Actual source code: hyperbolic.c

petsc-master 2017-01-20
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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[]="";

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

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

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

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

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

250:   VecWAXPY(user->uwork,-1.0,user->ur,user->u);
251:   VecPointwiseMult(user->uwork,user->uwork,user->uwork);
252:   MatMult(user->L,user->uwork,user->lwork);
253:   VecDot(user->y,user->lwork,&d2);
254:   *f = 0.5 * (d1 + user->alpha*d2);
255:   return(0);
256: }

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

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

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

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

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

284:   Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
285:   return(0);
286: }

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

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

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

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

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

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

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

314:   *f = 0.5 * (d1 + user->alpha*d2);
315:   Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
316:   return(0);
317: }

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

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

337:     MatDiagonalScale(user->C[i],NULL,user->uxi[i]);
338:     MatDiagonalScale(user->Cwork[i],NULL,user->uyi[i]);
339:     MatAXPY(user->C[i],1.0,user->Cwork[i],SUBSET_NONZERO_PATTERN);
340:     MatScale(user->C[i],user->ht);
341:     MatShift(user->C[i],1.0);
342:   }
343:   return(0);
344: }

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

354:   Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
355:   return(0);
356: }

358: PetscErrorCode StateMatMult(Mat J_shell, Vec X, Vec Y)
359: {
361:   PetscInt       i;
362:   AppCtx         *user;

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

370:   for (i=1; i<user->nt; i++){
371:     user->block_index = i;
372:     MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
373:     MatMult(user->M,user->yi[i-1],user->ziwork[i-1]);
374:     VecAXPY(user->yiwork[i],-1.0,user->ziwork[i-1]);
375:   }
376:   Gather_yi(Y,user->yiwork,user->yi_scatter,user->nt);
377:   return(0);
378: }

380: PetscErrorCode StateMatMultTranspose(Mat J_shell, Vec X, Vec Y)
381: {
383:   PetscInt       i;
384:   AppCtx         *user;

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

390:   for (i=0; i<user->nt-1; i++){
391:     user->block_index = i;
392:     MatMultTranspose(user->JsBlock,user->yi[i],user->yiwork[i]);
393:     MatMult(user->M,user->yi[i+1],user->ziwork[i+1]);
394:     VecAXPY(user->yiwork[i],-1.0,user->ziwork[i+1]);
395:   }

397:   i = user->nt-1;
398:   user->block_index = i;
399:   MatMultTranspose(user->JsBlock,user->yi[i],user->yiwork[i]);
400:   Gather_yi(Y,user->yiwork,user->yi_scatter,user->nt);
401:   return(0);
402: }

404: PetscErrorCode StateMatBlockMult(Mat J_shell, Vec X, Vec Y)
405: {
407:   PetscInt       i;
408:   AppCtx         *user;

411:   MatShellGetContext(J_shell,(void**)&user);
412:   i = user->block_index;
413:   VecPointwiseMult(user->uxiwork[i],X,user->uxi[i]);
414:   VecPointwiseMult(user->uyiwork[i],X,user->uyi[i]);
415:   Gather(user->uiwork[i],user->uxiwork[i],user->ux_scatter[i],user->uyiwork[i],user->uy_scatter[i]);
416:   MatMult(user->Div,user->uiwork[i],Y);
417:   VecAYPX(Y,user->ht,X);
418:   return(0);
419: }

421: PetscErrorCode StateMatBlockMultTranspose(Mat J_shell, Vec X, Vec Y)
422: {
424:   PetscInt       i;
425:   AppCtx         *user;

428:   MatShellGetContext(J_shell,(void**)&user);
429:   i = user->block_index;
430:   MatMult(user->Grad,X,user->uiwork[i]);
431:   Scatter(user->uiwork[i],user->uxiwork[i],user->ux_scatter[i],user->uyiwork[i],user->uy_scatter[i]);
432:   VecPointwiseMult(user->uxiwork[i],user->uxi[i],user->uxiwork[i]);
433:   VecPointwiseMult(user->uyiwork[i],user->uyi[i],user->uyiwork[i]);
434:   VecWAXPY(Y,1.0,user->uxiwork[i],user->uyiwork[i]);
435:   VecAYPX(Y,user->ht,X);
436:   return(0);
437: }

439: PetscErrorCode DesignMatMult(Mat J_shell, Vec X, Vec Y)
440: {
442:   PetscInt       i;
443:   AppCtx         *user;

446:   MatShellGetContext(J_shell,(void**)&user);
447:   Scatter_yi(user->y,user->yi,user->yi_scatter,user->nt);
448:   Scatter_uxi_uyi(X,user->uxiwork,user->uxi_scatter,user->uyiwork,user->uyi_scatter,user->nt);
449:   for (i=0; i<user->nt; i++){
450:     VecPointwiseMult(user->uxiwork[i],user->yi[i],user->uxiwork[i]);
451:     VecPointwiseMult(user->uyiwork[i],user->yi[i],user->uyiwork[i]);
452:     Gather(user->uiwork[i],user->uxiwork[i],user->ux_scatter[i],user->uyiwork[i],user->uy_scatter[i]);
453:     MatMult(user->Div,user->uiwork[i],user->ziwork[i]);
454:     VecScale(user->ziwork[i],user->ht);
455:   }
456:   Gather_yi(Y,user->ziwork,user->yi_scatter,user->nt);
457:   return(0);
458: }

460: PetscErrorCode DesignMatMultTranspose(Mat J_shell, Vec X, Vec Y)
461: {
463:   PetscInt       i;
464:   AppCtx         *user;

467:   MatShellGetContext(J_shell,(void**)&user);
468:   Scatter_yi(user->y,user->yi,user->yi_scatter,user->nt);
469:   Scatter_yi(X,user->yiwork,user->yi_scatter,user->nt);
470:   for (i=0; i<user->nt; i++){
471:     MatMult(user->Grad,user->yiwork[i],user->uiwork[i]);
472:     Scatter(user->uiwork[i],user->uxiwork[i],user->ux_scatter[i],user->uyiwork[i],user->uy_scatter[i]);
473:     VecPointwiseMult(user->uxiwork[i],user->yi[i],user->uxiwork[i]);
474:     VecPointwiseMult(user->uyiwork[i],user->yi[i],user->uyiwork[i]);
475:     Gather(user->uiwork[i],user->uxiwork[i],user->ux_scatter[i],user->uyiwork[i],user->uy_scatter[i]);
476:     VecScale(user->uiwork[i],user->ht);
477:   }
478:   Gather_yi(Y,user->uiwork,user->ui_scatter,user->nt);
479:   return(0);
480: }

482: PetscErrorCode StateMatBlockPrecMult(PC PC_shell, Vec X, Vec Y)
483: {
485:   PetscInt       i;
486:   AppCtx         *user;

489:   PCShellGetContext(PC_shell,(void**)&user);
490:   i = user->block_index;
491:   if (user->c_formed) {
492:     MatSOR(user->C[i],X,1.0,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_SYMMETRIC_SWEEP),0.0,1,1,Y);
493:   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not formed");
494:   return(0);
495: }

497: PetscErrorCode StateMatBlockPrecMultTranspose(PC PC_shell, Vec X, Vec Y)
498: {
500:   PetscInt       i;
501:   AppCtx         *user;

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

506:   i = user->block_index;
507:   if (user->c_formed) {
508:     MatSOR(user->C[i],X,1.0,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_SYMMETRIC_SWEEP),0.0,1,1,Y);
509:   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not formed");
510:   return(0);
511: }

513: PetscErrorCode StateMatInvMult(Mat J_shell, Vec X, Vec Y)
514: {
516:   AppCtx         *user;
517:   PetscInt       its,i;

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

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

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

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

543:     KSPGetIterationNumber(user->solver,&its);
544:     user->ksp_its = user->ksp_its + its;
545:   }
546:   Gather_yi(Y,user->yiwork,user->yi_scatter,user->nt);
547:   return(0);
548: }

550: PetscErrorCode StateMatInvTransposeMult(Mat J_shell, Vec X, Vec Y)
551: {
553:   AppCtx         *user;
554:   PetscInt       its,i;

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

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

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

567:   KSPGetIterationNumber(user->solver,&its);
568:   user->ksp_its = user->ksp_its + its;

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

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

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

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

591:   MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,new_shell);
592:   MatShellSetOperation(*new_shell,MATOP_MULT,(void(*)(void))StateMatMult);
593:   MatShellSetOperation(*new_shell,MATOP_DUPLICATE,(void(*)(void))StateMatDuplicate);
594:   MatShellSetOperation(*new_shell,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMultTranspose);
595:   MatShellSetOperation(*new_shell,MATOP_GET_DIAGONAL,(void(*)(void))StateMatGetDiagonal);
596:   return(0);
597: }

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

605:   MatShellGetContext(J_shell,(void**)&user);
606:    VecCopy(user->js_diag,X);
607:   return(0);
608: }

610: PetscErrorCode FormConstraints(Tao tao, Vec X, Vec C, void *ptr)
611: {
612:   /* con = Ay - q, A = [C(u1)  0     0     ...   0;
613:                          -M  C(u2)   0     ...   0;
614:                           0   -M   C(u3)   ...   0;
615:                                       ...         ;
616:                           0    ...      -M C(u_nt)]
617:      C(u) = eye + ht*Div*[diag(u1); diag(u2)]       */
619:   PetscInt       i;
620:   AppCtx         *user = (AppCtx*)ptr;

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

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

630:   for (i=1; i<user->nt; i++){
631:     user->block_index = i;
632:     MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
633:     MatMult(user->M,user->yi[i-1],user->ziwork[i-1]);
634:     VecAXPY(user->yiwork[i],-1.0,user->ziwork[i-1]);
635:   }

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

640:   return(0);
641: }


644: PetscErrorCode Scatter(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat)
645: {

649:   VecScatterBegin(s_scat,x,state,INSERT_VALUES,SCATTER_FORWARD);
650:   VecScatterEnd(s_scat,x,state,INSERT_VALUES,SCATTER_FORWARD);
651:   VecScatterBegin(d_scat,x,design,INSERT_VALUES,SCATTER_FORWARD);
652:   VecScatterEnd(d_scat,x,design,INSERT_VALUES,SCATTER_FORWARD);
653:   return(0);
654: }

656: PetscErrorCode Scatter_uxi_uyi(Vec u, Vec *uxi, VecScatter *scatx, Vec *uyi, VecScatter *scaty, PetscInt nt)
657: {
659:   PetscInt       i;

662:   for (i=0; i<nt; i++){
663:     VecScatterBegin(scatx[i],u,uxi[i],INSERT_VALUES,SCATTER_FORWARD);
664:     VecScatterEnd(scatx[i],u,uxi[i],INSERT_VALUES,SCATTER_FORWARD);
665:     VecScatterBegin(scaty[i],u,uyi[i],INSERT_VALUES,SCATTER_FORWARD);
666:     VecScatterEnd(scaty[i],u,uyi[i],INSERT_VALUES,SCATTER_FORWARD);
667:   }
668:   return(0);
669: }

671: PetscErrorCode Gather(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat)
672: {

676:   VecScatterBegin(s_scat,state,x,INSERT_VALUES,SCATTER_REVERSE);
677:   VecScatterEnd(s_scat,state,x,INSERT_VALUES,SCATTER_REVERSE);
678:   VecScatterBegin(d_scat,design,x,INSERT_VALUES,SCATTER_REVERSE);
679:   VecScatterEnd(d_scat,design,x,INSERT_VALUES,SCATTER_REVERSE);
680:   return(0);
681: }

683: PetscErrorCode Gather_uxi_uyi(Vec u, Vec *uxi, VecScatter *scatx, Vec *uyi, VecScatter *scaty, PetscInt nt)
684: {
686:   PetscInt       i;

689:   for (i=0; i<nt; i++){
690:     VecScatterBegin(scatx[i],uxi[i],u,INSERT_VALUES,SCATTER_REVERSE);
691:     VecScatterEnd(scatx[i],uxi[i],u,INSERT_VALUES,SCATTER_REVERSE);
692:     VecScatterBegin(scaty[i],uyi[i],u,INSERT_VALUES,SCATTER_REVERSE);
693:     VecScatterEnd(scaty[i],uyi[i],u,INSERT_VALUES,SCATTER_REVERSE);
694:   }
695:   return(0);
696: }

698: PetscErrorCode Scatter_yi(Vec y, Vec *yi, VecScatter *scat, PetscInt nt)
699: {
701:   PetscInt       i;

704:   for (i=0; i<nt; i++){
705:     VecScatterBegin(scat[i],y,yi[i],INSERT_VALUES,SCATTER_FORWARD);
706:     VecScatterEnd(scat[i],y,yi[i],INSERT_VALUES,SCATTER_FORWARD);
707:   }
708:   return(0);
709: }

711: PetscErrorCode Gather_yi(Vec y, Vec *yi, VecScatter *scat, PetscInt nt)
712: {
714:   PetscInt       i;

717:   for (i=0; i<nt; i++){
718:     VecScatterBegin(scat[i],yi[i],y,INSERT_VALUES,SCATTER_REVERSE);
719:     VecScatterEnd(scat[i],yi[i],y,INSERT_VALUES,SCATTER_REVERSE);
720:   }
721:   return(0);
722: }

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

735:   user->jformed = PETSC_FALSE;
736:   user->c_formed = PETSC_FALSE;

738:   user->ksp_its = 0;
739:   user->ksp_its_initial = 0;

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

743:   h = 1.0/user->mx;
744:   hinv = user->mx;
745:   neg_hinv = -hinv;
746:   half_hinv = hinv / 2.0;
747:   neg_half_hinv = neg_hinv / 2.0;

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

757:   for (i=istart; i<iend; i++){
758:     if (i<n){
759:       iblock = i / user->mx;
760:       j = iblock*user->mx + ((i+user->mx-1) % user->mx);
761:       MatSetValues(user->Grad,1,&i,1,&j,&half_hinv,INSERT_VALUES);
762:       j = iblock*user->mx + ((i+1) % user->mx);
763:       MatSetValues(user->Grad,1,&i,1,&j,&neg_half_hinv,INSERT_VALUES);
764:     }
765:     if (i>=n){
766:       j = (i - user->mx) % n;
767:       MatSetValues(user->Grad,1,&i,1,&j,&half_hinv,INSERT_VALUES);
768:       j = (j + 2*user->mx) % n;
769:       MatSetValues(user->Grad,1,&i,1,&j,&neg_half_hinv,INSERT_VALUES);
770:     }
771:   }

773:   MatAssemblyBegin(user->Grad,MAT_FINAL_ASSEMBLY);
774:   MatAssemblyEnd(user->Grad,MAT_FINAL_ASSEMBLY);

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

783:   for (i=istart; i<iend; i++){
784:     iblock = i / user->mx;
785:     j = iblock*user->mx + ((i+user->mx-1) % user->mx);
786:     MatSetValues(user->Gradxy[0],1,&i,1,&j,&half_hinv,INSERT_VALUES);
787:     j = iblock*user->mx + ((i+1) % user->mx);
788:     MatSetValues(user->Gradxy[0],1,&i,1,&j,&neg_half_hinv,INSERT_VALUES);
789:     MatSetValues(user->Gradxy[0],1,&i,1,&i,&zero,INSERT_VALUES);
790:   }
791:   MatAssemblyBegin(user->Gradxy[0],MAT_FINAL_ASSEMBLY);
792:   MatAssemblyEnd(user->Gradxy[0],MAT_FINAL_ASSEMBLY);

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

801:   for (i=istart; i<iend; i++){
802:     j = (i + n - user->mx) % n;
803:     MatSetValues(user->Gradxy[1],1,&i,1,&j,&half_hinv,INSERT_VALUES);
804:     j = (j + 2*user->mx) % n;
805:     MatSetValues(user->Gradxy[1],1,&i,1,&j,&neg_half_hinv,INSERT_VALUES);
806:     MatSetValues(user->Gradxy[1],1,&i,1,&i,&zero,INSERT_VALUES);
807:   }
808:   MatAssemblyBegin(user->Gradxy[1],MAT_FINAL_ASSEMBLY);
809:   MatAssemblyEnd(user->Gradxy[1],MAT_FINAL_ASSEMBLY);

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

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

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

832:     /* kron(Av,Id) */
833:     j = (i + user->mx) % n;
834:     MatSetValues(user->M,1,&i,1,&j,&quarter,INSERT_VALUES);
835:     j = (i + n - user->mx) % n;
836:     MatSetValues(user->M,1,&i,1,&j,&quarter,INSERT_VALUES);
837:   }
838:   MatAssemblyBegin(user->M,MAT_FINAL_ASSEMBLY);
839:   MatAssemblyEnd(user->M,MAT_FINAL_ASSEMBLY);

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

849:   VecDuplicate(XX,&YY);
850:   VecDuplicate(XX,&XXwork);
851:   VecDuplicate(XX,&YYwork);
852:   VecDuplicate(XX,&user->d);
853:   VecDuplicate(XX,&user->dwork);

855:   VecGetOwnershipRange(XX,&istart,&iend);
856:   for (linear_index=istart; linear_index<iend; linear_index++){
857:     i = linear_index % user->mx;
858:     j = (linear_index-i)/user->mx;
859:     vx = h*(i+0.5);
860:     vy = h*(j+0.5);
861:     VecSetValues(XX,1,&linear_index,&vx,INSERT_VALUES);
862:     VecSetValues(YY,1,&linear_index,&vy,INSERT_VALUES);
863:   }

865:   VecAssemblyBegin(XX);
866:   VecAssemblyEnd(XX);
867:   VecAssemblyBegin(YY);
868:   VecAssemblyEnd(YY);

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

876:   VecShift(XXwork,-0.25);
877:   VecShift(YYwork,-0.25);

879:   VecPointwiseMult(XXwork,XXwork,XXwork);
880:   VecPointwiseMult(YYwork,YYwork,YYwork);

882:   VecCopy(XXwork,user->dwork);
883:   VecAXPY(user->dwork,1.0,YYwork);
884:   VecScale(user->dwork,-30.0);
885:   VecExp(user->dwork);
886:   VecCopy(user->dwork,user->d);

888:   VecCopy(XX,XXwork);
889:   VecCopy(YY,YYwork);

891:   VecShift(XXwork,-0.75);
892:   VecShift(YYwork,-0.75);

894:   VecPointwiseMult(XXwork,XXwork,XXwork);
895:   VecPointwiseMult(YYwork,YYwork,YYwork);

897:   VecCopy(XXwork,user->dwork);
898:   VecAXPY(user->dwork,1.0,YYwork);
899:   VecScale(user->dwork,-30.0);
900:   VecExp(user->dwork);

902:   VecAXPY(user->d,1.0,user->dwork);
903:   VecShift(user->d,1.0);
904:   VecSum(user->d,&sum);
905:   VecScale(user->d,1.0/(h*h*sum));

907:   /* Initial conditions of forward problem */
908:   VecDuplicate(XX,&bc);
909:   VecCopy(XX,XXwork);
910:   VecCopy(YY,YYwork);

912:   VecShift(XXwork,-0.5);
913:   VecShift(YYwork,-0.5);

915:   VecPointwiseMult(XXwork,XXwork,XXwork);
916:   VecPointwiseMult(YYwork,YYwork,YYwork);

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

925:   /* Create scatter from y to y_1,y_2,...,y_nt */
926:   /*  TODO: Reorder for better parallelism. (This will require reordering Q and L as well.) */
927:   PetscMalloc1(user->nt*user->mx*user->mx,&user->yi_scatter);
928:   VecCreate(PETSC_COMM_WORLD,&yi);
929:   VecSetSizes(yi,PETSC_DECIDE,user->mx*user->mx);
930:   VecSetFromOptions(yi);
931:   VecDuplicateVecs(yi,user->nt,&user->yi);
932:   VecDuplicateVecs(yi,user->nt,&user->yiwork);
933:   VecDuplicateVecs(yi,user->nt,&user->ziwork);
934:   for (i=0; i<user->nt; i++){
935:     VecGetOwnershipRange(user->yi[i],&lo,&hi);
936:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_yi);
937:     ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+i*user->mx*user->mx,1,&is_from_y);
938:     VecScatterCreate(user->y,is_from_y,user->yi[i],is_to_yi,&user->yi_scatter[i]);
939:     ISDestroy(&is_to_yi);
940:     ISDestroy(&is_from_y);
941:   }

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

968:     ISDestroy(&is_to_uxi);
969:     ISDestroy(&is_from_u);

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

976:     ISDestroy(&is_to_uyi);
977:     ISDestroy(&is_from_u);

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

984:     ISDestroy(&is_to_uxi);
985:     ISDestroy(&is_from_u);

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

992:     ISDestroy(&is_to_uyi);
993:     ISDestroy(&is_from_u);

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

1000:     ISDestroy(&is_to_uxi);
1001:     ISDestroy(&is_from_u);
1002:   }

1004:   /* RHS of forward problem */
1005:   MatMult(user->M,bc,user->yiwork[0]);
1006:   for (i=1; i<user->nt; i++){
1007:     VecSet(user->yiwork[i],0.0);
1008:   }
1009:   Gather_yi(user->q,user->yiwork,user->yi_scatter,user->nt);

1011:   /* Compute true velocity field utrue */
1012:   VecDuplicate(user->u,&user->utrue);
1013:   for (i=0; i<user->nt; i++){
1014:     VecCopy(YY,user->uxi[i]);
1015:     VecScale(user->uxi[i],150.0*i*user->ht);
1016:     VecCopy(XX,user->uyi[i]);
1017:     VecShift(user->uyi[i],-10.0);
1018:     VecScale(user->uyi[i],15.0*i*user->ht);
1019:   }
1020:   Gather_uxi_uyi(user->utrue,user->uxi,user->uxi_scatter,user->uyi,user->uyi_scatter,user->nt);

1022:   /* Initial guess and reference model */
1023:   VecDuplicate(user->utrue,&user->ur);
1024:   for (i=0; i<user->nt; i++){
1025:     VecCopy(XX,user->uxi[i]);
1026:     VecShift(user->uxi[i],i*user->ht);
1027:     VecCopy(YY,user->uyi[i]);
1028:     VecShift(user->uyi[i],-i*user->ht);
1029:   }
1030:   Gather_uxi_uyi(user->ur,user->uxi,user->uxi_scatter,user->uyi,user->uyi_scatter,user->nt);

1032:   /* Generate regularization matrix L */
1033:   MatCreate(PETSC_COMM_WORLD,&user->LT);
1034:   MatSetSizes(user->LT,PETSC_DECIDE,PETSC_DECIDE,2*n*user->nt,n*user->nt);
1035:   MatSetFromOptions(user->LT);
1036:   MatMPIAIJSetPreallocation(user->LT,1,NULL,1,NULL);
1037:   MatSeqAIJSetPreallocation(user->LT,1,NULL);
1038:   MatGetOwnershipRange(user->LT,&istart,&iend);

1040:   for (i=istart; i<iend; i++){
1041:     iblock = (i+n) / (2*n);
1042:     j = i - iblock*n;
1043:     MatSetValues(user->LT,1,&i,1,&j,&user->gamma,INSERT_VALUES);
1044:   }

1046:   MatAssemblyBegin(user->LT,MAT_FINAL_ASSEMBLY);
1047:   MatAssemblyEnd(user->LT,MAT_FINAL_ASSEMBLY);

1049:   MatTranspose(user->LT,MAT_INITIAL_MATRIX,&user->L);

1051:   /* Build work vectors and matrices */
1052:   VecCreate(PETSC_COMM_WORLD,&user->lwork);
1053:   VecSetType(user->lwork,VECMPI);
1054:   VecSetSizes(user->lwork,PETSC_DECIDE,user->m);
1055:   VecSetFromOptions(user->lwork);

1057:   MatDuplicate(user->Div,MAT_SHARE_NONZERO_PATTERN,&user->Divwork);

1059:   VecDuplicate(user->y,&user->ywork);
1060:   VecDuplicate(user->u,&user->uwork);
1061:   VecDuplicate(user->u,&user->vwork);
1062:   VecDuplicate(user->u,&user->js_diag);
1063:   VecDuplicate(user->c,&user->cwork);

1065:   /* Create matrix-free shell user->Js for computing A*x */
1066:   MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,&user->Js);
1067:   MatShellSetOperation(user->Js,MATOP_MULT,(void(*)(void))StateMatMult);
1068:   MatShellSetOperation(user->Js,MATOP_DUPLICATE,(void(*)(void))StateMatDuplicate);
1069:   MatShellSetOperation(user->Js,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMultTranspose);
1070:   MatShellSetOperation(user->Js,MATOP_GET_DIAGONAL,(void(*)(void))StateMatGetDiagonal);

1072:   /* Diagonal blocks of user->Js */
1073:   MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,n,n,user,&user->JsBlock);
1074:   MatShellSetOperation(user->JsBlock,MATOP_MULT,(void(*)(void))StateMatBlockMult);
1075:   MatShellSetOperation(user->JsBlock,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatBlockMultTranspose);

1077:   /* Create a matrix-free shell user->JsBlockPrec for computing (U+D)\D*(L+D)\x, where JsBlock = L+D+U,
1078:      D is diagonal, L is strictly lower triangular, and U is strictly upper triangular.
1079:      This is an SOR preconditioner for user->JsBlock. */
1080:   MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,n,n,user,&user->JsBlockPrec);
1081:   MatShellSetOperation(user->JsBlockPrec,MATOP_MULT,(void(*)(void))StateMatBlockPrecMult);
1082:   MatShellSetOperation(user->JsBlockPrec,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatBlockPrecMultTranspose);

1084:   /* Create a matrix-free shell user->Jd for computing B*x */
1085:   MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->n-user->m,user,&user->Jd);
1086:   MatShellSetOperation(user->Jd,MATOP_MULT,(void(*)(void))DesignMatMult);
1087:   MatShellSetOperation(user->Jd,MATOP_MULT_TRANSPOSE,(void(*)(void))DesignMatMultTranspose);

1089:   /* User-defined routines for computing user->Js\x and user->Js^T\x*/
1090:   MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,&user->JsInv);
1091:   MatShellSetOperation(user->JsInv,MATOP_MULT,(void(*)(void))StateMatInvMult);
1092:   MatShellSetOperation(user->JsInv,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatInvTransposeMult);

1094:   /* Build matrices for SOR preconditioner */
1095:   Scatter_uxi_uyi(user->u,user->uxi,user->uxi_scatter,user->uyi,user->uyi_scatter,user->nt);
1096:   MatShift(user->Divxy[0],0.0); /*  Force C[i] and Divxy[0] to share same nonzero pattern */
1097:   MatAXPY(user->Divxy[0],0.0,user->Divxy[1],DIFFERENT_NONZERO_PATTERN);
1098:   PetscMalloc1(5*n,&user->C);
1099:   PetscMalloc1(2*n,&user->Cwork);
1100:   for (i=0; i<user->nt; i++){
1101:     MatDuplicate(user->Divxy[0],MAT_COPY_VALUES,&user->C[i]);
1102:     MatDuplicate(user->Divxy[1],MAT_COPY_VALUES,&user->Cwork[i]);

1104:     MatDiagonalScale(user->C[i],NULL,user->uxi[i]);
1105:     MatDiagonalScale(user->Cwork[i],NULL,user->uyi[i]);
1106:     MatAXPY(user->C[i],1.0,user->Cwork[i],SUBSET_NONZERO_PATTERN);
1107:     MatScale(user->C[i],user->ht);
1108:     MatShift(user->C[i],1.0);
1109:   }

1111:   /* Solver options and tolerances */
1112:   KSPCreate(PETSC_COMM_WORLD,&user->solver);
1113:   KSPSetType(user->solver,KSPGMRES);
1114:   KSPSetOperators(user->solver,user->JsBlock,user->JsBlockPrec);
1115:   KSPSetInitialGuessNonzero(user->solver,PETSC_FALSE); /*  TODO: why is true slower? */
1116:   KSPSetTolerances(user->solver,1e-4,1e-20,1e3,500);
1117:   /* KSPSetTolerances(user->solver,1e-8,1e-16,1e3,500); */
1118:   KSPGetPC(user->solver,&user->prec);
1119:   PCSetType(user->prec,PCSHELL);

1121:   PCShellSetApply(user->prec,StateMatBlockPrecMult);
1122:   PCShellSetApplyTranspose(user->prec,StateMatBlockPrecMultTranspose);
1123:   PCShellSetContext(user->prec,user);

1125:   /* Compute true state function yt given ut */
1126:   VecCreate(PETSC_COMM_WORLD,&user->ytrue);
1127:   VecSetSizes(user->ytrue,PETSC_DECIDE,n*user->nt);
1128:   VecSetFromOptions(user->ytrue);
1129:   user->c_formed = PETSC_TRUE;
1130:   VecCopy(user->utrue,user->u); /*  Set u=utrue temporarily for StateMatInv */
1131:   VecSet(user->ytrue,0.0); /*  Initial guess */
1132:   StateMatInvMult(user->Js,user->q,user->ytrue);
1133:   VecCopy(user->ur,user->u); /*  Reset u=ur */

1135:   /* Initial guess y0 for state given u0 */
1136:   StateMatInvMult(user->Js,user->q,user->y);

1138:   /* Data discretization */
1139:   MatCreate(PETSC_COMM_WORLD,&user->Q);
1140:   MatSetSizes(user->Q,PETSC_DECIDE,PETSC_DECIDE,user->mx*user->mx,user->m);
1141:   MatSetFromOptions(user->Q);
1142:   MatMPIAIJSetPreallocation(user->Q,0,NULL,1,NULL);
1143:   MatSeqAIJSetPreallocation(user->Q,1,NULL);

1145:   MatGetOwnershipRange(user->Q,&istart,&iend);

1147:   for (i=istart; i<iend; i++){
1148:     j = i + user->m - user->mx*user->mx;
1149:     MatSetValues(user->Q,1,&i,1,&j,&one,INSERT_VALUES);
1150:   }

1152:   MatAssemblyBegin(user->Q,MAT_FINAL_ASSEMBLY);
1153:   MatAssemblyEnd(user->Q,MAT_FINAL_ASSEMBLY);

1155:   MatTranspose(user->Q,MAT_INITIAL_MATRIX,&user->QT);

1157:   VecDestroy(&XX);
1158:   VecDestroy(&YY);
1159:   VecDestroy(&XXwork);
1160:   VecDestroy(&YYwork);
1161:   VecDestroy(&yi);
1162:   VecDestroy(&uxi);
1163:   VecDestroy(&ui);
1164:   VecDestroy(&bc);

1166:   /* Now that initial conditions have been set, let the user pass tolerance options to the KSP solver */
1167:   KSPSetFromOptions(user->solver);
1168:   return(0);
1169: }

1171: PetscErrorCode HyperbolicDestroy(AppCtx *user)
1172: {
1174:   PetscInt       i;

1177:   MatDestroy(&user->Q);
1178:   MatDestroy(&user->QT);
1179:   MatDestroy(&user->Div);
1180:   MatDestroy(&user->Divwork);
1181:   MatDestroy(&user->Grad);
1182:   MatDestroy(&user->L);
1183:   MatDestroy(&user->LT);
1184:   KSPDestroy(&user->solver);
1185:   MatDestroy(&user->Js);
1186:   MatDestroy(&user->Jd);
1187:   MatDestroy(&user->JsBlockPrec);
1188:   MatDestroy(&user->JsInv);
1189:   MatDestroy(&user->JsBlock);
1190:   MatDestroy(&user->Divxy[0]);
1191:   MatDestroy(&user->Divxy[1]);
1192:   MatDestroy(&user->Gradxy[0]);
1193:   MatDestroy(&user->Gradxy[1]);
1194:   MatDestroy(&user->M);
1195:   for (i=0; i<user->nt; i++){
1196:     MatDestroy(&user->C[i]);
1197:     MatDestroy(&user->Cwork[i]);
1198:   }
1199:   PetscFree(user->C);
1200:   PetscFree(user->Cwork);
1201:   VecDestroy(&user->u);
1202:   VecDestroy(&user->uwork);
1203:   VecDestroy(&user->vwork);
1204:   VecDestroy(&user->utrue);
1205:   VecDestroy(&user->y);
1206:   VecDestroy(&user->ywork);
1207:   VecDestroy(&user->ytrue);
1208:   VecDestroyVecs(user->nt,&user->yi);
1209:   VecDestroyVecs(user->nt,&user->yiwork);
1210:   VecDestroyVecs(user->nt,&user->ziwork);
1211:   VecDestroyVecs(user->nt,&user->uxi);
1212:   VecDestroyVecs(user->nt,&user->uyi);
1213:   VecDestroyVecs(user->nt,&user->uxiwork);
1214:   VecDestroyVecs(user->nt,&user->uyiwork);
1215:   VecDestroyVecs(user->nt,&user->ui);
1216:   VecDestroyVecs(user->nt,&user->uiwork);
1217:   VecDestroy(&user->c);
1218:   VecDestroy(&user->cwork);
1219:   VecDestroy(&user->ur);
1220:   VecDestroy(&user->q);
1221:   VecDestroy(&user->d);
1222:   VecDestroy(&user->dwork);
1223:   VecDestroy(&user->lwork);
1224:   VecDestroy(&user->js_diag);
1225:   ISDestroy(&user->s_is);
1226:   ISDestroy(&user->d_is);
1227:   VecScatterDestroy(&user->state_scatter);
1228:   VecScatterDestroy(&user->design_scatter);
1229:   for (i=0; i<user->nt; i++){
1230:     VecScatterDestroy(&user->uxi_scatter[i]);
1231:     VecScatterDestroy(&user->uyi_scatter[i]);
1232:     VecScatterDestroy(&user->ux_scatter[i]);
1233:     VecScatterDestroy(&user->uy_scatter[i]);
1234:     VecScatterDestroy(&user->ui_scatter[i]);
1235:     VecScatterDestroy(&user->yi_scatter[i]);
1236:   }
1237:   PetscFree(user->uxi_scatter);
1238:   PetscFree(user->uyi_scatter);
1239:   PetscFree(user->ux_scatter);
1240:   PetscFree(user->uy_scatter);
1241:   PetscFree(user->ui_scatter);
1242:   PetscFree(user->yi_scatter);
1243:   return(0);
1244: }

1246: PetscErrorCode HyperbolicMonitor(Tao tao, void *ptr)
1247: {
1249:   Vec            X;
1250:   PetscReal      unorm,ynorm;
1251:   AppCtx         *user = (AppCtx*)ptr;

1254:   TaoGetSolutionVector(tao,&X);
1255:   Scatter(X,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
1256:   VecAXPY(user->ywork,-1.0,user->ytrue);
1257:   VecAXPY(user->uwork,-1.0,user->utrue);
1258:   VecNorm(user->uwork,NORM_2,&unorm);
1259:   VecNorm(user->ywork,NORM_2,&ynorm);
1260:   PetscPrintf(MPI_COMM_WORLD, "||u-ut||=%g ||y-yt||=%g\n",(double)unorm,(double)ynorm);
1261:   return(0);
1262: }