Actual source code: hyperbolic.c

petsc-3.7.4 2016-10-02
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  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: TaoSetHistory(); TaoGetHistory();
 16:    Routines: TaoSolve();
 17:    Routines: TaoDestroy();
 18:    Processors: 1
 19: T*/

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

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

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

 51:   Vec d;
 52:   Vec dwork;

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

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

 64:   Vec js_diag;

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

 69:   Vec lwork;

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

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


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

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

103: PetscErrorCode DesignMatMult(Mat,Vec,Vec);
104: PetscErrorCode DesignMatMultTranspose(Mat,Vec,Vec);

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

111: static  char help[]="";

115: int main(int argc, char **argv)
116: {
117:   PetscErrorCode     ierr;
118:   Vec                x,x0;
119:   Tao                tao;
120:   AppCtx             user;
121:   IS                 is_allstate,is_alldesign;
122:   PetscInt           lo,hi,hi2,lo2,ksp_old;
123:   PetscInt           ntests = 1;
124:   PetscInt           i;
125: #if defined(PETSC_USE_LOG)
126:   PetscLogStage      stages[1];
127: #endif
128: 
129:   PetscInitialize(&argc, &argv, (char*)0,help);

131:   user.mx = 32;
132:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,NULL,NULL);
133:   PetscOptionsInt("-mx","Number of grid points in each direction","",user.mx,&user.mx,NULL);
134:   user.nt = 16;
135:   PetscOptionsInt("-nt","Number of time steps","",user.nt,&user.nt,NULL);
136:   user.ndata = 64;
137:   PetscOptionsInt("-ndata","Numbers of data points per sample","",user.ndata,&user.ndata,NULL);
138:   user.alpha = 10.0;
139:   PetscOptionsReal("-alpha","Regularization parameter","",user.alpha,&user.alpha,NULL);
140:   user.T = 1.0/32.0;
141:   PetscOptionsReal("-Tfinal","Final time","",user.T,&user.T,NULL);

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

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

158:   /* Create scatters for reduced spaces.
159:      If the state vector y and design vector u are partitioned as
160:      [y_1; y_2; ...; y_np] and [u_1; u_2; ...; u_np] (with np = # of processors),
161:      then the solution vector x is organized as
162:      [y_1; u_1; y_2; u_2; ...; y_np; u_np].
163:      The index sets user.s_is and user.d_is correspond to the indices of the
164:      state and design variables owned by the current processor.
165:   */
166:   VecCreate(PETSC_COMM_WORLD,&x);

168:   VecGetOwnershipRange(user.y,&lo,&hi);
169:   VecGetOwnershipRange(user.u,&lo2,&hi2);

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

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

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

180:   VecScatterCreate(x,user.s_is,user.y,is_allstate,&user.state_scatter);
181:   VecScatterCreate(x,user.d_is,user.u,is_alldesign,&user.design_scatter);
182:   ISDestroy(&is_alldesign);
183:   ISDestroy(&is_allstate);

185:   /* Create TAO solver and set desired solution method */
186:   TaoCreate(PETSC_COMM_WORLD,&tao);
187:   TaoSetType(tao,TAOLCL);

189:   /* Set up initial vectors and matrices */
190:   HyperbolicInitialize(&user);

192:   Gather(x,user.y,user.state_scatter,user.u,user.design_scatter);
193:   VecDuplicate(x,&x0);
194:   VecCopy(x,x0);

196:   /* Set solution vector with an initial guess */
197:   TaoSetInitialVector(tao,x);
198:   TaoSetObjectiveRoutine(tao, FormFunction, (void *)&user);
199:   TaoSetGradientRoutine(tao, FormGradient, (void *)&user);
200:   TaoSetConstraintsRoutine(tao, user.c, FormConstraints, (void *)&user);

202:   TaoSetJacobianStateRoutine(tao, user.Js, user.Js, user.JsInv, FormJacobianState, (void *)&user);

204:   TaoSetJacobianDesignRoutine(tao, user.Jd, FormJacobianDesign, (void *)&user);

206:   TaoSetFromOptions(tao);
207:   TaoSetStateDesignIS(tao,user.s_is,user.d_is);

209:   /* SOLVE THE APPLICATION */
210:   PetscOptionsInt("-ntests","Number of times to repeat TaoSolve","",ntests,&ntests,NULL);
211:   PetscOptionsEnd();
212:   PetscLogStageRegister("Trials",&stages[0]);
213:   PetscLogStagePush(stages[0]);
214:   user.ksp_its_initial = user.ksp_its;
215:   ksp_old = user.ksp_its;
216:   for (i=0; i<ntests; i++){
217:     TaoSolve(tao);
218:     PetscPrintf(PETSC_COMM_WORLD,"KSP Iterations = %D\n",user.ksp_its-ksp_old);
219:     VecCopy(x0,x);
220:     TaoSetInitialVector(tao,x);
221:   }
222:   PetscLogStagePop();
223:   PetscBarrier((PetscObject)x);
224:   PetscPrintf(PETSC_COMM_WORLD,"KSP iterations within initialization: ");
225:   PetscPrintf(PETSC_COMM_WORLD,"%D\n",user.ksp_its_initial);
226:   PetscPrintf(PETSC_COMM_WORLD,"Total KSP iterations over %D trial(s): ",ntests);
227:   PetscPrintf(PETSC_COMM_WORLD,"%D\n",user.ksp_its);
228:   PetscPrintf(PETSC_COMM_WORLD,"KSP iterations per trial: ");
229:   PetscPrintf(PETSC_COMM_WORLD,"%D\n",(user.ksp_its-user.ksp_its_initial)/ntests);

231:   TaoDestroy(&tao);
232:   VecDestroy(&x);
233:   VecDestroy(&x0);
234:   HyperbolicDestroy(&user);
235:   PetscFinalize();
236:   return 0;
237: }
238: /* ------------------------------------------------------------------- */
241: /*
242:    dwork = Qy - d
243:    lwork = L*(u-ur).^2
244:    f = 1/2 * (dwork.dork + alpha*y.lwork)
245: */
246: PetscErrorCode FormFunction(Tao tao,Vec X,PetscReal *f,void *ptr)
247: {
249:   PetscReal      d1=0,d2=0;
250:   AppCtx         *user = (AppCtx*)ptr;

253:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
254:   MatMult(user->Q,user->y,user->dwork);
255:   VecAXPY(user->dwork,-1.0,user->d);
256:   VecDot(user->dwork,user->dwork,&d1);

258:   VecWAXPY(user->uwork,-1.0,user->ur,user->u);
259:   VecPointwiseMult(user->uwork,user->uwork,user->uwork);
260:   MatMult(user->L,user->uwork,user->lwork);
261:   VecDot(user->y,user->lwork,&d2);
262:   *f = 0.5 * (d1 + user->alpha*d2);
263:   return(0);
264: }

266: /* ------------------------------------------------------------------- */
269: /*
270:     state: g_s = Q' *(Qy - d) + 0.5*alpha*L*(u-ur).^2
271:     design: g_d = alpha*(L'y).*(u-ur)
272: */
273: PetscErrorCode FormGradient(Tao tao,Vec X,Vec G,void *ptr)
274: {
276:   AppCtx         *user = (AppCtx*)ptr;

279:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
280:   MatMult(user->Q,user->y,user->dwork);
281:   VecAXPY(user->dwork,-1.0,user->d);

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

285:   MatMult(user->LT,user->y,user->uwork);
286:   VecWAXPY(user->vwork,-1.0,user->ur,user->u);
287:   VecPointwiseMult(user->uwork,user->vwork,user->uwork);
288:   VecScale(user->uwork,user->alpha);

290:   VecPointwiseMult(user->vwork,user->vwork,user->vwork);
291:   MatMult(user->L,user->vwork,user->lwork);
292:   VecAXPY(user->ywork,0.5*user->alpha,user->lwork);

294:   Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
295:   return(0);
296: }

300: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *f, Vec G, void *ptr)
301: {
303:   PetscReal      d1,d2;
304:   AppCtx         *user = (AppCtx*)ptr;

307:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
308:   MatMult(user->Q,user->y,user->dwork);
309:   VecAXPY(user->dwork,-1.0,user->d);

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

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

315:   MatMult(user->LT,user->y,user->uwork);
316:   VecWAXPY(user->vwork,-1.0,user->ur,user->u);
317:   VecPointwiseMult(user->uwork,user->vwork,user->uwork);
318:   VecScale(user->uwork,user->alpha);

320:   VecPointwiseMult(user->vwork,user->vwork,user->vwork);
321:   MatMult(user->L,user->vwork,user->lwork);
322:   VecAXPY(user->ywork,0.5*user->alpha,user->lwork);

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

326:   *f = 0.5 * (d1 + user->alpha*d2);
327:   Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
328:   return(0);
329: }

331: /* ------------------------------------------------------------------- */
334: /* A
335: MatShell object
336: */
337: PetscErrorCode FormJacobianState(Tao tao, Vec X, Mat J, Mat JPre, Mat JInv, void *ptr)
338: {
340:   PetscInt       i;
341:   AppCtx         *user = (AppCtx*)ptr;

344:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
345:   Scatter_yi(user->u,user->ui,user->ui_scatter,user->nt);
346:   Scatter_uxi_uyi(user->u,user->uxi,user->uxi_scatter,user->uyi,user->uyi_scatter,user->nt);
347:   for (i=0; i<user->nt; i++){
348:     MatCopy(user->Divxy[0],user->C[i],SAME_NONZERO_PATTERN);
349:     MatCopy(user->Divxy[1],user->Cwork[i],SAME_NONZERO_PATTERN);

351:     MatDiagonalScale(user->C[i],NULL,user->uxi[i]);
352:     MatDiagonalScale(user->Cwork[i],NULL,user->uyi[i]);
353:     MatAXPY(user->C[i],1.0,user->Cwork[i],SUBSET_NONZERO_PATTERN);
354:     MatScale(user->C[i],user->ht);
355:     MatShift(user->C[i],1.0);
356:   }
357:   return(0);
358: }

360: /* ------------------------------------------------------------------- */
363: /* B */
364: PetscErrorCode FormJacobianDesign(Tao tao, Vec X, Mat J, void *ptr)
365: {
367:   AppCtx         *user = (AppCtx*)ptr;

370:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
371:   return(0);
372: }

376: PetscErrorCode StateMatMult(Mat J_shell, Vec X, Vec Y)
377: {
379:   PetscInt       i;
380:   AppCtx         *user;

383:   MatShellGetContext(J_shell,(void**)&user);
384:   Scatter_yi(X,user->yi,user->yi_scatter,user->nt);
385:   user->block_index = 0;
386:   MatMult(user->JsBlock,user->yi[0],user->yiwork[0]);

388:   for (i=1; i<user->nt; i++){
389:     user->block_index = i;
390:     MatMult(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:   }
394:   Gather_yi(Y,user->yiwork,user->yi_scatter,user->nt);
395:   return(0);
396: }

400: PetscErrorCode StateMatMultTranspose(Mat J_shell, Vec X, Vec Y)
401: {
403:   PetscInt       i;
404:   AppCtx         *user;

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

410:   for (i=0; i<user->nt-1; i++){
411:     user->block_index = i;
412:     MatMultTranspose(user->JsBlock,user->yi[i],user->yiwork[i]);
413:     MatMult(user->M,user->yi[i+1],user->ziwork[i+1]);
414:     VecAXPY(user->yiwork[i],-1.0,user->ziwork[i+1]);
415:   }

417:   i = user->nt-1;
418:   user->block_index = i;
419:   MatMultTranspose(user->JsBlock,user->yi[i],user->yiwork[i]);
420:   Gather_yi(Y,user->yiwork,user->yi_scatter,user->nt);
421:   return(0);
422: }

426: PetscErrorCode StateMatBlockMult(Mat J_shell, Vec X, Vec Y)
427: {
429:   PetscInt       i;
430:   AppCtx         *user;

433:   MatShellGetContext(J_shell,(void**)&user);
434:   i = user->block_index;
435:   VecPointwiseMult(user->uxiwork[i],X,user->uxi[i]);
436:   VecPointwiseMult(user->uyiwork[i],X,user->uyi[i]);
437:   Gather(user->uiwork[i],user->uxiwork[i],user->ux_scatter[i],user->uyiwork[i],user->uy_scatter[i]);
438:   MatMult(user->Div,user->uiwork[i],Y);
439:   VecAYPX(Y,user->ht,X);
440:   return(0);
441: }

445: PetscErrorCode StateMatBlockMultTranspose(Mat J_shell, Vec X, Vec Y)
446: {
448:   PetscInt       i;
449:   AppCtx         *user;

452:   MatShellGetContext(J_shell,(void**)&user);
453:   i = user->block_index;
454:   MatMult(user->Grad,X,user->uiwork[i]);
455:   Scatter(user->uiwork[i],user->uxiwork[i],user->ux_scatter[i],user->uyiwork[i],user->uy_scatter[i]);
456:   VecPointwiseMult(user->uxiwork[i],user->uxi[i],user->uxiwork[i]);
457:   VecPointwiseMult(user->uyiwork[i],user->uyi[i],user->uyiwork[i]);
458:   VecWAXPY(Y,1.0,user->uxiwork[i],user->uyiwork[i]);
459:   VecAYPX(Y,user->ht,X);
460:   return(0);
461: }

465: PetscErrorCode DesignMatMult(Mat J_shell, Vec X, Vec Y)
466: {
468:   PetscInt       i;
469:   AppCtx         *user;

472:   MatShellGetContext(J_shell,(void**)&user);
473:   Scatter_yi(user->y,user->yi,user->yi_scatter,user->nt);
474:   Scatter_uxi_uyi(X,user->uxiwork,user->uxi_scatter,user->uyiwork,user->uyi_scatter,user->nt);
475:   for (i=0; i<user->nt; i++){
476:     VecPointwiseMult(user->uxiwork[i],user->yi[i],user->uxiwork[i]);
477:     VecPointwiseMult(user->uyiwork[i],user->yi[i],user->uyiwork[i]);
478:     Gather(user->uiwork[i],user->uxiwork[i],user->ux_scatter[i],user->uyiwork[i],user->uy_scatter[i]);
479:     MatMult(user->Div,user->uiwork[i],user->ziwork[i]);
480:     VecScale(user->ziwork[i],user->ht);
481:   }
482:   Gather_yi(Y,user->ziwork,user->yi_scatter,user->nt);
483:   return(0);
484: }

488: PetscErrorCode DesignMatMultTranspose(Mat J_shell, Vec X, Vec Y)
489: {
491:   PetscInt       i;
492:   AppCtx         *user;

495:   MatShellGetContext(J_shell,(void**)&user);
496:   Scatter_yi(user->y,user->yi,user->yi_scatter,user->nt);
497:   Scatter_yi(X,user->yiwork,user->yi_scatter,user->nt);
498:   for (i=0; i<user->nt; i++){
499:     MatMult(user->Grad,user->yiwork[i],user->uiwork[i]);
500:     Scatter(user->uiwork[i],user->uxiwork[i],user->ux_scatter[i],user->uyiwork[i],user->uy_scatter[i]);
501:     VecPointwiseMult(user->uxiwork[i],user->yi[i],user->uxiwork[i]);
502:     VecPointwiseMult(user->uyiwork[i],user->yi[i],user->uyiwork[i]);
503:     Gather(user->uiwork[i],user->uxiwork[i],user->ux_scatter[i],user->uyiwork[i],user->uy_scatter[i]);
504:     VecScale(user->uiwork[i],user->ht);
505:   }
506:   Gather_yi(Y,user->uiwork,user->ui_scatter,user->nt);
507:   return(0);
508: }

512: PetscErrorCode StateMatBlockPrecMult(PC PC_shell, Vec X, Vec Y)
513: {
515:   PetscInt       i;
516:   AppCtx         *user;

519:   PCShellGetContext(PC_shell,(void**)&user);
520:   i = user->block_index;
521:   if (user->c_formed) {
522:     MatSOR(user->C[i],X,1.0,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_SYMMETRIC_SWEEP),0.0,1,1,Y);
523:   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not formed");
524:   return(0);
525: }

529: PetscErrorCode StateMatBlockPrecMultTranspose(PC PC_shell, Vec X, Vec Y)
530: {
532:   PetscInt       i;
533:   AppCtx         *user;

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

538:   i = user->block_index;
539:   if (user->c_formed) {
540:     MatSOR(user->C[i],X,1.0,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_SYMMETRIC_SWEEP),0.0,1,1,Y);
541:   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not formed");
542:   return(0);
543: }

547: PetscErrorCode StateMatInvMult(Mat J_shell, Vec X, Vec Y)
548: {
550:   AppCtx         *user;
551:   PetscInt       its,i;

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

556:   if (Y == user->ytrue) {
557:     /* First solve is done using true solution to set up problem */
558:     KSPSetTolerances(user->solver,1e-4,1e-20,PETSC_DEFAULT,PETSC_DEFAULT);
559:   } else {
560:     KSPSetTolerances(user->solver,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
561:   }
562:   Scatter_yi(X,user->yi,user->yi_scatter,user->nt);
563:   Scatter_yi(Y,user->yiwork,user->yi_scatter,user->nt);
564:   Scatter_uxi_uyi(user->u,user->uxi,user->uxi_scatter,user->uyi,user->uyi_scatter,user->nt);

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

569:   KSPGetIterationNumber(user->solver,&its);
570:   user->ksp_its = user->ksp_its + its;
571:   for (i=1; i<user->nt; i++){
572:     MatMult(user->M,user->yiwork[i-1],user->ziwork[i-1]);
573:     VecAXPY(user->yi[i],1.0,user->ziwork[i-1]);
574:     user->block_index = i;
575:     KSPSolve(user->solver,user->yi[i],user->yiwork[i]);

577:     KSPGetIterationNumber(user->solver,&its);
578:     user->ksp_its = user->ksp_its + its;
579:   }
580:   Gather_yi(Y,user->yiwork,user->yi_scatter,user->nt);
581:   return(0);
582: }

586: PetscErrorCode StateMatInvTransposeMult(Mat J_shell, Vec X, Vec Y)
587: {
589:   AppCtx         *user;
590:   PetscInt       its,i;

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

595:   Scatter_yi(X,user->yi,user->yi_scatter,user->nt);
596:   Scatter_yi(Y,user->yiwork,user->yi_scatter,user->nt);
597:   Scatter_uxi_uyi(user->u,user->uxi,user->uxi_scatter,user->uyi,user->uyi_scatter,user->nt);

599:   i = user->nt - 1;
600:   user->block_index = i;
601:   KSPSolveTranspose(user->solver,user->yi[i],user->yiwork[i]);

603:   KSPGetIterationNumber(user->solver,&its);
604:   user->ksp_its = user->ksp_its + its;

606:   for (i=user->nt-2; i>=0; i--){
607:     MatMult(user->M,user->yiwork[i+1],user->ziwork[i+1]);
608:     VecAXPY(user->yi[i],1.0,user->ziwork[i+1]);
609:     user->block_index = i;
610:     KSPSolveTranspose(user->solver,user->yi[i],user->yiwork[i]);

612:     KSPGetIterationNumber(user->solver,&its);
613:     user->ksp_its = user->ksp_its + its;
614:   }
615:   Gather_yi(Y,user->yiwork,user->yi_scatter,user->nt);
616:   return(0);
617: }

621: PetscErrorCode StateMatDuplicate(Mat J_shell, MatDuplicateOption opt, Mat *new_shell)
622: {
624:   AppCtx         *user;

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

629:   MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,new_shell);
630:   MatShellSetOperation(*new_shell,MATOP_MULT,(void(*)(void))StateMatMult);
631:   MatShellSetOperation(*new_shell,MATOP_DUPLICATE,(void(*)(void))StateMatDuplicate);
632:   MatShellSetOperation(*new_shell,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMultTranspose);
633:   MatShellSetOperation(*new_shell,MATOP_GET_DIAGONAL,(void(*)(void))StateMatGetDiagonal);
634:   return(0);
635: }

639: PetscErrorCode StateMatGetDiagonal(Mat J_shell, Vec X)
640: {
642:   AppCtx         *user;

645:   MatShellGetContext(J_shell,(void**)&user);
646:    VecCopy(user->js_diag,X);
647:   return(0);
648: }

652: PetscErrorCode FormConstraints(Tao tao, Vec X, Vec C, void *ptr)
653: {
654:   /* con = Ay - q, A = [C(u1)  0     0     ...   0;
655:                          -M  C(u2)   0     ...   0;
656:                           0   -M   C(u3)   ...   0;
657:                                       ...         ;
658:                           0    ...      -M C(u_nt)]
659:      C(u) = eye + ht*Div*[diag(u1); diag(u2)]       */
661:   PetscInt       i;
662:   AppCtx         *user = (AppCtx*)ptr;

665:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
666:   Scatter_yi(user->y,user->yi,user->yi_scatter,user->nt);
667:   Scatter_uxi_uyi(user->u,user->uxi,user->uxi_scatter,user->uyi,user->uyi_scatter,user->nt);

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

672:   for (i=1; i<user->nt; i++){
673:     user->block_index = i;
674:     MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
675:     MatMult(user->M,user->yi[i-1],user->ziwork[i-1]);
676:     VecAXPY(user->yiwork[i],-1.0,user->ziwork[i-1]);
677:   }

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

682:   return(0);
683: }


688: PetscErrorCode Scatter(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat)
689: {

693:   VecScatterBegin(s_scat,x,state,INSERT_VALUES,SCATTER_FORWARD);
694:   VecScatterEnd(s_scat,x,state,INSERT_VALUES,SCATTER_FORWARD);
695:   VecScatterBegin(d_scat,x,design,INSERT_VALUES,SCATTER_FORWARD);
696:   VecScatterEnd(d_scat,x,design,INSERT_VALUES,SCATTER_FORWARD);
697:   return(0);
698: }

702: PetscErrorCode Scatter_uxi_uyi(Vec u, Vec *uxi, VecScatter *scatx, Vec *uyi, VecScatter *scaty, PetscInt nt)
703: {
705:   PetscInt       i;

708:   for (i=0; i<nt; i++){
709:     VecScatterBegin(scatx[i],u,uxi[i],INSERT_VALUES,SCATTER_FORWARD);
710:     VecScatterEnd(scatx[i],u,uxi[i],INSERT_VALUES,SCATTER_FORWARD);
711:     VecScatterBegin(scaty[i],u,uyi[i],INSERT_VALUES,SCATTER_FORWARD);
712:     VecScatterEnd(scaty[i],u,uyi[i],INSERT_VALUES,SCATTER_FORWARD);
713:   }
714:   return(0);
715: }

719: PetscErrorCode Gather(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat)
720: {

724:   VecScatterBegin(s_scat,state,x,INSERT_VALUES,SCATTER_REVERSE);
725:   VecScatterEnd(s_scat,state,x,INSERT_VALUES,SCATTER_REVERSE);
726:   VecScatterBegin(d_scat,design,x,INSERT_VALUES,SCATTER_REVERSE);
727:   VecScatterEnd(d_scat,design,x,INSERT_VALUES,SCATTER_REVERSE);
728:   return(0);
729: }

733: PetscErrorCode Gather_uxi_uyi(Vec u, Vec *uxi, VecScatter *scatx, Vec *uyi, VecScatter *scaty, PetscInt nt)
734: {
736:   PetscInt       i;

739:   for (i=0; i<nt; i++){
740:     VecScatterBegin(scatx[i],uxi[i],u,INSERT_VALUES,SCATTER_REVERSE);
741:     VecScatterEnd(scatx[i],uxi[i],u,INSERT_VALUES,SCATTER_REVERSE);
742:     VecScatterBegin(scaty[i],uyi[i],u,INSERT_VALUES,SCATTER_REVERSE);
743:     VecScatterEnd(scaty[i],uyi[i],u,INSERT_VALUES,SCATTER_REVERSE);
744:   }
745:   return(0);
746: }

750: PetscErrorCode Scatter_yi(Vec y, Vec *yi, VecScatter *scat, PetscInt nt)
751: {
753:   PetscInt       i;

756:   for (i=0; i<nt; i++){
757:     VecScatterBegin(scat[i],y,yi[i],INSERT_VALUES,SCATTER_FORWARD);
758:     VecScatterEnd(scat[i],y,yi[i],INSERT_VALUES,SCATTER_FORWARD);
759:   }
760:   return(0);
761: }

765: PetscErrorCode Gather_yi(Vec y, Vec *yi, VecScatter *scat, PetscInt nt)
766: {
768:   PetscInt       i;

771:   for (i=0; i<nt; i++){
772:     VecScatterBegin(scat[i],yi[i],y,INSERT_VALUES,SCATTER_REVERSE);
773:     VecScatterEnd(scat[i],yi[i],y,INSERT_VALUES,SCATTER_REVERSE);
774:   }
775:   return(0);
776: }

780: PetscErrorCode HyperbolicInitialize(AppCtx *user)
781: {
783:   PetscInt       n,i,j,linear_index,istart,iend,iblock,lo,hi;
784:   Vec            XX,YY,XXwork,YYwork,yi,uxi,ui,bc;
785:   PetscReal      h,sum;
786:   PetscScalar    hinv,neg_hinv,quarter=0.25,one=1.0,half_hinv,neg_half_hinv;
787:   PetscScalar    vx,vy,zero=0.0;
788:   IS             is_from_y,is_to_yi,is_from_u,is_to_uxi,is_to_uyi;

791:   user->jformed = PETSC_FALSE;
792:   user->c_formed = PETSC_FALSE;

794:   user->ksp_its = 0;
795:   user->ksp_its_initial = 0;

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

799:   h = 1.0/user->mx;
800:   hinv = user->mx;
801:   neg_hinv = -hinv;
802:   half_hinv = hinv / 2.0;
803:   neg_half_hinv = neg_hinv / 2.0;

805:   /* Generate Grad matrix */
806:   MatCreate(PETSC_COMM_WORLD,&user->Grad);
807:   MatSetSizes(user->Grad,PETSC_DECIDE,PETSC_DECIDE,2*n,n);
808:   MatSetFromOptions(user->Grad);
809:   MatMPIAIJSetPreallocation(user->Grad,3,NULL,3,NULL);
810:   MatSeqAIJSetPreallocation(user->Grad,3,NULL);
811:   MatGetOwnershipRange(user->Grad,&istart,&iend);

813:   for (i=istart; i<iend; i++){
814:     if (i<n){
815:       iblock = i / user->mx;
816:       j = iblock*user->mx + ((i+user->mx-1) % user->mx);
817:       MatSetValues(user->Grad,1,&i,1,&j,&half_hinv,INSERT_VALUES);
818:       j = iblock*user->mx + ((i+1) % user->mx);
819:       MatSetValues(user->Grad,1,&i,1,&j,&neg_half_hinv,INSERT_VALUES);
820:     }
821:     if (i>=n){
822:       j = (i - user->mx) % n;
823:       MatSetValues(user->Grad,1,&i,1,&j,&half_hinv,INSERT_VALUES);
824:       j = (j + 2*user->mx) % n;
825:       MatSetValues(user->Grad,1,&i,1,&j,&neg_half_hinv,INSERT_VALUES);
826:     }
827:   }

829:   MatAssemblyBegin(user->Grad,MAT_FINAL_ASSEMBLY);
830:   MatAssemblyEnd(user->Grad,MAT_FINAL_ASSEMBLY);

832:   MatCreate(PETSC_COMM_WORLD,&user->Gradxy[0]);
833:   MatSetSizes(user->Gradxy[0],PETSC_DECIDE,PETSC_DECIDE,n,n);
834:   MatSetFromOptions(user->Gradxy[0]);
835:   MatMPIAIJSetPreallocation(user->Gradxy[0],3,NULL,3,NULL);
836:   MatSeqAIJSetPreallocation(user->Gradxy[0],3,NULL);
837:   MatGetOwnershipRange(user->Gradxy[0],&istart,&iend);

839:   for (i=istart; i<iend; i++){
840:     iblock = i / user->mx;
841:     j = iblock*user->mx + ((i+user->mx-1) % user->mx);
842:     MatSetValues(user->Gradxy[0],1,&i,1,&j,&half_hinv,INSERT_VALUES);
843:     j = iblock*user->mx + ((i+1) % user->mx);
844:     MatSetValues(user->Gradxy[0],1,&i,1,&j,&neg_half_hinv,INSERT_VALUES);
845:     MatSetValues(user->Gradxy[0],1,&i,1,&i,&zero,INSERT_VALUES);
846:   }
847:   MatAssemblyBegin(user->Gradxy[0],MAT_FINAL_ASSEMBLY);
848:   MatAssemblyEnd(user->Gradxy[0],MAT_FINAL_ASSEMBLY);

850:   MatCreate(PETSC_COMM_WORLD,&user->Gradxy[1]);
851:   MatSetSizes(user->Gradxy[1],PETSC_DECIDE,PETSC_DECIDE,n,n);
852:   MatSetFromOptions(user->Gradxy[1]);
853:   MatMPIAIJSetPreallocation(user->Gradxy[1],3,NULL,3,NULL);
854:   MatSeqAIJSetPreallocation(user->Gradxy[1],3,NULL);
855:   MatGetOwnershipRange(user->Gradxy[1],&istart,&iend);

857:   for (i=istart; i<iend; i++){
858:     j = (i + n - user->mx) % n;
859:     MatSetValues(user->Gradxy[1],1,&i,1,&j,&half_hinv,INSERT_VALUES);
860:     j = (j + 2*user->mx) % n;
861:     MatSetValues(user->Gradxy[1],1,&i,1,&j,&neg_half_hinv,INSERT_VALUES);
862:     MatSetValues(user->Gradxy[1],1,&i,1,&i,&zero,INSERT_VALUES);
863:   }
864:   MatAssemblyBegin(user->Gradxy[1],MAT_FINAL_ASSEMBLY);
865:   MatAssemblyEnd(user->Gradxy[1],MAT_FINAL_ASSEMBLY);

867:   /* Generate Div matrix */
868:   MatTranspose(user->Grad,MAT_INITIAL_MATRIX,&user->Div);
869:   MatTranspose(user->Gradxy[0],MAT_INITIAL_MATRIX,&user->Divxy[0]);
870:   MatTranspose(user->Gradxy[1],MAT_INITIAL_MATRIX,&user->Divxy[1]);

872:   /* Off-diagonal averaging matrix */
873:   MatCreate(PETSC_COMM_WORLD,&user->M);
874:   MatSetSizes(user->M,PETSC_DECIDE,PETSC_DECIDE,n,n);
875:   MatSetFromOptions(user->M);
876:   MatMPIAIJSetPreallocation(user->M,4,NULL,4,NULL);
877:   MatSeqAIJSetPreallocation(user->M,4,NULL);
878:   MatGetOwnershipRange(user->M,&istart,&iend);

880:   for (i=istart; i<iend; i++){
881:     /* kron(Id,Av) */
882:     iblock = i / user->mx;
883:     j = iblock*user->mx + ((i+user->mx-1) % user->mx);
884:     MatSetValues(user->M,1,&i,1,&j,&quarter,INSERT_VALUES);
885:     j = iblock*user->mx + ((i+1) % user->mx);
886:     MatSetValues(user->M,1,&i,1,&j,&quarter,INSERT_VALUES);

888:     /* kron(Av,Id) */
889:     j = (i + user->mx) % n;
890:     MatSetValues(user->M,1,&i,1,&j,&quarter,INSERT_VALUES);
891:     j = (i + n - user->mx) % n;
892:     MatSetValues(user->M,1,&i,1,&j,&quarter,INSERT_VALUES);
893:   }
894:   MatAssemblyBegin(user->M,MAT_FINAL_ASSEMBLY);
895:   MatAssemblyEnd(user->M,MAT_FINAL_ASSEMBLY);

897:   /* Generate 2D grid */
898:   VecCreate(PETSC_COMM_WORLD,&XX);
899:   VecCreate(PETSC_COMM_WORLD,&user->q);
900:   VecSetSizes(XX,PETSC_DECIDE,n);
901:   VecSetSizes(user->q,PETSC_DECIDE,n*user->nt);
902:   VecSetFromOptions(XX);
903:   VecSetFromOptions(user->q);

905:   VecDuplicate(XX,&YY);
906:   VecDuplicate(XX,&XXwork);
907:   VecDuplicate(XX,&YYwork);
908:   VecDuplicate(XX,&user->d);
909:   VecDuplicate(XX,&user->dwork);

911:   VecGetOwnershipRange(XX,&istart,&iend);
912:   for (linear_index=istart; linear_index<iend; linear_index++){
913:     i = linear_index % user->mx;
914:     j = (linear_index-i)/user->mx;
915:     vx = h*(i+0.5);
916:     vy = h*(j+0.5);
917:     VecSetValues(XX,1,&linear_index,&vx,INSERT_VALUES);
918:     VecSetValues(YY,1,&linear_index,&vy,INSERT_VALUES);
919:   }

921:   VecAssemblyBegin(XX);
922:   VecAssemblyEnd(XX);
923:   VecAssemblyBegin(YY);
924:   VecAssemblyEnd(YY);

926:   /* Compute final density function yT
927:      yT = 1.0 + exp(-30*((x-0.25)^2+(y-0.25)^2)) + exp(-30*((x-0.75)^2+(y-0.75)^2))
928:      yT = yT / (h^2*sum(yT)) */
929:   VecCopy(XX,XXwork);
930:   VecCopy(YY,YYwork);

932:   VecShift(XXwork,-0.25);
933:   VecShift(YYwork,-0.25);

935:   VecPointwiseMult(XXwork,XXwork,XXwork);
936:   VecPointwiseMult(YYwork,YYwork,YYwork);

938:   VecCopy(XXwork,user->dwork);
939:   VecAXPY(user->dwork,1.0,YYwork);
940:   VecScale(user->dwork,-30.0);
941:   VecExp(user->dwork);
942:   VecCopy(user->dwork,user->d);

944:   VecCopy(XX,XXwork);
945:   VecCopy(YY,YYwork);

947:   VecShift(XXwork,-0.75);
948:   VecShift(YYwork,-0.75);

950:   VecPointwiseMult(XXwork,XXwork,XXwork);
951:   VecPointwiseMult(YYwork,YYwork,YYwork);

953:   VecCopy(XXwork,user->dwork);
954:   VecAXPY(user->dwork,1.0,YYwork);
955:   VecScale(user->dwork,-30.0);
956:   VecExp(user->dwork);

958:   VecAXPY(user->d,1.0,user->dwork);
959:   VecShift(user->d,1.0);
960:   VecSum(user->d,&sum);
961:   VecScale(user->d,1.0/(h*h*sum));

963:   /* Initial conditions of forward problem */
964:   VecDuplicate(XX,&bc);
965:   VecCopy(XX,XXwork);
966:   VecCopy(YY,YYwork);

968:   VecShift(XXwork,-0.5);
969:   VecShift(YYwork,-0.5);

971:   VecPointwiseMult(XXwork,XXwork,XXwork);
972:   VecPointwiseMult(YYwork,YYwork,YYwork);

974:   VecWAXPY(bc,1.0,XXwork,YYwork);
975:   VecScale(bc,-50.0);
976:   VecExp(bc);
977:   VecShift(bc,1.0);
978:   VecSum(bc,&sum);
979:   VecScale(bc,1.0/(h*h*sum));

981:   /* Create scatter from y to y_1,y_2,...,y_nt */
982:   /*  TODO: Reorder for better parallelism. (This will require reordering Q and L as well.) */
983:   PetscMalloc1(user->nt*user->mx*user->mx,&user->yi_scatter);
984:   VecCreate(PETSC_COMM_WORLD,&yi);
985:   VecSetSizes(yi,PETSC_DECIDE,user->mx*user->mx);
986:   VecSetFromOptions(yi);
987:   VecDuplicateVecs(yi,user->nt,&user->yi);
988:   VecDuplicateVecs(yi,user->nt,&user->yiwork);
989:   VecDuplicateVecs(yi,user->nt,&user->ziwork);
990:   for (i=0; i<user->nt; i++){
991:     VecGetOwnershipRange(user->yi[i],&lo,&hi);
992:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_yi);
993:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+i*user->mx*user->mx,1,&is_from_y);
994:     VecScatterCreate(user->y,is_from_y,user->yi[i],is_to_yi,&user->yi_scatter[i]);
995:     ISDestroy(&is_to_yi);
996:     ISDestroy(&is_from_y);
997:   }

999:   /* Create scatter from u to ux_1,uy_1,ux_2,uy_2,...,ux_nt,uy_nt */
1000:   /*  TODO: reorder for better parallelism */
1001:   PetscMalloc1(user->nt*user->mx*user->mx,&user->uxi_scatter);
1002:   PetscMalloc1(user->nt*user->mx*user->mx,&user->uyi_scatter);
1003:   PetscMalloc1(user->nt*user->mx*user->mx,&user->ux_scatter);
1004:   PetscMalloc1(user->nt*user->mx*user->mx,&user->uy_scatter);
1005:   PetscMalloc1(2*user->nt*user->mx*user->mx,&user->ui_scatter);
1006:   VecCreate(PETSC_COMM_WORLD,&uxi);
1007:   VecCreate(PETSC_COMM_WORLD,&ui);
1008:   VecSetSizes(uxi,PETSC_DECIDE,user->mx*user->mx);
1009:   VecSetSizes(ui,PETSC_DECIDE,2*user->mx*user->mx);
1010:   VecSetFromOptions(uxi);
1011:   VecSetFromOptions(ui);
1012:   VecDuplicateVecs(uxi,user->nt,&user->uxi);
1013:   VecDuplicateVecs(uxi,user->nt,&user->uyi);
1014:   VecDuplicateVecs(uxi,user->nt,&user->uxiwork);
1015:   VecDuplicateVecs(uxi,user->nt,&user->uyiwork);
1016:   VecDuplicateVecs(ui,user->nt,&user->ui);
1017:   VecDuplicateVecs(ui,user->nt,&user->uiwork);
1018:   for (i=0; i<user->nt; i++){
1019:     VecGetOwnershipRange(user->uxi[i],&lo,&hi);
1020:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_uxi);
1021:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+2*i*user->mx*user->mx,1,&is_from_u);
1022:     VecScatterCreate(user->u,is_from_u,user->uxi[i],is_to_uxi,&user->uxi_scatter[i]);

1024:     ISDestroy(&is_to_uxi);
1025:     ISDestroy(&is_from_u);

1027:     VecGetOwnershipRange(user->uyi[i],&lo,&hi);
1028:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_uyi);
1029:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+(2*i+1)*user->mx*user->mx,1,&is_from_u);
1030:     VecScatterCreate(user->u,is_from_u,user->uyi[i],is_to_uyi,&user->uyi_scatter[i]);

1032:     ISDestroy(&is_to_uyi);
1033:     ISDestroy(&is_from_u);

1035:     VecGetOwnershipRange(user->uxi[i],&lo,&hi);
1036:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_uxi);
1037:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_from_u);
1038:     VecScatterCreate(user->ui[i],is_from_u,user->uxi[i],is_to_uxi,&user->ux_scatter[i]);

1040:     ISDestroy(&is_to_uxi);
1041:     ISDestroy(&is_from_u);

1043:     VecGetOwnershipRange(user->uyi[i],&lo,&hi);
1044:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_uyi);
1045:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+user->mx*user->mx,1,&is_from_u);
1046:     VecScatterCreate(user->ui[i],is_from_u,user->uyi[i],is_to_uyi,&user->uy_scatter[i]);

1048:     ISDestroy(&is_to_uyi);
1049:     ISDestroy(&is_from_u);

1051:     VecGetOwnershipRange(user->ui[i],&lo,&hi);
1052:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_uxi);
1053:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+2*i*user->mx*user->mx,1,&is_from_u);
1054:     VecScatterCreate(user->u,is_from_u,user->ui[i],is_to_uxi,&user->ui_scatter[i]);

1056:     ISDestroy(&is_to_uxi);
1057:     ISDestroy(&is_from_u);
1058:   }

1060:   /* RHS of forward problem */
1061:   MatMult(user->M,bc,user->yiwork[0]);
1062:   for (i=1; i<user->nt; i++){
1063:     VecSet(user->yiwork[i],0.0);
1064:   }
1065:   Gather_yi(user->q,user->yiwork,user->yi_scatter,user->nt);

1067:   /* Compute true velocity field utrue */
1068:   VecDuplicate(user->u,&user->utrue);
1069:   for (i=0; i<user->nt; i++){
1070:     VecCopy(YY,user->uxi[i]);
1071:     VecScale(user->uxi[i],150.0*i*user->ht);
1072:     VecCopy(XX,user->uyi[i]);
1073:     VecShift(user->uyi[i],-10.0);
1074:     VecScale(user->uyi[i],15.0*i*user->ht);
1075:   }
1076:   Gather_uxi_uyi(user->utrue,user->uxi,user->uxi_scatter,user->uyi,user->uyi_scatter,user->nt);

1078:   /* Initial guess and reference model */
1079:   VecDuplicate(user->utrue,&user->ur);
1080:   for (i=0; i<user->nt; i++){
1081:     VecCopy(XX,user->uxi[i]);
1082:     VecShift(user->uxi[i],i*user->ht);
1083:     VecCopy(YY,user->uyi[i]);
1084:     VecShift(user->uyi[i],-i*user->ht);
1085:   }
1086:   Gather_uxi_uyi(user->ur,user->uxi,user->uxi_scatter,user->uyi,user->uyi_scatter,user->nt);

1088:   /* Generate regularization matrix L */
1089:   MatCreate(PETSC_COMM_WORLD,&user->LT);
1090:   MatSetSizes(user->LT,PETSC_DECIDE,PETSC_DECIDE,2*n*user->nt,n*user->nt);
1091:   MatSetFromOptions(user->LT);
1092:   MatMPIAIJSetPreallocation(user->LT,1,NULL,1,NULL);
1093:   MatSeqAIJSetPreallocation(user->LT,1,NULL);
1094:   MatGetOwnershipRange(user->LT,&istart,&iend);

1096:   for (i=istart; i<iend; i++){
1097:     iblock = (i+n) / (2*n);
1098:     j = i - iblock*n;
1099:     MatSetValues(user->LT,1,&i,1,&j,&user->gamma,INSERT_VALUES);
1100:   }

1102:   MatAssemblyBegin(user->LT,MAT_FINAL_ASSEMBLY);
1103:   MatAssemblyEnd(user->LT,MAT_FINAL_ASSEMBLY);

1105:   MatTranspose(user->LT,MAT_INITIAL_MATRIX,&user->L);

1107:   /* Build work vectors and matrices */
1108:   VecCreate(PETSC_COMM_WORLD,&user->lwork);
1109:   VecSetType(user->lwork,VECMPI);
1110:   VecSetSizes(user->lwork,PETSC_DECIDE,user->m);
1111:   VecSetFromOptions(user->lwork);

1113:   MatDuplicate(user->Div,MAT_SHARE_NONZERO_PATTERN,&user->Divwork);

1115:   VecDuplicate(user->y,&user->ywork);
1116:   VecDuplicate(user->u,&user->uwork);
1117:   VecDuplicate(user->u,&user->vwork);
1118:   VecDuplicate(user->u,&user->js_diag);
1119:   VecDuplicate(user->c,&user->cwork);

1121:   /* Create matrix-free shell user->Js for computing A*x */
1122:   MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,&user->Js);
1123:   MatShellSetOperation(user->Js,MATOP_MULT,(void(*)(void))StateMatMult);
1124:   MatShellSetOperation(user->Js,MATOP_DUPLICATE,(void(*)(void))StateMatDuplicate);
1125:   MatShellSetOperation(user->Js,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMultTranspose);
1126:   MatShellSetOperation(user->Js,MATOP_GET_DIAGONAL,(void(*)(void))StateMatGetDiagonal);

1128:   /* Diagonal blocks of user->Js */
1129:   MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,n,n,user,&user->JsBlock);
1130:   MatShellSetOperation(user->JsBlock,MATOP_MULT,(void(*)(void))StateMatBlockMult);
1131:   MatShellSetOperation(user->JsBlock,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatBlockMultTranspose);

1133:   /* Create a matrix-free shell user->JsBlockPrec for computing (U+D)\D*(L+D)\x, where JsBlock = L+D+U,
1134:      D is diagonal, L is strictly lower triangular, and U is strictly upper triangular.
1135:      This is an SOR preconditioner for user->JsBlock. */
1136:   MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,n,n,user,&user->JsBlockPrec);
1137:   MatShellSetOperation(user->JsBlockPrec,MATOP_MULT,(void(*)(void))StateMatBlockPrecMult);
1138:   MatShellSetOperation(user->JsBlockPrec,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatBlockPrecMultTranspose);

1140:   /* Create a matrix-free shell user->Jd for computing B*x */
1141:   MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->n-user->m,user,&user->Jd);
1142:   MatShellSetOperation(user->Jd,MATOP_MULT,(void(*)(void))DesignMatMult);
1143:   MatShellSetOperation(user->Jd,MATOP_MULT_TRANSPOSE,(void(*)(void))DesignMatMultTranspose);

1145:   /* User-defined routines for computing user->Js\x and user->Js^T\x*/
1146:   MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,&user->JsInv);
1147:   MatShellSetOperation(user->JsInv,MATOP_MULT,(void(*)(void))StateMatInvMult);
1148:   MatShellSetOperation(user->JsInv,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatInvTransposeMult);

1150:   /* Build matrices for SOR preconditioner */
1151:   Scatter_uxi_uyi(user->u,user->uxi,user->uxi_scatter,user->uyi,user->uyi_scatter,user->nt);
1152:   MatShift(user->Divxy[0],0.0); /*  Force C[i] and Divxy[0] to share same nonzero pattern */
1153:   MatAXPY(user->Divxy[0],0.0,user->Divxy[1],DIFFERENT_NONZERO_PATTERN);
1154:   PetscMalloc1(5*n,&user->C);
1155:   PetscMalloc1(2*n,&user->Cwork);
1156:   for (i=0; i<user->nt; i++){
1157:     MatDuplicate(user->Divxy[0],MAT_COPY_VALUES,&user->C[i]);
1158:     MatDuplicate(user->Divxy[1],MAT_COPY_VALUES,&user->Cwork[i]);

1160:     MatDiagonalScale(user->C[i],NULL,user->uxi[i]);
1161:     MatDiagonalScale(user->Cwork[i],NULL,user->uyi[i]);
1162:     MatAXPY(user->C[i],1.0,user->Cwork[i],SUBSET_NONZERO_PATTERN);
1163:     MatScale(user->C[i],user->ht);
1164:     MatShift(user->C[i],1.0);
1165:   }

1167:   /* Solver options and tolerances */
1168:   KSPCreate(PETSC_COMM_WORLD,&user->solver);
1169:   KSPSetType(user->solver,KSPGMRES);
1170:   KSPSetOperators(user->solver,user->JsBlock,user->JsBlockPrec);
1171:   KSPSetInitialGuessNonzero(user->solver,PETSC_FALSE); /*  TODO: why is true slower? */
1172:   KSPSetTolerances(user->solver,1e-4,1e-20,1e3,500);
1173:   /* KSPSetTolerances(user->solver,1e-8,1e-16,1e3,500); */
1174:   KSPGetPC(user->solver,&user->prec);
1175:   PCSetType(user->prec,PCSHELL);

1177:   PCShellSetApply(user->prec,StateMatBlockPrecMult);
1178:   PCShellSetApplyTranspose(user->prec,StateMatBlockPrecMultTranspose);
1179:   PCShellSetContext(user->prec,user);

1181:   /* Compute true state function yt given ut */
1182:   VecCreate(PETSC_COMM_WORLD,&user->ytrue);
1183:   VecSetSizes(user->ytrue,PETSC_DECIDE,n*user->nt);
1184:   VecSetFromOptions(user->ytrue);
1185:   user->c_formed = PETSC_TRUE;
1186:   VecCopy(user->utrue,user->u); /*  Set u=utrue temporarily for StateMatInv */
1187:   VecSet(user->ytrue,0.0); /*  Initial guess */
1188:   StateMatInvMult(user->Js,user->q,user->ytrue);
1189:   VecCopy(user->ur,user->u); /*  Reset u=ur */

1191:   /* Initial guess y0 for state given u0 */
1192:   StateMatInvMult(user->Js,user->q,user->y);

1194:   /* Data discretization */
1195:   MatCreate(PETSC_COMM_WORLD,&user->Q);
1196:   MatSetSizes(user->Q,PETSC_DECIDE,PETSC_DECIDE,user->mx*user->mx,user->m);
1197:   MatSetFromOptions(user->Q);
1198:   MatMPIAIJSetPreallocation(user->Q,0,NULL,1,NULL);
1199:   MatSeqAIJSetPreallocation(user->Q,1,NULL);

1201:   MatGetOwnershipRange(user->Q,&istart,&iend);

1203:   for (i=istart; i<iend; i++){
1204:     j = i + user->m - user->mx*user->mx;
1205:     MatSetValues(user->Q,1,&i,1,&j,&one,INSERT_VALUES);
1206:   }

1208:   MatAssemblyBegin(user->Q,MAT_FINAL_ASSEMBLY);
1209:   MatAssemblyEnd(user->Q,MAT_FINAL_ASSEMBLY);

1211:   MatTranspose(user->Q,MAT_INITIAL_MATRIX,&user->QT);

1213:   VecDestroy(&XX);
1214:   VecDestroy(&YY);
1215:   VecDestroy(&XXwork);
1216:   VecDestroy(&YYwork);
1217:   VecDestroy(&yi);
1218:   VecDestroy(&uxi);
1219:   VecDestroy(&ui);
1220:   VecDestroy(&bc);

1222:   /* Now that initial conditions have been set, let the user pass tolerance options to the KSP solver */
1223:   KSPSetFromOptions(user->solver);
1224:   return(0);
1225: }

1229: PetscErrorCode HyperbolicDestroy(AppCtx *user)
1230: {
1232:   PetscInt       i;

1235:   MatDestroy(&user->Q);
1236:   MatDestroy(&user->QT);
1237:   MatDestroy(&user->Div);
1238:   MatDestroy(&user->Divwork);
1239:   MatDestroy(&user->Grad);
1240:   MatDestroy(&user->L);
1241:   MatDestroy(&user->LT);
1242:   KSPDestroy(&user->solver);
1243:   MatDestroy(&user->Js);
1244:   MatDestroy(&user->Jd);
1245:   MatDestroy(&user->JsBlockPrec);
1246:   MatDestroy(&user->JsInv);
1247:   MatDestroy(&user->JsBlock);
1248:   MatDestroy(&user->Divxy[0]);
1249:   MatDestroy(&user->Divxy[1]);
1250:   MatDestroy(&user->Gradxy[0]);
1251:   MatDestroy(&user->Gradxy[1]);
1252:   MatDestroy(&user->M);
1253:   for (i=0; i<user->nt; i++){
1254:     MatDestroy(&user->C[i]);
1255:     MatDestroy(&user->Cwork[i]);
1256:   }
1257:   PetscFree(user->C);
1258:   PetscFree(user->Cwork);
1259:   VecDestroy(&user->u);
1260:   VecDestroy(&user->uwork);
1261:   VecDestroy(&user->vwork);
1262:   VecDestroy(&user->utrue);
1263:   VecDestroy(&user->y);
1264:   VecDestroy(&user->ywork);
1265:   VecDestroy(&user->ytrue);
1266:   VecDestroyVecs(user->nt,&user->yi);
1267:   VecDestroyVecs(user->nt,&user->yiwork);
1268:   VecDestroyVecs(user->nt,&user->ziwork);
1269:   VecDestroyVecs(user->nt,&user->uxi);
1270:   VecDestroyVecs(user->nt,&user->uyi);
1271:   VecDestroyVecs(user->nt,&user->uxiwork);
1272:   VecDestroyVecs(user->nt,&user->uyiwork);
1273:   VecDestroyVecs(user->nt,&user->ui);
1274:   VecDestroyVecs(user->nt,&user->uiwork);
1275:   VecDestroy(&user->c);
1276:   VecDestroy(&user->cwork);
1277:   VecDestroy(&user->ur);
1278:   VecDestroy(&user->q);
1279:   VecDestroy(&user->d);
1280:   VecDestroy(&user->dwork);
1281:   VecDestroy(&user->lwork);
1282:   VecDestroy(&user->js_diag);
1283:   ISDestroy(&user->s_is);
1284:   ISDestroy(&user->d_is);
1285:   VecScatterDestroy(&user->state_scatter);
1286:   VecScatterDestroy(&user->design_scatter);
1287:   for (i=0; i<user->nt; i++){
1288:     VecScatterDestroy(&user->uxi_scatter[i]);
1289:     VecScatterDestroy(&user->uyi_scatter[i]);
1290:     VecScatterDestroy(&user->ux_scatter[i]);
1291:     VecScatterDestroy(&user->uy_scatter[i]);
1292:     VecScatterDestroy(&user->ui_scatter[i]);
1293:     VecScatterDestroy(&user->yi_scatter[i]);
1294:   }
1295:   PetscFree(user->uxi_scatter);
1296:   PetscFree(user->uyi_scatter);
1297:   PetscFree(user->ux_scatter);
1298:   PetscFree(user->uy_scatter);
1299:   PetscFree(user->ui_scatter);
1300:   PetscFree(user->yi_scatter);
1301:   return(0);
1302: }

1306: PetscErrorCode HyperbolicMonitor(Tao tao, void *ptr)
1307: {
1309:   Vec            X;
1310:   PetscReal      unorm,ynorm;
1311:   AppCtx         *user = (AppCtx*)ptr;

1314:   TaoGetSolutionVector(tao,&X);
1315:   Scatter(X,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
1316:   VecAXPY(user->ywork,-1.0,user->ytrue);
1317:   VecAXPY(user->uwork,-1.0,user->utrue);
1318:   VecNorm(user->uwork,NORM_2,&unorm);
1319:   VecNorm(user->ywork,NORM_2,&ynorm);
1320:   PetscPrintf(MPI_COMM_WORLD, "||u-ut||=%g ||y-yt||=%g\n",(double)unorm,(double)ynorm);
1321:   return(0);
1322: }