);
213:   }
214:   PetscLogStagePop();
215:   PetscBarrier((PetscObject)x);
216:   PetscPrintf(PETSC_COMM_WORLD,"KSP iterations within initialization: ");
217:   PetscPrintf(PETSC_COMM_WORLD,"%D\n",user.ksp_its_initial);
218:   PetscPrintf(PETSC_COMM_WORLD,"Total KSP iterations over %D trial(s): ",ntests);
219:   PetscPrintf(PETSC_COMM_WORLD,"%D\n",user.ksp_its);
220:   PetscPrintf(PETSC_COMM_WORLD,"KSP iterations per trial: ");
221:   PetscPrintf(PETSC_COMM_WORLD,"%D\n",(user.ksp_its-user.ksp_its_initial)/ntests);

223:   TaoDestroy(&tao);
224:   VecDestroy(&x);
225:   VecDestroy(&x0);
226:   HyperbolicDestroy(&user);
227:   PetscFinalize();
228:   return ierr;
229: }
230: /* ------------------------------------------------------------------- */
231: /*
232:    dwork = Qy - d
233:    lwork = L*(u-ur).^2
234:    f = 1/2 * (dwork.dork + alpha*y.lwork)
235: */
236: PetscErrorCode FormFunction(Tao tao,Vec X,PetscReal *f,void *ptr)
237: {
239:   PetscReal      d1=0,d2=0;
240:   AppCtx         *user = (AppCtx*)ptr;

243:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
244:   MatMult(user->Q,user->y,user->dwork);
245:   VecAXPY(user->dwork,-1.0,user->d);
246:   VecDot(user->dwork,user->dwork,&d1);

248:   VecWAXPY(user->uwork,-1.0,user->ur,user->u);
249:   VecPointwiseMult(user->uwork,user->uwork,user->uwork);
250:   MatMult(user->L,user->uwork,user->lwork);
251:   VecDot(user->y,user->lwork,&d2);
252:   *f = 0.5 * (d1 + user->alpha*d2);
253:   return(0);
254: }

256: /* ------------------------------------------------------------------- */
257: /*
258:     state: g_s = Q' *(Qy - d) + 0.5*alpha*L*(u-ur).^2
259:     design: g_d = alpha*(L'y).*(u-ur)
260: */
261: PetscErrorCode FormGradient(Tao tao,Vec X,Vec G,void *ptr)
262: {
264:   AppCtx         *user = (AppCtx*)ptr;

267:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
268:   MatMult(user->Q,user->y,user->dwork);
269:   VecAXPY(user->dwork,-1.0,user->d);

271:   MatMult(user->QT,user->dwork,user->ywork);

273:   MatMult(user->LT,user->y,user->uwork);
274:   VecWAXPY(user->vwork,-1.0,user->ur,user->u);
275:   VecPointwiseMult(user->uwork,user->vwork,user->uwork);
276:   VecScale(user->uwork,user->alpha);

278:   VecPointwiseMult(user->vwork,user->vwork,user->vwork);
279:   MatMult(user->L,user->vwork,user->lwork);
280:   VecAXPY(user->ywork,0.5*user->alpha,user->lwork);

282:   Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
283:   return(0);
284: }

286: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *f, Vec G, void *ptr)
287: {
289:   PetscReal      d1,d2;
290:   AppCtx         *user = (AppCtx*)ptr;

293:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
294:   MatMult(user->Q,user->y,user->dwork);
295:   VecAXPY(user->dwork,-1.0,user->d);

297:   MatMult(user->QT,user->dwork,user->ywork);

299:   VecDot(user->dwork,user->dwork,&d1);

301:   MatMult(user->LT,user->y,user->uwork);
302:   VecWAXPY(user->vwork,-1.0,user->ur,user->u);
303:   VecPointwiseMult(user->uwork,user->vwork,user->uwork);
304:   VecScale(user->uwork,user->alpha);

306:   VecPointwiseMult(user->vwork,user->vwork,user->vwork);
307:   MatMult(user->L,user->vwork,user->lwork);
308:   VecAXPY(user->ywork,0.5*user->alpha,user->lwork);

310:   VecDot(user->y,user->lwork,&d2);

312:   *f = 0.5 * (d1 + user->alpha*d2);
313:   Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
314:   return(0);
315: }

317: /* ------------------------------------------------------------------- */
318: /* A
319: MatShell object
320: */
321: PetscErrorCode FormJacobianState(Tao tao, Vec X, Mat J, Mat JPre, Mat JInv, void *ptr)
322: {
324:   PetscInt       i;
325:   AppCtx         *user = (AppCtx*)ptr;

328:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
329:   Scatter_yi(user->u,user->ui,user->ui_scatter,user->nt);
330:   Scatter_uxi_uyi(user->u,user->uxi,user->uxi_scatter,user->uyi,user->uyi_scatter,user->nt);
331:   for (i=0; i<user->nt; i++) {
332:     MatCopy(user->Divxy[0],user->C[i],SUBSET_NONZERO_PATTERN);
333:     MatCopy(user->Divxy[1],user->Cwork[i],SAME_NONZERO_PATTERN);

335:     MatDiagonalScale(user->C[i],NULL,user->uxi[i]);
336:     MatDiagonalScale(user->Cwork[i],NULL,user->uyi[i]);
337:     MatAXPY(user->C[i],1.0,user->Cwork[i],SUBSET_NONZERO_PATTERN);
338:     MatScale(user->C[i],user->ht);
339:     MatShift(user->C[i],1.0);
340:   }
341:   return(0);
342: }

344: /* ------------------------------------------------------------------- */
345: /* B */
346: PetscErrorCode FormJacobianDesign(Tao tao, Vec X, Mat J, void *ptr)
347: {
349:   AppCtx         *user = (AppCtx*)ptr;

352:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
353:   return(0);
354: }

356: PetscErrorCode StateMatMult(Mat J_shell, Vec X, Vec Y)
357: {
359:   PetscInt       i;
360:   AppCtx         *user;

363:   MatShellGetContext(J_shell,(void**)&user);
364:   Scatter_yi(X,user->yi,user->yi_scatter,user->nt);
365:   user->block_index = 0;
366:   MatMult(user->JsBlock,user->yi[0],user->yiwork[0]);

368:   for (i=1; i<user->nt; i++) {
369:     user->block_index = i;
370:     MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
371:     MatMult(user->M,user->yi[i-1],user->ziwork[i-1]);
372:     VecAXPY(user->yiwork[i],-1.0,user->ziwork[i-1]);
373:   }
374:   Gather_yi(Y,user->yiwork,user->yi_scatter,user->nt);
375:   return(0);
376: }

378: PetscErrorCode StateMatMultTranspose(Mat J_shell, Vec X, Vec Y)
379: {
381:   PetscInt       i;
382:   AppCtx         *user;

385:   MatShellGetContext(J_shell,(void**)&user);
386:   Scatter_yi(X,user->yi,user->yi_scatter,user->nt);

388:   for (i=0; i<user->nt-1; i++) {
389:     user->block_index = i;
390:     MatMultTranspose(user->JsBlock,user->yi[i],user->yiwork[i]);
391:     MatMult(user->M,user->yi[i+1],user->ziwork[i+1]);
392:     VecAXPY(user->yiwork[i],-1.0,user->ziwork[i+1]);
393:   }

395:   i = user->nt-1;
396:   user->block_index = i;
397:   MatMultTranspose(user->JsBlock,user->yi[i],user->yiwork[i]);
398:   Gather_yi(Y,user->yiwork,user->yi_scatter,user->nt);
399:   return(0);
400: }

402: PetscErrorCode StateMatBlockMult(Mat J_shell, Vec X, Vec Y)
403: {
405:   PetscInt       i;
406:   AppCtx         *user;

409:   MatShellGetContext(J_shell,(void**)&user);
410:   i = user->block_index;
411:   VecPointwiseMult(user->uxiwork[i],X,user->uxi[i]);
412:   VecPointwiseMult(user->uyiwork[i],X,user->uyi[i]);
413:   Gather(user->uiwork[i],user->uxiwork[i],user->ux_scatter[i],user->uyiwork[i],user->uy_scatter[i]);
414:   MatMult(user->Div,user->uiwork[i],Y);
415:   VecAYPX(Y,user->ht,X);
416:   return(0);
417: }

419: PetscErrorCode StateMatBlockMultTranspose(Mat J_shell, Vec X, Vec Y)
420: {
422:   PetscInt       i;
423:   AppCtx         *user;

426:   MatShellGetContext(J_shell,(void**)&user);
427:   i = user->block_index;
428:   MatMult(user->Grad,X,user->uiwork[i]);
429:   Scatter(user->uiwork[i],user->uxiwork[i],user->ux_scatter[i],user->uyiwork[i],user->uy_scatter[i]);
430:   VecPointwiseMult(user->uxiwork[i],user->uxi[i],user->uxiwork[i]);
431:   VecPointwiseMult(user->uyiwork[i],user->uyi[i],user->uyiwork[i]);
432:   VecWAXPY(Y,1.0,user->uxiwork[i],user->uyiwork[i]);
433:   VecAYPX(Y,user->ht,X);
434:   return(0);
435: }

437: PetscErrorCode DesignMatMult(Mat J_shell, Vec X, Vec Y)
438: {
440:   PetscInt       i;
441:   AppCtx         *user;

444:   MatShellGetContext(J_shell,(void**)&user);
445:   Scatter_yi(user->y,user->yi,user->yi_scatter,user->nt);
446:   Scatter_uxi_uyi(X,user->uxiwork,user->uxi_scatter,user->uyiwork,user->uyi_scatter,user->nt);
447:   for (i=0; i<user->nt; i++) {
448:     VecPointwiseMult(user->uxiwork[i],user->yi[i],user->uxiwork[i]);
449:     VecPointwiseMult(user->uyiwork[i],user->yi[i],user->uyiwork[i]);
450:     Gather(user->uiwork[i],user->uxiwork[i],user->ux_scatter[i],user->uyiwork[i],user->uy_scatter[i]);
451:     MatMult(user->Div,user->uiwork[i],user->ziwork[i]);
452:     VecScale(user->ziwork[i],user->ht);
453:   }
454:   Gather_yi(Y,user->ziwork,user->yi_scatter,user->nt);
455:   return(0);
456: }

458: PetscErrorCode DesignMatMultTranspose(Mat J_shell, Vec X, Vec Y)
459: {
461:   PetscInt       i;
462:   AppCtx         *user;

465:   MatShellGetContext(J_shell,(void**)&user);
466:   Scatter_yi(user->y,user->yi,user->yi_scatter,user->nt);
467:   Scatter_yi(X,user->yiwork,user->yi_scatter,user->nt);
468:   for (i=0; i<user->nt; i++) {
469:     MatMult(user->Grad,user->yiwork[i],user->uiwork[i]);
470:     Scatter(user->uiwork[i],user->uxiwork[i],user->ux_scatter[i],user->uyiwork[i],user->uy_scatter[i]);
471:     VecPointwiseMult(user->uxiwork[i],user->yi[i],user->uxiwork[i]);
472:     VecPointwiseMult(user->uyiwork[i],user->yi[i],user->uyiwork[i]);
473:     Gather(user->uiwork[i],user->uxiwork[i],user->ux_scatter[i],user->uyiwork[i],user->uy_scatter[i]);
474:     VecScale(user->uiwork[i],user->ht);
475:   }
476:   Gather_yi(Y,user->uiwork,user->ui_scatter,user->nt);
477:   return(0);
478: }

480: PetscErrorCode StateMatBlockPrecMult(PC PC_shell, Vec X, Vec Y)
481: {
483:   PetscInt       i;
484:   AppCtx         *user;

487:   PCShellGetContext(PC_shell,(void**)&user);
488:   i = user->block_index;
489:   if (user->c_formed) {
490:     MatSOR(user->C[i],X,1.0,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_SYMMETRIC_SWEEP),0.0,1,1,Y);
491:   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not formed");
492:   return(0);
493: }

495: PetscErrorCode StateMatBlockPrecMultTranspose(PC PC_shell, Vec X, Vec Y)
496: {
498:   PetscInt       i;
499:   AppCtx         *user;

502:   PCShellGetContext(PC_shell,(void**)&user);

504:   i = user->block_index;
505:   if (user->c_formed) {
506:     MatSOR(user->C[i],X,1.0,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_SYMMETRIC_SWEEP),0.0,1,1,Y);
507:   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not formed");
508:   return(0);
509: }

511: PetscErrorCode StateMatInvMult(Mat J_shell, Vec X, Vec Y)
512: {
514:   AppCtx         *user;
515:   PetscInt       its,i;

518:   MatShellGetContext(J_shell,(void**)&user);

520:   if (Y == user->ytrue) {
521:     /* First solve is done using true solution to set up problem */
522:     KSPSetTolerances(user->solver,1e-4,1e-20,PETSC_DEFAULT,PETSC_DEFAULT);
523:   } else {
524:     KSPSetTolerances(user->solver,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
525:   }
526:   Scatter_yi(X,user->yi,user->yi_scatter,user->nt);
527:   Scatter_yi(Y,user->yiwork,user->yi_scatter,user->nt);
528:   Scatter_uxi_uyi(user->u,user->uxi,user->uxi_scatter,user->uyi,user->uyi_scatter,user->nt);

530:   user->block_index = 0;
531:   KSPSolve(user->solver,user->yi[0],user->yiwork[0]);

533:   KSPGetIterationNumber(user->solver,&its);
534:   user->ksp_its = user->ksp_its + its;
535:   for (i=1; i<user->nt; i++) {
536:     MatMult(user->M,user->yiwork[i-1],user->ziwork[i-1]);
537:     VecAXPY(user->yi[i],1.0,user->ziwork[i-1]);
538:     user->block_index = i;
539:     KSPSolve(user->solver,user->yi[i],user->yiwork[i]);

541:     KSPGetIterationNumber(user->solver,&its);
542:     user->ksp_its = user->ksp_its + its;
543:   }
544:   Gather_yi(Y,user->yiwork,user->yi_scatter,user->nt);
545:   return(0);
546: }

548: PetscErrorCode StateMatInvTransposeMult(Mat J_shell, Vec X, Vec Y)
549: {
551:   AppCtx         *user;
552:   PetscInt       its,i;

555:   MatShellGetContext(J_shell,(void**)&user);

557:   Scatter_yi(X,user->yi,user->yi_scatter,user->nt);
558:   Scatter_yi(Y,user->yiwork,user->yi_scatter,user->nt);
559:   Scatter_uxi_uyi(user->u,user->uxi,user->uxi_scatter,user->uyi,user->uyi_scatter,user->nt);

561:   i = user->nt - 1;
562:   user->block_index = i;
563:   KSPSolveTranspose(user->solver,user->yi[i],user->yiwork[i]);

565:   KSPGetIterationNumber(user->solver,&its);
566:   user->ksp_its = user->ksp_its + its;

568:   for (i=user->nt-2; i>=0; i--) {
569:     MatMult(user->M,user->yiwork[i+1],user->ziwork[i+1]);
570:     VecAXPY(user->yi[i],1.0,user->ziwork[i+1]);
571:     user->block_index = i;
572:     KSPSolveTranspose(user->solver,user->yi[i],user->yiwork[i]);

574:     KSPGetIterationNumber(user->solver,&its);
575:     user->ksp_its = user->ksp_its + its;
576:   }
577:   Gather_yi(Y,user->yiwork,user->yi_scatter,user->nt);
578:   return(0);
579: }

581: PetscErrorCode StateMatDuplicate(Mat J_shell, MatDuplicateOption opt, Mat *new_shell)
582: {
584:   AppCtx         *user;

587:   MatShellGetContext(J_shell,(void**)&user);

589:   MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,new_shell);
590:   MatShellSetOperation(*new_shell,MATOP_MULT,(void(*)(void))StateMatMult);
591:   MatShellSetOperation(*new_shell,MATOP_DUPLICATE,(void(*)(void))StateMatDuplicate);
592:   MatShellSetOperation(*new_shell,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMultTranspose);
593:   MatShellSetOperation(*new_shell,MATOP_GET_DIAGONAL,(void(*)(void))StateMatGetDiagonal);
594:   return(0);
595: }

597: PetscErrorCode StateMatGetDiagonal(Mat J_shell, Vec X)
598: {
600:   AppCtx         *user;

603:   MatShellGetContext(J_shell,(void**)&user);
604:    VecCopy(user->js_diag,X);
605:   return(0);
606: }

608: PetscErrorCode FormConstraints(Tao tao, Vec X, Vec C, void *ptr)
609: {
610:   /* con = Ay - q, A = [C(u1)  0     0     ...   0;
611:                          -M  C(u2)   0     ...   0;
612:                           0   -M   C(u3)   ...   0;
613:                                       ...         ;
614:                           0    ...      -M C(u_nt)]
615:      C(u) = eye + ht*Div*[diag(u1); diag(u2)]       */
617:   PetscInt       i;
618:   AppCtx         *user = (AppCtx*)ptr;

621:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
622:   Scatter_yi(user->y,user->yi,user->yi_scatter,user->nt);
623:   Scatter_uxi_uyi(user->u,user->uxi,user->uxi_scatter,user->uyi,user->uyi_scatter,user->nt);

625:   user->block_index = 0;
626:   MatMult(user->JsBlock,user->yi[0],user->yiwork[0]);

628:   for (i=1; i<user->nt; i++) {
629:     user->block_index = i;
630:     MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
631:     MatMult(user->M,user->yi[i-1],user->ziwork[i-1]);
632:     VecAXPY(user->yiwork[i],-1.0,user->ziwork[i-1]);
633:   }

635:   Gather_yi(C,user->yiwork,user->yi_scatter,user->nt);
636:   VecAXPY(C,-1.0,user->q);

638:   return(0);
639: }

641: PetscErrorCode Scatter(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat)
642: {

646:   VecScatterBegin(s_scat,x,state,INSERT_VALUES,SCATTER_FORWARD);
647:   VecScatterEnd(s_scat,x,state,INSERT_VALUES,SCATTER_FORWARD);
648:   VecScatterBegin(d_scat,x,design,INSERT_VALUES,SCATTER_FORWARD);
649:   VecScatterEnd(d_scat,x,design,INSERT_VALUES,SCATTER_FORWARD);
650:   return(0);
651: }

653: PetscErrorCode Scatter_uxi_uyi(Vec u, Vec *uxi, VecScatter *scatx, Vec *uyi, VecScatter *scaty, PetscInt nt)
654: {
656:   PetscInt       i;

659:   for (i=0; i<nt; i++) {
660:     VecScatterBegin(scatx[i],u,uxi[i],INSERT_VALUES,SCATTER_FORWARD);
661:     VecScatterEnd(scatx[i],u,uxi[i],INSERT_VALUES,SCATTER_FORWARD);
662:     VecScatterBegin(scaty[i],u,uyi[i],INSERT_VALUES,SCATTER_FORWARD);
663:     VecScatterEnd(scaty[i],u,uyi[i],INSERT_VALUES,SCATTER_FORWARD);
664:   }
665:   return(0);
666: }

668: PetscErrorCode Gather(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat)
669: {

673:   VecScatterBegin(s_scat,state,x,INSERT_VALUES,SCATTER_REVERSE);
674:   VecScatterEnd(s_scat,state,x,INSERT_VALUES,SCATTER_REVERSE);
675:   VecScatterBegin(d_scat,design,x,INSERT_VALUES,SCATTER_REVERSE);
676:   VecScatterEnd(d_scat,design,x,INSERT_VALUES,SCATTER_REVERSE);
677:   return(0);
678: }

680: PetscErrorCode Gather_uxi_uyi(Vec u, Vec *uxi, VecScatter *scatx, Vec *uyi, VecScatter *scaty, PetscInt nt)
681: {
683:   PetscInt       i;

686:   for (i=0; i<nt; i++) {
687:     VecScatterBegin(scatx[i],uxi[i],u,INSERT_VALUES,SCATTER_REVERSE);
688:     VecScatterEnd(scatx[i],uxi[i],u,INSERT_VALUES,SCATTER_REVERSE);
689:     VecScatterBegin(scaty[i],uyi[i],u,INSERT_VALUES,SCATTER_REVERSE);
690:     VecScatterEnd(scaty[i],uyi[i],u,INSERT_VALUES,SCATTER_REVERSE);
691:   }
692:   return(0);
693: }

695: PetscErrorCode Scatter_yi(Vec y, Vec *yi, VecScatter *scat, PetscInt nt)
696: {
698:   PetscInt       i;

701:   for (i=0; i<nt; i++) {
702:     VecScatterBegin(scat[i],y,yi[i],INSERT_VALUES,SCATTER_FORWARD);
703:     VecScatterEnd(scat[i],y,yi[i],INSERT_VALUES,SCATTER_FORWARD);
704:   }
705:   return(0);
706: }

708: PetscErrorCode Gather_yi(Vec y, Vec *yi, VecScatter *scat, PetscInt nt)
709: {
711:   PetscInt       i;

714:   for (i=0; i<nt; i++) {
715:     VecScatterBegin(scat[i],yi[i],y,INSERT_VALUES,SCATTER_REVERSE);
716:     VecScatterEnd(scat[i],yi[i],y,INSERT_VALUES,SCATTER_REVERSE);
717:   }
718:   return(0);
719: }

721: PetscErrorCode HyperbolicInitialize(AppCtx *user)
722: {
724:   PetscInt       n,i,j,linear_index,istart,iend,iblock,lo,hi;
725:   Vec            XX,YY,XXwork,YYwork,yi,uxi,ui,bc;
726:   PetscReal      h,sum;
727:   PetscScalar    hinv,neg_hinv,quarter=0.25,one=1.0,half_hinv,neg_half_hinv;
728:   PetscScalar    vx,vy,zero=0.0;
729:   IS             is_from_y,is_to_yi,is_from_u,is_to_uxi,is_to_uyi;

732:   user->jformed = PETSC_FALSE;
733:   user->c_formed = PETSC_FALSE;

735:   user->ksp_its = 0;
736:   user->ksp_its_initial = 0;

738:   n = user->mx * user->mx;

740:   h = 1.0/user->mx;
741:   hinv = user->mx;
742:   neg_hinv = -hinv;
743:   half_hinv = hinv / 2.0;
744:   neg_half_hinv = neg_hinv / 2.0;

746:   /* Generate Grad matrix */
747:   MatCreate(PETSC_COMM_WORLD,&user->Grad);
748:   MatSetSizes(user->Grad,PETSC_DECIDE,PETSC_DECIDE,2*n,n);
749:   MatSetFromOptions(user->Grad);
750:   MatMPIAIJSetPreallocation(user->Grad,3,NULL,3,NULL);
751:   MatSeqAIJSetPreallocation(user->Grad,3,NULL);
752:   MatGetOwnershipRange(user->Grad,&istart,&iend);

754:   for (i=istart; i<iend; i++) {
755:     if (i<n) {
756:       iblock = i / user->mx;
757:       j = iblock*user->mx + ((i+user->mx-1) % user->mx);
758:       MatSetValues(user->Grad,1,&i,1,&j,&half_hinv,INSERT_VALUES);
759:       j = iblock*user->mx + ((i+1) % user->mx);
760:       MatSetValues(user->Grad,1,&i,1,&j,&neg_half_hinv,INSERT_VALUES);
761:     }
762:     if (i>=n) {
763:       j = (i - user->mx) % n;
764:       MatSetValues(user->Grad,1,&i,1,&j,&half_hinv,INSERT_VALUES);
765:       j = (j + 2*user->mx) % n;
766:       MatSetValues(user->Grad,1,&i,1,&j,&neg_half_hinv,INSERT_VALUES);
767:     }
768:   }

770:   MatAssemblyBegin(user->Grad,MAT_FINAL_ASSEMBLY);
771:   MatAssemblyEnd(user->Grad,MAT_FINAL_ASSEMBLY);

773:   MatCreate(PETSC_COMM_WORLD,&user->Gradxy[0]);
774:   MatSetSizes(user->Gradxy[0],PETSC_DECIDE,PETSC_DECIDE,n,n);
775:   MatSetFromOptions(user->Gradxy[0]);
776:   MatMPIAIJSetPreallocation(user->Gradxy[0],3,NULL,3,NULL);
777:   MatSeqAIJSetPreallocation(user->Gradxy[0],3,NULL);
778:   MatGetOwnershipRange(user->Gradxy[0],&istart,&iend);

780:   for (i=istart; i<iend; i++) {
781:     iblock = i / user->mx;
782:     j = iblock*user->mx + ((i+user->mx-1) % user->mx);
783:     MatSetValues(user->Gradxy[0],1,&i,1,&j,&half_hinv,INSERT_VALUES);
784:     j = iblock*user->mx + ((i+1) % user->mx);
785:     MatSetValues(user->Gradxy[0],1,&i,1,&j,&neg_half_hinv,INSERT_VALUES);
786:     MatSetValues(user->Gradxy[0],1,&i,1,&i,&zero,INSERT_VALUES);
787:   }
788:   MatAssemblyBegin(user->Gradxy[0],MAT_FINAL_ASSEMBLY);
789:   MatAssemblyEnd(user->Gradxy[0],MAT_FINAL_ASSEMBLY);

791:   MatCreate(PETSC_COMM_WORLD,&user->Gradxy[1]);
792:   MatSetSizes(user->Gradxy[1],PETSC_DECIDE,PETSC_DECIDE,n,n);
793:   MatSetFromOptions(user->Gradxy[1]);
794:   MatMPIAIJSetPreallocation(user->Gradxy[1],3,NULL,3,NULL);
795:   MatSeqAIJSetPreallocation(user->Gradxy[1],3,NULL);
796:   MatGetOwnershipRange(user->Gradxy[1],&istart,&iend);

798:   for (i=istart; i<iend; i++) {
799:     j = (i + n - user->mx) % n;
800:     MatSetValues(user->Gradxy[1],1,&i,1,&j,&half_hinv,INSERT_VALUES);
801:     j = (j + 2*user->mx) % n;
802:     MatSetValues(user->Gradxy[1],1,&i,1,&j,&neg_half_hinv,INSERT_VALUES);
803:     MatSetValues(user->Gradxy[1],1,&i,1,&i,&zero,INSERT_VALUES);
804:   }
805:   MatAssemblyBegin(user->Gradxy[1],MAT_FINAL_ASSEMBLY);
806:   MatAssemblyEnd(user->Gradxy[1],MAT_FINAL_ASSEMBLY);

808:   /* Generate Div matrix */
809:   MatTranspose(user->Grad,MAT_INITIAL_MATRIX,&user->Div);
810:   MatTranspose(user->Gradxy[0],MAT_INITIAL_MATRIX,&user->Divxy[0]);
811:   MatTranspose(user->Gradxy[1],MAT_INITIAL_MATRIX,&user->Divxy[1]);

813:   /* Off-diagonal averaging matrix */
814:   MatCreate(PETSC_COMM_WORLD,&user->M);
815:   MatSetSizes(user->M,PETSC_DECIDE,PETSC_DECIDE,n,n);
816:   MatSetFromOptions(user->M);
817:   MatMPIAIJSetPreallocation(user->M,4,NULL,4,NULL);
818:   MatSeqAIJSetPreallocation(user->M,4,NULL);
819:   MatGetOwnershipRange(user->M,&istart,&iend);

821:   for (i=istart; i<iend; i++) {
822:     /* kron(Id,Av) */
823:     iblock = i / user->mx;
824:     j = iblock*user->mx + ((i+user->mx-1) % user->mx);
825:     MatSetValues(user->M,1,&i,1,&j,&quarter,INSERT_VALUES);
826:     j = iblock*user->mx + ((i+1) % user->mx);
827:     MatSetValues(user->M,1,&i,1,&j,&quarter,INSERT_VALUES);

829:     /* kron(Av,Id) */
830:     j = (i + user->mx) % n;
831:     MatSetValues(user->M,1,&i,1,&j,&quarter,INSERT_VALUES);
832:     j = (i + n - user->mx) % n;
833:     MatSetValues(user->M,1,&i,1,&j,&quarter,INSERT_VALUES);
834:   }
835:   MatAssemblyBegin(user->M,MAT_FINAL_ASSEMBLY);
836:   MatAssemblyEnd(user->M,MAT_FINAL_ASSEMBLY);

838:   /* Generate 2D grid */
839:   VecCreate(PETSC_COMM_WORLD,&XX);
840:   VecCreate(PETSC_COMM_WORLD,&user->q);
841:   VecSetSizes(XX,PETSC_DECIDE,n);
842:   VecSetSizes(user->q,PETSC_DECIDE,n*user->nt);
843:   VecSetFromOptions(XX);
844:   VecSetFromOptions(user->q);

846:   VecDuplicate(XX,&YY);
847:   VecDuplicate(XX,&XXwork);
848:   VecDuplicate(XX,&YYwork);
849:   VecDuplicate(XX,&user->d);
850:   VecDuplicate(XX,&user->dwork);

852:   VecGetOwnershipRange(XX,&istart,&iend);
853:   for (linear_index=istart; linear_index<iend; linear_index++) {
854:     i = linear_index % user->mx;
855:     j = (linear_index-i)/user->mx;
856:     vx = h*(i+0.5);
857:     vy = h*(j+0.5);
858:     VecSetValues(XX,1,&linear_index,&vx,INSERT_VALUES);
859:     VecSetValues(YY,1,&linear_index,&vy,INSERT_VALUES);
860:   }

862:   VecAssemblyBegin(XX);
863:   VecAssemblyEnd(XX);
864:   VecAssemblyBegin(YY);
865:   VecAssemblyEnd(YY);

867:   /* Compute final density function yT
868:      yT = 1.0 + exp(-30*((x-0.25)^2+(y-0.25)^2)) + exp(-30*((x-0.75)^2+(y-0.75)^2))
869:      yT = yT / (h^2*sum(yT)) */
870:   VecCopy(XX,XXwork);
871:   VecCopy(YY,YYwork);

873:   VecShift(XXwork,-0.25);
874:   VecShift(YYwork,-0.25);

876:   VecPointwiseMult(XXwork,XXwork,XXwork);
877:   VecPointwiseMult(YYwork,YYwork,YYwork);

879:   VecCopy(XXwork,user->dwork);
880:   VecAXPY(user->dwork,1.0,YYwork);
881:   VecScale(user->dwork,-30.0);
882:   VecExp(user->dwork);
883:   VecCopy(user->dwork,user->d);

885:   VecCopy(XX,XXwork);
886:   VecCopy(YY,YYwork);

888:   VecShift(XXwork,-0.75);
889:   VecShift(YYwork,-0.75);

891:   VecPointwiseMult(XXwork,XXwork,XXwork);
892:   VecPointwiseMult(YYwork,YYwork,YYwork);

894:   VecCopy(XXwork,user->dwork);
895:   VecAXPY(user->dwork,1.0,YYwork);
896:   VecScale(user->dwork,-30.0);
897:   VecExp(user->dwork);

899:   VecAXPY(user->d,1.0,user->dwork);
900:   VecShift(user->d,1.0);
901:   VecSum(user->d,&sum);
902:   VecScale(user->d,1.0/(h*h*sum));

904:   /* Initial conditions of forward problem */
905:   VecDuplicate(XX,&bc);
906:   VecCopy(XX,XXwork);
907:   VecCopy(YY,YYwork);

909:   VecShift(XXwork,-0.5);
910:   VecShift(YYwork,-0.5);

912:   VecPointwiseMult(XXwork,XXwork,XXwork);
913:   VecPointwiseMult(YYwork,YYwork,YYwork);

915:   VecWAXPY(bc,1.0,XXwork,YYwork);
916:   VecScale(bc,-50.0);
917:   VecExp(bc);
918:   VecShift(bc,1.0);
919:   VecSum(bc,&sum);
920:   VecScale(bc,1.0/(h*h*sum));

922:   /* Create scatter from y to y_1,y_2,...,y_nt */
923:   /*  TODO: Reorder for better parallelism. (This will require reordering Q and L as well.) */
924:   PetscMalloc1(user->nt*user->mx*user->mx,&user->yi_scatter);
925:   VecCreate(PETSC_COMM_WORLD,&yi);
926:   VecSetSizes(yi,PETSC_DECIDE,user->mx*user->mx);
927:   VecSetFromOptions(yi);
928:   VecDuplicateVecs(yi,user->nt,&user->yi);
929:   VecDuplicateVecs(yi,user->nt,&user->yiwork);
930:   VecDuplicateVecs(yi,user->nt,&user->ziwork);
931:   for (i=0; i<user->nt; i++) {
932:     VecGetOwnershipRange(user->yi[i],&lo,&hi);
933:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_yi);
934:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+i*user->mx*user->mx,1,&is_from_y);
935:     VecScatterCreate(user->y,is_from_y,user->yi[i],is_to_yi,&user->yi_scatter[i]);
936:     ISDestroy(&is_to_yi);
937:     ISDestroy(&is_from_y);
938:   }

940:   /* Create scatter from u to ux_1,uy_1,ux_2,uy_2,...,ux_nt,uy_nt */
941:   /*  TODO: reorder for better parallelism */
942:   PetscMalloc1(user->nt*user->mx*user->mx,&user->uxi_scatter);
943:   PetscMalloc1(user->nt*user->mx*user->mx,&user->uyi_scatter);
944:   PetscMalloc1(user->nt*user->mx*user->mx,&user->ux_scatter);
945:   PetscMalloc1(user->nt*user->mx*user->mx,&user->uy_scatter);
946:   PetscMalloc1(2*user->nt*user->mx*user->mx,&user->ui_scatter);
947:   VecCreate(PETSC_COMM_WORLD,&uxi);
948:   VecCreate(PETSC_COMM_WORLD,&ui);
949:   VecSetSizes(uxi,PETSC_DECIDE,user->mx*user->mx);
950:   VecSetSizes(ui,PETSC_DECIDE,2*user->mx*user->mx);
951:   VecSetFromOptions(uxi);
952:   VecSetFromOptions(ui);
953:   VecDuplicateVecs(uxi,user->nt,&user->uxi);
954:   VecDuplicateVecs(uxi,user->nt,&user->uyi);
955:   VecDuplicateVecs(uxi,user->nt,&user->uxiwork);
956:   VecDuplicateVecs(uxi,user->nt,&user->uyiwork);
957:   VecDuplicateVecs(ui,user->nt,&user->ui);
958:   VecDuplicateVecs(ui,user->nt,&user->uiwork);
959:   for (i=0; i<user->nt; i++) {
960:     VecGetOwnershipRange(user->uxi[i],&lo,&hi);
961:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_uxi);
962:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+2*i*user->mx*user->mx,1,&is_from_u);
963:     VecScatterCreate(user->u,is_from_u,user->uxi[i],is_to_uxi,&user->uxi_scatter[i]);

965:     ISDestroy(&is_to_uxi);
966:     ISDestroy(&is_from_u);

968:     VecGetOwnershipRange(user->uyi[i],&lo,&hi);
969:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_uyi);
970:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+(2*i+1)*user->mx*user->mx,1,&is_from_u);
971:     VecScatterCreate(user->u,is_from_u,user->uyi[i],is_to_uyi,&user->uyi_scatter[i]);

973:     ISDestroy(&is_to_uyi);
974:     ISDestroy(&is_from_u);

976:     VecGetOwnershipRange(user->uxi[i],&lo,&hi);
977:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_uxi);
978:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_from_u);
979:     VecScatterCreate(user->ui[i],is_from_u,user->uxi[i],is_to_uxi,&user->ux_scatter[i]);

981:     ISDestroy(&is_to_uxi);
982:     ISDestroy(&is_from_u);

984:     VecGetOwnershipRange(user->uyi[i],&lo,&hi);
985:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_uyi);
986:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+user->mx*user->mx,1,&is_from_u);
987:     VecScatterCreate(user->ui[i],is_from_u,user->uyi[i],is_to_uyi,&user->uy_scatter[i]);

989:     ISDestroy(&is_to_uyi);
990:     ISDestroy(&is_from_u);

992:     VecGetOwnershipRange(user->ui[i],&lo,&hi);
993:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_uxi);
994:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+2*i*user->mx*user->mx,1,&is_from_u);
995:     VecScatterCreate(user->u,is_from_u,user->ui[i],is_to_uxi,&user->ui_scatter[i]);

997:     ISDestroy(&is_to_uxi);
998:     ISDestroy(&is_from_u);
999:   }

1001:   /* RHS of forward problem */
1002:   MatMult(user->M,bc,user->yiwork[0]);
1003:   for (i=1; i<user->nt; i++) {
1004:     VecSet(user->yiwork[i],0.0);
1005:   }
1006:   Gather_yi(user->q,user->yiwork,user->yi_scatter,user->nt);

1008:   /* Compute true velocity field utrue */
1009:   VecDuplicate(user->u,&user->utrue);
1010:   for (i=0; i<user->nt; i++) {
1011:     VecCopy(YY,user->uxi[i]);
1012:     VecScale(user->uxi[i],150.0*i*user->ht);
1013:     VecCopy(XX,user->uyi[i]);
1014:     VecShift(user->uyi[i],-10.0);
1015:     VecScale(user->uyi[i],15.0*i*user->ht);
1016:   }
1017:   Gather_uxi_uyi(user->utrue,user->uxi,user->uxi_scatter,user->uyi,user->uyi_scatter,user->nt);

1019:   /* Initial guess and reference model */
1020:   VecDuplicate(user->utrue,&user->ur);
1021:   for (i=0; i<user->nt; i++) {
1022:     VecCopy(XX,user->uxi[i]);
1023:     VecShift(user->uxi[i],i*user->ht);
1024:     VecCopy(YY,user->uyi[i]);
1025:     VecShift(user->uyi[i],-i*user->ht);
1026:   }
1027:   Gather_uxi_uyi(user->ur,user->uxi,user->uxi_scatter,user->uyi,user->uyi_scatter,user->nt);

1029:   /* Generate regularization matrix L */
1030:   MatCreate(PETSC_COMM_WORLD,&user->LT);
1031:   MatSetSizes(user->LT,PETSC_DECIDE,PETSC_DECIDE,2*n*user->nt,n*user->nt);
1032:   MatSetFromOptions(user->LT);
1033:   MatMPIAIJSetPreallocation(user->LT,1,NULL,1,NULL);
1034:   MatSeqAIJSetPreallocation(user->LT,1,NULL);
1035:   MatGetOwnershipRange(user->LT,&istart,&iend);

1037:   for (i=istart; i<iend; i++) {
1038:     iblock = (i+n) / (2*n);
1039:     j = i - iblock*n;
1040:     MatSetValues(user->LT,1,&i,1,&j,&user->gamma,INSERT_VALUES);
1041:   }

1043:   MatAssemblyBegin(user->LT,MAT_FINAL_ASSEMBLY);
1044:   MatAssemblyEnd(user->LT,MAT_FINAL_ASSEMBLY);

1046:   MatTranspose(user->LT,MAT_INITIAL_MATRIX,&user->L);

1048:   /* Build work vectors and matrices */
1049:   VecCreate(PETSC_COMM_WORLD,&user->lwork);
1050:   VecSetType(user->lwork,VECMPI);
1051:   VecSetSizes(user->lwork,PETSC_DECIDE,user->m);
1052:   VecSetFromOptions(user->lwork);

1054:   MatDuplicate(user->Div,MAT_SHARE_NONZERO_PATTERN,&user->Divwork);

1056:   VecDuplicate(user->y,&user->ywork);
1057:   VecDuplicate(user->u,&user->uwork);
1058:   VecDuplicate(user->u,&user->vwork);
1059:   VecDuplicate(user->u,&user->js_diag);
1060:   VecDuplicate(user->c,&user->cwork);

1062:   /* Create matrix-free shell user->Js for computing A*x */
1063:   MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,&user->Js);
1064:   MatShellSetOperation(user->Js,MATOP_MULT,(void(*)(void))StateMatMult);
1065:   MatShellSetOperation(user->Js,MATOP_DUPLICATE,(void(*)(void))StateMatDuplicate);
1066:   MatShellSetOperation(user->Js,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMultTranspose);
1067:   MatShellSetOperation(user->Js,MATOP_GET_DIAGONAL,(void(*)(void))StateMatGetDiagonal);

1069:   /* Diagonal blocks of user->Js */
1070:   MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,n,n,user,&user->JsBlock);
1071:   MatShellSetOperation(user->JsBlock,MATOP_MULT,(void(*)(void))StateMatBlockMult);
1072:   MatShellSetOperation(user->JsBlock,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatBlockMultTranspose);

1074:   /* Create a matrix-free shell user->JsBlockPrec for computing (U+D)\D*(L+D)\x, where JsBlock = L+D+U,
1075:      D is diagonal, L is strictly lower triangular, and U is strictly upper triangular.
1076:      This is an SOR preconditioner for user->JsBlock. */
1077:   MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,n,n,user,&user->JsBlockPrec);
1078:   MatShellSetOperation(user->JsBlockPrec,MATOP_MULT,(void(*)(void))StateMatBlockPrecMult);
1079:   MatShellSetOperation(user->JsBlockPrec,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatBlockPrecMultTranspose);

1081:   /* Create a matrix-free shell user->Jd for computing B*x */
1082:   MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->n-user->m,user,&user->Jd);
1083:   MatShellSetOperation(user->Jd,MATOP_MULT,(void(*)(void))DesignMatMult);
1084:   MatShellSetOperation(user->Jd,MATOP_MULT_TRANSPOSE,(void(*)(void))DesignMatMultTranspose);

1086:   /* User-defined routines for computing user->Js\x and user->Js^T\x*/
1087:   MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,&user->JsInv);
1088:   MatShellSetOperation(user->JsInv,MATOP_MULT,(void(*)(void))StateMatInvMult);
1089:   MatShellSetOperation(user->JsInv,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatInvTransposeMult);

1091:   /* Build matrices for SOR preconditioner */
1092:   Scatter_uxi_uyi(user->u,user->uxi,user->uxi_scatter,user->uyi,user->uyi_scatter,user->nt);
1093:   PetscMalloc1(5*n,&user->C);
1094:   PetscMalloc1(2*n,&user->Cwork);
1095:   for (i=0; i<user->nt; i++) {
1096:     MatDuplicate(user->Divxy[0],MAT_COPY_VALUES,&user->C[i]);
1097:     MatDuplicate(user->Divxy[1],MAT_COPY_VALUES,&user->Cwork[i]);

1099:     MatDiagonalScale(user->C[i],NULL,user->uxi[i]);
1100:     MatDiagonalScale(user->Cwork[i],NULL,user->uyi[i]);
1101:     MatAXPY(user->C[i],1.0,user->Cwork[i],DIFFERENT_NONZERO_PATTERN);
1102:     MatScale(user->C[i],user->ht);
1103:     MatShift(user->C[i],1.0);
1104:   }

1106:   /* Solver options and tolerances */
1107:   KSPCreate(PETSC_COMM_WORLD,&user->solver);
1108:   KSPSetType(user->solver,KSPGMRES);
1109:   KSPSetOperators(user->solver,user->JsBlock,user->JsBlockPrec);
1110:   KSPSetTolerances(user->solver,1e-4,1e-20,1e3,500);
1111:   /* KSPSetTolerances(user->solver,1e-8,1e-16,1e3,500); */
1112:   KSPGetPC(user->solver,&user->prec);
1113:   PCSetType(user->prec,PCSHELL);

1115:   PCShellSetApply(user->prec,StateMatBlockPrecMult);
1116:   PCShellSetApplyTranspose(user->prec,StateMatBlockPrecMultTranspose);
1117:   PCShellSetContext(user->prec,user);

1119:   /* Compute true state function yt given ut */
1120:   VecCreate(PETSC_COMM_WORLD,&user->ytrue);
1121:   VecSetSizes(user->ytrue,PETSC_DECIDE,n*user->nt);
1122:   VecSetFromOptions(user->ytrue);
1123:   user->c_formed = PETSC_TRUE;
1124:   VecCopy(user->utrue,user->u); /*  Set u=utrue temporarily for StateMatInv */
1125:   VecSet(user->ytrue,0.0); /*  Initial guess */
1126:   StateMatInvMult(user->Js,user->q,user->ytrue);
1127:   VecCopy(user->ur,user->u); /*  Reset u=ur */

1129:   /* Initial guess y0 for state given u0 */
1130:   StateMatInvMult(user->Js,user->q,user->y);

1132:   /* Data discretization */
1133:   MatCreate(PETSC_COMM_WORLD,&user->Q);
1134:   MatSetSizes(user->Q,PETSC_DECIDE,PETSC_DECIDE,user->mx*user->mx,user->m);
1135:   MatSetFromOptions(user->Q);
1136:   MatMPIAIJSetPreallocation(user->Q,0,NULL,1,NULL);
1137:   MatSeqAIJSetPreallocation(user->Q,1,NULL);

1139:   MatGetOwnershipRange(user->Q,&istart,&iend);

1141:   for (i=istart; i<iend; i++) {
1142:     j = i + user->m - user->mx*user->mx;
1143:     MatSetValues(user->Q,1,&i,1,&j,&one,INSERT_VALUES);
1144:   }

1146:   MatAssemblyBegin(user->Q,MAT_FINAL_ASSEMBLY);
1147:   MatAssemblyEnd(user->Q,MAT_FINAL_ASSEMBLY);

1149:   MatTranspose(user->Q,MAT_INITIAL_MATRIX,&user->QT);

1151:   VecDestroy(&XX);
1152:   VecDestroy(&YY);
1153:   VecDestroy(&XXwork);
1154:   VecDestroy(&YYwork);
1155:   VecDestroy(&yi);
1156:   VecDestroy(&uxi);
1157:   VecDestroy(&ui);
1158:   VecDestroy(&bc);

1160:   /* Now that initial conditions have been set, let the user pass tolerance options to the KSP solver */
1161:   KSPSetFromOptions(user->solver);
1162:   return(0);
1163: }

1165: PetscErrorCode HyperbolicDestroy(AppCtx *user)
1166: {
1168:   PetscInt       i;

1171:   MatDestroy(&user->Q);
1172:   MatDestroy(&user->QT);
1173:   MatDestroy(&user->Div);
1174:   MatDestroy(&user->Divwork);
1175:   MatDestroy(&user->Grad);
1176:   MatDestroy(&user->L);
1177:   MatDestroy(&user->LT);
1178:   KSPDestroy(&user->solver);
1179:   MatDestroy(&user->Js);
1180:   MatDestroy(&user->Jd);
1181:   MatDestroy(&user->JsBlockPrec);
1182:   MatDestroy(&user->JsInv);
1183:   MatDestroy(&user->JsBlock);
1184:   MatDestroy(&user->Divxy[0]);
1185:   MatDestroy(&user->Divxy[1]);
1186:   MatDestroy(&user->Gradxy[0]);
1187:   MatDestroy(&user->Gradxy[1]);
1188:   MatDestroy(&user->M);
1189:   for (i=0; i<user->nt; i++) {
1190:     MatDestroy(&user->C[i]);
1191:     MatDestroy(&user->Cwork[i]);
1192:   }
1193:   PetscFree(user->C);
1194:   PetscFree(user->Cwork);
1195:   VecDestroy(&user->u);
1196:   VecDestroy(&user->uwork);
1197:   VecDestroy(&user->vwork);
1198:   VecDestroy(&user->utrue);
1199:   VecDestroy(&user->y);
1200:   VecDestroy(&user->ywork);
1201:   VecDestroy(&user->ytrue);
1202:   VecDestroyVecs(user->nt,&user->yi);
1203:   VecDestroyVecs(user->nt,&user->yiwork);
1204:   VecDestroyVecs(user->nt,&user->ziwork);
1205:   VecDestroyVecs(user->nt,&user->uxi);
1206:   VecDestroyVecs(user->nt,&user->uyi);
1207:   VecDestroyVecs(user->nt,&user->uxiwork);
1208:   VecDestroyVecs(user->nt,&user->uyiwork);
1209:   VecDestroyVecs(user->nt,&user->ui);
1210:   VecDestroyVecs(user->nt,&user->uiwork);
1211:   VecDestroy(&user->c);
1212:   VecDestroy(&user->cwork);
1213:   VecDestroy(&user->ur);
1214:   VecDestroy(&user->q);
1215:   VecDestroy(&user->d);
1216:   VecDestroy(&user->dwork);
1217:   VecDestroy(&user->lwork);
1218:   VecDestroy(&user->js_diag);
1219:   ISDestroy(&user->s_is);
1220:   ISDestroy(&user->d_is);
1221:   VecScatterDestroy(&user->state_scatter);
1222:   VecScatterDestroy(&user->design_scatter);
1223:   for (i=0; i<user->nt; i++) {
1224:     VecScatterDestroy(&user->uxi_scatter[i]);
1225:     VecScatterDestroy(&user->uyi_scatter[i]);
1226:     VecScatterDestroy(&user->ux_scatter[i]);
1227:     VecScatterDestroy(&user->uy_scatter[i]);
1228:     VecScatterDestroy(&user->ui_scatter[i]);
1229:     VecScatterDestroy(&user->yi_scatter[i]);
1230:   }
1231:   PetscFree(user->uxi_scatter);
1232:   PetscFree(user->uyi_scatter);
1233:   PetscFree(user->ux_scatter);
1234:   PetscFree(user->uy_scatter);
1235:   PetscFree(user->ui_scatter);
1236:   PetscFree(user->yi_scatter);
1237:   return(0);
1238: }

1240: PetscErrorCode HyperbolicMonitor(Tao tao, void *ptr)
1241: {
1243:   Vec            X;
1244:   PetscReal      unorm,ynorm;
1245:   AppCtx         *user = (AppCtx*)ptr;

1248:   TaoGetSolutionVector(tao,&X);
1249:   Scatter(X,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
1250:   VecAXPY(user->ywork,-1.0,user->ytrue);
1251:   VecAXPY(user->uwork,-1.0,user->utrue);
1252:   VecNorm(user->uwork,NORM_2,&unorm);
1253:   VecNorm(user->ywork,NORM_2,&ynorm);
1254:   PetscPrintf(MPI_COMM_WORLD, "||u-ut||=%g ||y-yt||=%g\n",(double)unorm,(double)ynorm);
1255:   return(0);
1256: }

1258: /*TEST

1260:    build:
1261:       requires: !complex

1263:    test:
1264:       requires: !single
1265:       args: -tao_cmonitor -tao_max_funcs 10 -tao_type lcl -tao_gatol 1.e-5

1267:    test:
1268:       suffix: guess_pod
1269:       requires: !single
1270:       args: -tao_cmonitor -tao_max_funcs 10 -tao_type lcl -ksp_guess_type pod -tao_gatol 1.e-5

1272: TEST*/