Actual source code: hyperbolic.c
1: #include "taosolver.h"
2: #include "src/pde_constrained/impls/lcl/lcl.h"
3: #include "petsctime.h"
5: /*T
6: Concepts: TAO - Solving a system of nonlinear equations, nonlinear ;east squares
7: Routines: TaoInitialize(); TaoFinalize();
8: Routines: TaoCreate();
9: Routines: TaoSetType();
10: Routines: TaoSetInitialVector();
11: Routines: TaoSetObjectiveRoutine();
12: Routines: TaoSetGradientRoutine();
13: Routines: TaoSetConstraintsRoutine();
14: Routines: TaoSetJacobianStateRoutine();
15: Routines: TaoSetJacobianDesignRoutine();
16: Routines: TaoSetStateDesignIS();
17: Routines: TaoSetFromOptions();
18: Routines: TaoSetHistory(); TaoGetHistory();
19: Routines: TaoSolve();
20: Routines: TaoGetTerminationReason(); TaoDestroy();
21: Processors: 1
22: T*/
24: typedef struct {
25: PetscInt n; /* Number of variables */
26: PetscInt m; /* Number of constraints */
27: PetscInt mx; /* grid points in each direction */
28: PetscInt nt; /* Number of time steps */
29: PetscInt ndata; /* Number of data points per sample */
30: IS s_is;
31: IS d_is;
32: VecScatter state_scatter;
33: VecScatter design_scatter;
34: VecScatter *uxi_scatter,*uyi_scatter,*ux_scatter,*uy_scatter,*ui_scatter;
35: VecScatter *yi_scatter;
37: Mat Js,Jd,JsBlockPrec,JsInv,JsBlock;
38: PetscBool jformed,c_formed;
40: PetscReal alpha; /* Regularization parameter */
41: PetscReal gamma;
42: PetscReal ht; /* Time step */
43: PetscReal T; /* Final time */
44: Mat Q,QT;
45: Mat L,LT;
46: Mat Div,Divwork,Divxy[2];
47: Mat Grad,Gradxy[2];
48: Mat M;
49: Mat *C,*Cwork;
50: /* Mat Hs,Hd,Hsd; */
51: Vec q;
52: Vec ur; /* reference */
54: Vec d;
55: Vec dwork;
57: Vec y; /* state variables */
58: Vec ywork;
59: /* Vec ysave; */
60: Vec ytrue;
61: Vec *yi,*yiwork,*ziwork;
62: Vec *uxi,*uyi,*uxiwork,*uyiwork,*ui,*uiwork;
64: Vec u; /* design variables */
65: Vec uwork,vwork;
66: /* Vec usave; */
67: Vec utrue;
68:
69: Vec js_diag;
70:
71: Vec c; /* constraint vector */
72: Vec cwork;
73:
74: Vec lwork;
76: KSP solver;
77: PC prec;
78: PetscInt block_index;
80: TAO_LCL *lcl;
81: PetscReal tau[4];
82: PetscInt ksp_its;
83: PetscInt ksp_its_initial;
85: } AppCtx;
88: PetscErrorCode FormFunction(TaoSolver, Vec, PetscReal*, void*);
89: PetscErrorCode FormGradient(TaoSolver, Vec, Vec, void*);
90: PetscErrorCode FormFunctionGradient(TaoSolver, Vec, PetscReal*, Vec, void*);
91: PetscErrorCode FormJacobianState(TaoSolver, Vec, Mat*, Mat*, Mat*, MatStructure*,void*);
92: PetscErrorCode FormJacobianDesign(TaoSolver, Vec, Mat*,void*);
93: PetscErrorCode FormConstraints(TaoSolver, Vec, Vec, void*);
94: PetscErrorCode FormHessian(TaoSolver, Vec, Mat*, Mat*, MatStructure*, void*);
95: PetscErrorCode Gather(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat);
96: PetscErrorCode Scatter(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat);
97: PetscErrorCode HyperbolicInitialize(AppCtx *user);
98: PetscErrorCode HyperbolicDestroy(AppCtx *user);
99: PetscErrorCode HyperbolicMonitor(TaoSolver, void*);
101: PetscErrorCode StateMatMult(Mat,Vec,Vec);
102: PetscErrorCode StateMatBlockMult(Mat,Vec,Vec);
103: PetscErrorCode StateMatBlockMultTranspose(Mat,Vec,Vec);
104: PetscErrorCode StateMatMultTranspose(Mat,Vec,Vec);
105: PetscErrorCode StateMatGetDiagonal(Mat,Vec);
106: PetscErrorCode StateMatDuplicate(Mat,MatDuplicateOption,Mat*);
107: PetscErrorCode StateMatInvMult(Mat,Vec,Vec);
108: PetscErrorCode StateMatInvTransposeMult(Mat,Vec,Vec);
109: PetscErrorCode StateMatBlockPrecMult(PC,Vec,Vec);
111: PetscErrorCode DesignMatMult(Mat,Vec,Vec);
112: PetscErrorCode DesignMatMultTranspose(Mat,Vec,Vec);
114: PetscErrorCode Scatter_yi(Vec,Vec*,VecScatter*,PetscInt); /* y to y1,y2,...,y_nt */
115: PetscErrorCode Gather_yi(Vec,Vec*,VecScatter*,PetscInt);
116: PetscErrorCode Scatter_uxi_uyi(Vec,Vec*,VecScatter*,Vec*,VecScatter*,PetscInt); /* u to ux_1,uy_1,ux_2,uy_2,...,u */
117: PetscErrorCode Gather_uxi_uyi(Vec,Vec*,VecScatter*,Vec*,VecScatter*,PetscInt);
119: static char help[]="";
123: int main(int argc, char **argv)
124: {
126: Vec x,x0;
127:
128: TaoSolver tao;
129: TaoSolverTerminationReason reason;
130: AppCtx user;
131: IS is_allstate,is_alldesign;
132: PetscInt lo,hi,hi2,lo2,ksp_old;
133: PetscBool flag,showtime;
134: PetscInt ntests = 1;
135: PetscLogDouble v1,v2;
136: PetscInt i;
137: int stages[1];
138:
140: PetscInitialize(&argc, &argv, (char*)0,help);
141: TaoInitialize(&argc, &argv, (char*)0,help);
143: showtime = PETSC_FALSE;
144: PetscOptionsBool("-showtime","Display time elapsed","",showtime,&showtime,&flag);
145: user.mx = 32;
146: PetscOptionsInt("-mx","Number of grid points in each direction","",user.mx,&user.mx,&flag);
147: user.nt = 16;
148: PetscOptionsInt("-nt","Number of time steps","",user.nt,&user.nt,&flag);
149: user.ndata = 64;
150: PetscOptionsInt("-ndata","Numbers of data points per sample","",user.ndata,&user.ndata,&flag);
151: user.alpha = 10.0;
152: PetscOptionsReal("-alpha","Regularization parameter","",user.alpha,&user.alpha,&flag);
153: user.T = 1.0/32.0;
154: PetscOptionsReal("-Tfinal","Final time","",user.T,&user.T,&flag);
157: user.tau[0] = 1e-4;
158: PetscOptionsReal("-tola","Tolerance for first forward solve","",user.tau[0],&user.tau[0],&flag);
159: user.tau[1] = 1e-4;
160: PetscOptionsReal("-tolb","Tolerance for first adjoint solve","",user.tau[1],&user.tau[1],&flag);
161: user.tau[2] = 1e-4;
162: PetscOptionsReal("-tolc","Tolerance for second forward solve","",user.tau[2],&user.tau[2],&flag);
163: user.tau[3] = 1e-4;
164: PetscOptionsReal("-told","Tolerance for second adjoint solve","",user.tau[3],&user.tau[3],&flag);
166: user.m = user.mx*user.mx*user.nt; /* number of constraints */
167: user.n = user.mx*user.mx*3*user.nt; /* number of variables */
168: user.ht = user.T/user.nt; /* Time step */
169: user.gamma = user.T*user.ht / (user.mx*user.mx);
171: VecCreate(PETSC_COMM_WORLD,&user.u);
172: VecCreate(PETSC_COMM_WORLD,&user.y);
173: VecCreate(PETSC_COMM_WORLD,&user.c);
174: VecSetSizes(user.u,PETSC_DECIDE,user.n-user.m);
175: VecSetSizes(user.y,PETSC_DECIDE,user.m);
176: VecSetSizes(user.c,PETSC_DECIDE,user.m);
177: VecSetFromOptions(user.u);
178: VecSetFromOptions(user.y);
179: VecSetFromOptions(user.c);
181: /* Create scatters for reduced spaces.
182: If the state vector y and design vector u are partitioned as
183: [y_1; y_2; ...; y_np] and [u_1; u_2; ...; u_np] (with np = # of processors),
184: then the solution vector x is organized as
185: [y_1; u_1; y_2; u_2; ...; y_np; u_np].
186: The index sets user.s_is and user.d_is correspond to the indices of the
187: state and design variables owned by the current processor.
188: */
189: VecCreate(PETSC_COMM_WORLD,&x);
191: VecGetOwnershipRange(user.y,&lo,&hi);
192: VecGetOwnershipRange(user.u,&lo2,&hi2);
194: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_allstate);
195: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+lo2,1,&user.s_is);
197: ISCreateStride(PETSC_COMM_SELF,hi2-lo2,lo2,1,&is_alldesign);
198: ISCreateStride(PETSC_COMM_SELF,hi2-lo2,hi+lo2,1,&user.d_is);
200: VecSetSizes(x,hi-lo+hi2-lo2,user.n);
201: VecSetFromOptions(x);
203: VecScatterCreate(x,user.s_is,user.y,is_allstate,&user.state_scatter);
204: VecScatterCreate(x,user.d_is,user.u,is_alldesign,&user.design_scatter);
205: ISDestroy(&is_alldesign);
206: ISDestroy(&is_allstate);
210: /* Create TAO solver and set desired solution method */
211: TaoCreate(PETSC_COMM_WORLD,&tao);
212: TaoSetType(tao,"tao_lcl");
213: user.lcl = (TAO_LCL*)(tao->data);
215: /* Set up initial vectors and matrices */
216: HyperbolicInitialize(&user);
218: Gather(x,user.y,user.state_scatter,user.u,user.design_scatter);
219: VecDuplicate(x,&x0);
220: VecCopy(x,x0);
222: /* Set solution vector with an initial guess */
223: TaoSetInitialVector(tao,x);
224: TaoSetObjectiveRoutine(tao, FormFunction, (void *)&user);
225: TaoSetGradientRoutine(tao, FormGradient, (void *)&user);
226: TaoSetConstraintsRoutine(tao, user.c, FormConstraints, (void *)&user);
228: TaoSetJacobianStateRoutine(tao, user.Js, user.Js, user.JsInv, FormJacobianState, (void *)&user);
230: TaoSetJacobianDesignRoutine(tao, user.Jd, FormJacobianDesign, (void *)&user);
232: TaoSetFromOptions(tao);
233: TaoSetStateDesignIS(tao,user.s_is,user.d_is);
235: /* SOLVE THE APPLICATION */
236: PetscOptionsInt("-ntests","Number of times to repeat TaoSolve","",ntests,&ntests,&flag);
237: PetscLogStageRegister("Trials",&stages[0]);
238: PetscLogStagePush(stages[0]);
239: user.ksp_its_initial = user.ksp_its;
240: ksp_old = user.ksp_its;
241: for (i=0; i<ntests; i++){
242: PetscGetTime(&v1);
243: TaoSolve(tao);
244: PetscGetTime(&v2);
245: if (showtime) {
246: PetscPrintf(PETSC_COMM_WORLD,"Elapsed time = %G\n",v2-v1);
247: }
248: PetscPrintf(PETSC_COMM_WORLD,"KSP Iterations = %D\n",user.ksp_its-ksp_old);
249: VecCopy(x0,x);
250: TaoSetInitialVector(tao,x);
251: }
252: PetscLogStagePop();
253: PetscBarrier((PetscObject)x);
254: PetscPrintf(PETSC_COMM_WORLD,"KSP iterations within initialization: ");
255: PetscPrintf(PETSC_COMM_WORLD,"%D\n",user.ksp_its_initial);
256: PetscPrintf(PETSC_COMM_WORLD,"Total KSP iterations over %D trial(s): ",ntests);
257: PetscPrintf(PETSC_COMM_WORLD,"%D\n",user.ksp_its);
258: PetscPrintf(PETSC_COMM_WORLD,"KSP iterations per trial: ");
259: PetscPrintf(PETSC_COMM_WORLD,"%D\n",(user.ksp_its-user.ksp_its_initial)/ntests);
261: TaoGetTerminationReason(tao,&reason);
263: if (reason < 0)
264: {
265: PetscPrintf(MPI_COMM_WORLD, "TAO failed to converge.\n");
266: }
267: else
268: {
269: PetscPrintf(MPI_COMM_WORLD, "Optimization terminated with status %D.\n", reason);
270: }
273: /* Free TAO data structures */
274: TaoDestroy(&tao);
276: /* Free PETSc data structures */
277: VecDestroy(&x);
278: VecDestroy(&x0);
279: HyperbolicDestroy(&user);
281: /* Finalize TAO, PETSc */
282: TaoFinalize();
283: PetscFinalize();
285: return 0;
286: }
287: /* ------------------------------------------------------------------- */
290: /*
291: dwork = Qy - d
292: lwork = L*(u-ur).^2
293: f = 1/2 * (dwork.dork + alpha*y.lwork)
294: */
295: PetscErrorCode FormFunction(TaoSolver tao,Vec X,PetscReal *f,void *ptr)
296: {
298: PetscReal d1=0,d2=0;
299: AppCtx *user = (AppCtx*)ptr;
301: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
302: MatMult(user->Q,user->y,user->dwork);
303: VecAXPY(user->dwork,-1.0,user->d);
304: VecDot(user->dwork,user->dwork,&d1);
306: VecWAXPY(user->uwork,-1.0,user->ur,user->u);
307: VecPointwiseMult(user->uwork,user->uwork,user->uwork);
308: MatMult(user->L,user->uwork,user->lwork);
309: VecDot(user->y,user->lwork,&d2);
310:
311: *f = 0.5 * (d1 + user->alpha*d2);
312: return(0);
313: }
315: /* ------------------------------------------------------------------- */
318: /*
319: state: g_s = Q' *(Qy - d) + 0.5*alpha*L*(u-ur).^2
320: design: g_d = alpha*(L'y).*(u-ur)
321: */
322: PetscErrorCode FormGradient(TaoSolver tao,Vec X,Vec G,void *ptr)
323: {
325: AppCtx *user = (AppCtx*)ptr;
327: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
328: MatMult(user->Q,user->y,user->dwork);
329: VecAXPY(user->dwork,-1.0,user->d);
331: MatMult(user->QT,user->dwork,user->ywork);
332:
333: MatMult(user->LT,user->y,user->uwork);
334: VecWAXPY(user->vwork,-1.0,user->ur,user->u);
335: VecPointwiseMult(user->uwork,user->vwork,user->uwork);
336: VecScale(user->uwork,user->alpha);
338: VecPointwiseMult(user->vwork,user->vwork,user->vwork);
339: MatMult(user->L,user->vwork,user->lwork);
340: VecAXPY(user->ywork,0.5*user->alpha,user->lwork);
341:
342: Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
343: return(0);
344: }
348: PetscErrorCode FormFunctionGradient(TaoSolver tao, Vec X, PetscReal *f, Vec G, void *ptr)
349: {
351: PetscReal d1,d2;
352: AppCtx *user = (AppCtx*)ptr;
355: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
356: MatMult(user->Q,user->y,user->dwork);
357: VecAXPY(user->dwork,-1.0,user->d);
359: MatMult(user->QT,user->dwork,user->ywork);
360:
361: VecDot(user->dwork,user->dwork,&d1);
363: MatMult(user->LT,user->y,user->uwork);
364: VecWAXPY(user->vwork,-1.0,user->ur,user->u);
365: VecPointwiseMult(user->uwork,user->vwork,user->uwork);
366: VecScale(user->uwork,user->alpha);
368: VecPointwiseMult(user->vwork,user->vwork,user->vwork);
369: MatMult(user->L,user->vwork,user->lwork);
370: VecAXPY(user->ywork,0.5*user->alpha,user->lwork);
372: VecDot(user->y,user->lwork,&d2);
374: *f = 0.5 * (d1 + user->alpha*d2);
376: Gather(G,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
378: return(0);
380: }
383: /* ------------------------------------------------------------------- */
386: /* A
387: MatShell object
388: */
389: PetscErrorCode FormJacobianState(TaoSolver tao, Vec X, Mat *J, Mat* JPre, Mat* JInv, MatStructure* flag, void *ptr)
390: {
392: PetscInt i;
393: AppCtx *user = (AppCtx*)ptr;
395: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
396:
397: Scatter_yi(user->u,user->ui,user->ui_scatter,user->nt);
398: Scatter_uxi_uyi(user->u,user->uxi,user->uxi_scatter,user->uyi,user->uyi_scatter,user->nt);
399: for (i=0; i<user->nt; i++){
400: MatCopy(user->Divxy[0],user->C[i],SAME_NONZERO_PATTERN);
401: MatCopy(user->Divxy[1],user->Cwork[i],SAME_NONZERO_PATTERN);
403: MatDiagonalScale(user->C[i],PETSC_NULL,user->uxi[i]);
404: MatDiagonalScale(user->Cwork[i],PETSC_NULL,user->uyi[i]);
405: MatAXPY(user->C[i],1.0,user->Cwork[i],SUBSET_NONZERO_PATTERN);
406: MatScale(user->C[i],user->ht);
407: MatShift(user->C[i],1.0);
408: }
409:
410: *JInv = user->JsInv;
412: return(0);
413: }
414: /* ------------------------------------------------------------------- */
417: /* B */
418: PetscErrorCode FormJacobianDesign(TaoSolver tao, Vec X, Mat *J, void *ptr)
419: {
421: AppCtx *user = (AppCtx*)ptr;
424: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
426: *J = user->Jd;
428: return(0);
429: }
435: PetscErrorCode StateMatMult(Mat J_shell, Vec X, Vec Y)
436: {
438: PetscInt i;
439: void *ptr;
440: AppCtx *user;
442: MatShellGetContext(J_shell,&ptr);
443: user = (AppCtx*)ptr;
445: Scatter_yi(X,user->yi,user->yi_scatter,user->nt);
446:
447: user->block_index = 0;
448: MatMult(user->JsBlock,user->yi[0],user->yiwork[0]);
450: for (i=1; i<user->nt; i++){
451: user->block_index = i;
452: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
453: MatMult(user->M,user->yi[i-1],user->ziwork[i-1]);
454: VecAXPY(user->yiwork[i],-1.0,user->ziwork[i-1]);
455: }
457: Gather_yi(Y,user->yiwork,user->yi_scatter,user->nt);
459: return(0);
460: }
464: PetscErrorCode StateMatMultTranspose(Mat J_shell, Vec X, Vec Y)
465: {
467: PetscInt i;
468: void *ptr;
469: AppCtx *user;
471: MatShellGetContext(J_shell,&ptr);
472: user = (AppCtx*)ptr;
474: Scatter_yi(X,user->yi,user->yi_scatter,user->nt);
476: for (i=0; i<user->nt-1; i++){
477: user->block_index = i;
478: MatMultTranspose(user->JsBlock,user->yi[i],user->yiwork[i]);
479: MatMult(user->M,user->yi[i+1],user->ziwork[i+1]);
480: VecAXPY(user->yiwork[i],-1.0,user->ziwork[i+1]);
481: }
483: i = user->nt-1;
484: user->block_index = i;
485: MatMultTranspose(user->JsBlock,user->yi[i],user->yiwork[i]);
487: Gather_yi(Y,user->yiwork,user->yi_scatter,user->nt);
489: return(0);
490: }
494: PetscErrorCode StateMatBlockMult(Mat J_shell, Vec X, Vec Y)
495: {
497: PetscInt i;
498: void *ptr;
499: AppCtx *user;
501: MatShellGetContext(J_shell,&ptr);
502: user = (AppCtx*)ptr;
503:
504: i = user->block_index;
505: VecPointwiseMult(user->uxiwork[i],X,user->uxi[i]);
506: VecPointwiseMult(user->uyiwork[i],X,user->uyi[i]);
507: Gather(user->uiwork[i],user->uxiwork[i],user->ux_scatter[i],user->uyiwork[i],user->uy_scatter[i]);
508: MatMult(user->Div,user->uiwork[i],Y);
509: VecAYPX(Y,user->ht,X);
511: return(0);
512: }
516: PetscErrorCode StateMatBlockMultTranspose(Mat J_shell, Vec X, Vec Y)
517: {
519: PetscInt i;
520: void *ptr;
521: AppCtx *user;
523: MatShellGetContext(J_shell,&ptr);
524: user = (AppCtx*)ptr;
525:
526: i = user->block_index;
527: MatMult(user->Grad,X,user->uiwork[i]);
528: Scatter(user->uiwork[i],user->uxiwork[i],user->ux_scatter[i],user->uyiwork[i],user->uy_scatter[i]);
529: VecPointwiseMult(user->uxiwork[i],user->uxi[i],user->uxiwork[i]);
530: VecPointwiseMult(user->uyiwork[i],user->uyi[i],user->uyiwork[i]);
531: VecWAXPY(Y,1.0,user->uxiwork[i],user->uyiwork[i]);
532: VecAYPX(Y,user->ht,X);
534: return(0);
535: }
539: PetscErrorCode DesignMatMult(Mat J_shell, Vec X, Vec Y)
540: {
542: void *ptr;
543: PetscInt i;
544: AppCtx *user;
546: MatShellGetContext(J_shell,&ptr);
547: user = (AppCtx*)ptr;
549: Scatter_yi(user->y,user->yi,user->yi_scatter,user->nt);
550: Scatter_uxi_uyi(X,user->uxiwork,user->uxi_scatter,user->uyiwork,user->uyi_scatter,user->nt);
551: for (i=0; i<user->nt; i++){
552: VecPointwiseMult(user->uxiwork[i],user->yi[i],user->uxiwork[i]);
553: VecPointwiseMult(user->uyiwork[i],user->yi[i],user->uyiwork[i]);
554: Gather(user->uiwork[i],user->uxiwork[i],user->ux_scatter[i],user->uyiwork[i],user->uy_scatter[i]);
555: MatMult(user->Div,user->uiwork[i],user->ziwork[i]);
556: VecScale(user->ziwork[i],user->ht);
557: }
558: Gather_yi(Y,user->ziwork,user->yi_scatter,user->nt);
560: return(0);
561: }
565: PetscErrorCode DesignMatMultTranspose(Mat J_shell, Vec X, Vec Y)
566: {
568: void *ptr;
569: PetscInt i;
570: AppCtx *user;
572: MatShellGetContext(J_shell,&ptr);
573: user = (AppCtx*)ptr;
575: Scatter_yi(user->y,user->yi,user->yi_scatter,user->nt);
576: Scatter_yi(X,user->yiwork,user->yi_scatter,user->nt);
577: for (i=0; i<user->nt; i++){
578: MatMult(user->Grad,user->yiwork[i],user->uiwork[i]);
579: Scatter(user->uiwork[i],user->uxiwork[i],user->ux_scatter[i],user->uyiwork[i],user->uy_scatter[i]);
580: VecPointwiseMult(user->uxiwork[i],user->yi[i],user->uxiwork[i]);
581: VecPointwiseMult(user->uyiwork[i],user->yi[i],user->uyiwork[i]);
582: Gather(user->uiwork[i],user->uxiwork[i],user->ux_scatter[i],user->uyiwork[i],user->uy_scatter[i]);
583: VecScale(user->uiwork[i],user->ht);
584: }
585: Gather_yi(Y,user->uiwork,user->ui_scatter,user->nt);
587: return(0);
588: }
592: PetscErrorCode StateMatBlockPrecMult(PC PC_shell, Vec X, Vec Y)
593: {
595: PetscInt i;
596: void *ptr;
597: AppCtx *user;
599: PCShellGetContext(PC_shell,&ptr);
600: user = (AppCtx*)ptr;
602: i = user->block_index;
603: if (user->c_formed) {
604: MatSOR(user->C[i],X,1.0,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_SYMMETRIC_SWEEP),0.0,1,1,Y);
605: }
606: else {
607: printf("C not formed"); abort();
608: }
610: return(0);
611: }
615: PetscErrorCode StateMatBlockPrecMultTranspose(PC PC_shell, Vec X, Vec Y)
616: {
618: PetscInt i;
619: void *ptr;
620: AppCtx *user;
622: PCShellGetContext(PC_shell,&ptr);
623: user = (AppCtx*)ptr;
625: i = user->block_index;
626: if (user->c_formed) {
627: MatSOR(user->C[i],X,1.0,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_SYMMETRIC_SWEEP),0.0,1,1,Y);
628: }
629: else {
630: printf("C not formed"); abort();
631: }
633: return(0);
634: }
638: PetscErrorCode StateMatInvMult(Mat J_shell, Vec X, Vec Y)
639: {
641: PetscReal tau;
642: void *ptr;
643: AppCtx *user;
644: PetscInt its,i;
646: MatShellGetContext(J_shell,&ptr);
647: user = (AppCtx*)ptr;
649: if (Y == user->ytrue) {
650: KSPSetTolerances(user->solver,1e-4,1e-20,PETSC_DEFAULT,PETSC_DEFAULT);
651: } else if (user->lcl) {
652: tau = user->tau[user->lcl->solve_type];
653: KSPSetTolerances(user->solver,tau,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
654: }
655:
656: Scatter_yi(X,user->yi,user->yi_scatter,user->nt);
657: Scatter_yi(Y,user->yiwork,user->yi_scatter,user->nt);
658: Scatter_uxi_uyi(user->u,user->uxi,user->uxi_scatter,user->uyi,user->uyi_scatter,user->nt);
659:
660: user->block_index = 0;
661: KSPSolve(user->solver,user->yi[0],user->yiwork[0]);
663: KSPGetIterationNumber(user->solver,&its);
664: user->ksp_its = user->ksp_its + its;
667: for (i=1; i<user->nt; i++){
668: MatMult(user->M,user->yiwork[i-1],user->ziwork[i-1]);
669: VecAXPY(user->yi[i],1.0,user->ziwork[i-1]);
670: user->block_index = i;
671: KSPSolve(user->solver,user->yi[i],user->yiwork[i]);
673: KSPGetIterationNumber(user->solver,&its);
674: user->ksp_its = user->ksp_its + its;
677: }
679: Gather_yi(Y,user->yiwork,user->yi_scatter,user->nt);
682: return(0);
683: }
687: PetscErrorCode StateMatInvTransposeMult(Mat J_shell, Vec X, Vec Y)
688: {
690: void *ptr;
691: AppCtx *user;
692: PetscReal tau;
693: PetscInt its,i;
695: MatShellGetContext(J_shell,&ptr);
696: user = (AppCtx*)ptr;
698: if (user->lcl) {
699: tau = user->tau[user->lcl->solve_type];
700: KSPSetTolerances(user->solver,tau,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
701: }
702: Scatter_yi(X,user->yi,user->yi_scatter,user->nt);
703: Scatter_yi(Y,user->yiwork,user->yi_scatter,user->nt);
704: Scatter_uxi_uyi(user->u,user->uxi,user->uxi_scatter,user->uyi,user->uyi_scatter,user->nt);
705:
706: i = user->nt - 1;
707: user->block_index = i;
708: KSPSolveTranspose(user->solver,user->yi[i],user->yiwork[i]);
710: KSPGetIterationNumber(user->solver,&its);
711: user->ksp_its = user->ksp_its + its;
714: for (i=user->nt-2; i>=0; i--){
715: MatMult(user->M,user->yiwork[i+1],user->ziwork[i+1]);
716: VecAXPY(user->yi[i],1.0,user->ziwork[i+1]);
717: user->block_index = i;
718: KSPSolveTranspose(user->solver,user->yi[i],user->yiwork[i]);
720: KSPGetIterationNumber(user->solver,&its);
721: user->ksp_its = user->ksp_its + its;
723:
724: }
726: Gather_yi(Y,user->yiwork,user->yi_scatter,user->nt);
729: return(0);
730: }
734: PetscErrorCode StateMatDuplicate(Mat J_shell, MatDuplicateOption opt, Mat *new_shell)
735: {
737: void *ptr;
738: AppCtx *user;
740: MatShellGetContext(J_shell,&ptr);
741: user = (AppCtx*)ptr;
743: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,new_shell);
744: MatShellSetOperation(*new_shell,MATOP_MULT,(void(*)(void))StateMatMult);
745: MatShellSetOperation(*new_shell,MATOP_DUPLICATE,(void(*)(void))StateMatDuplicate);
746: MatShellSetOperation(*new_shell,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMultTranspose);
747: MatShellSetOperation(*new_shell,MATOP_GET_DIAGONAL,(void(*)(void))StateMatGetDiagonal);
748:
750:
752: return(0);
753: }
757: PetscErrorCode StateMatGetDiagonal(Mat J_shell, Vec X)
758: {
760: void *ptr;
761: AppCtx *user;
763: MatShellGetContext(J_shell,&ptr);
764: user = (AppCtx*)ptr;
765: VecCopy(user->js_diag,X);
766: return(0);
767:
768: }
772: PetscErrorCode FormConstraints(TaoSolver tao, Vec X, Vec C, void *ptr)
773: {
774: /* con = Ay - q, A = [C(u1) 0 0 ... 0;
775: -M C(u2) 0 ... 0;
776: 0 -M C(u3) ... 0;
777: ... ;
778: 0 ... -M C(u_nt)]
779: C(u) = eye + ht*Div*[diag(u1); diag(u2)] */
781: PetscInt i;
782: AppCtx *user = (AppCtx*)ptr;
784:
785: Scatter(X,user->y,user->state_scatter,user->u,user->design_scatter);
786: Scatter_yi(user->y,user->yi,user->yi_scatter,user->nt);
787: Scatter_uxi_uyi(user->u,user->uxi,user->uxi_scatter,user->uyi,user->uyi_scatter,user->nt);
789: user->block_index = 0;
790: MatMult(user->JsBlock,user->yi[0],user->yiwork[0]);
792: for (i=1; i<user->nt; i++){
793: user->block_index = i;
794: MatMult(user->JsBlock,user->yi[i],user->yiwork[i]);
795: MatMult(user->M,user->yi[i-1],user->ziwork[i-1]);
796: VecAXPY(user->yiwork[i],-1.0,user->ziwork[i-1]);
797: }
799: Gather_yi(C,user->yiwork,user->yi_scatter,user->nt);
800: VecAXPY(C,-1.0,user->q);
802: return(0);
803: }
808: PetscErrorCode Scatter(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat)
809: {
812: VecScatterBegin(s_scat,x,state,INSERT_VALUES,SCATTER_FORWARD);
813: VecScatterEnd(s_scat,x,state,INSERT_VALUES,SCATTER_FORWARD);
815: VecScatterBegin(d_scat,x,design,INSERT_VALUES,SCATTER_FORWARD);
816: VecScatterEnd(d_scat,x,design,INSERT_VALUES,SCATTER_FORWARD);
817: return(0);
818: }
822: PetscErrorCode Scatter_uxi_uyi(Vec u, Vec *uxi, VecScatter *scatx, Vec *uyi, VecScatter *scaty, PetscInt nt)
823: {
825: PetscInt i;
827: for (i=0; i<nt; i++){
828: VecScatterBegin(scatx[i],u,uxi[i],INSERT_VALUES,SCATTER_FORWARD);
829: VecScatterEnd(scatx[i],u,uxi[i],INSERT_VALUES,SCATTER_FORWARD);
830: VecScatterBegin(scaty[i],u,uyi[i],INSERT_VALUES,SCATTER_FORWARD);
831: VecScatterEnd(scaty[i],u,uyi[i],INSERT_VALUES,SCATTER_FORWARD);
832: }
833: return(0);
834: }
838: PetscErrorCode Gather(Vec x, Vec state, VecScatter s_scat, Vec design, VecScatter d_scat)
839: {
842: VecScatterBegin(s_scat,state,x,INSERT_VALUES,SCATTER_REVERSE);
843: VecScatterEnd(s_scat,state,x,INSERT_VALUES,SCATTER_REVERSE);
844: VecScatterBegin(d_scat,design,x,INSERT_VALUES,SCATTER_REVERSE);
845: VecScatterEnd(d_scat,design,x,INSERT_VALUES,SCATTER_REVERSE);
846: return(0);
847: }
851: PetscErrorCode Gather_uxi_uyi(Vec u, Vec *uxi, VecScatter *scatx, Vec *uyi, VecScatter *scaty, PetscInt nt)
852: {
854: PetscInt i;
856: for (i=0; i<nt; i++){
857: VecScatterBegin(scatx[i],uxi[i],u,INSERT_VALUES,SCATTER_REVERSE);
858: VecScatterEnd(scatx[i],uxi[i],u,INSERT_VALUES,SCATTER_REVERSE);
859: VecScatterBegin(scaty[i],uyi[i],u,INSERT_VALUES,SCATTER_REVERSE);
860: VecScatterEnd(scaty[i],uyi[i],u,INSERT_VALUES,SCATTER_REVERSE);
861: }
862: return(0);
863: }
867: PetscErrorCode Scatter_yi(Vec y, Vec *yi, VecScatter *scat, PetscInt nt)
868: {
870: PetscInt i;
872: for (i=0; i<nt; i++){
873: VecScatterBegin(scat[i],y,yi[i],INSERT_VALUES,SCATTER_FORWARD);
874: VecScatterEnd(scat[i],y,yi[i],INSERT_VALUES,SCATTER_FORWARD);
875: }
876: return(0);
877: }
881: PetscErrorCode Gather_yi(Vec y, Vec *yi, VecScatter *scat, PetscInt nt)
882: {
884: PetscInt i;
886: for (i=0; i<nt; i++){
887: VecScatterBegin(scat[i],yi[i],y,INSERT_VALUES,SCATTER_REVERSE);
888: VecScatterEnd(scat[i],yi[i],y,INSERT_VALUES,SCATTER_REVERSE);
889: }
890: return(0);
891: }
892:
893:
896: PetscErrorCode HyperbolicInitialize(AppCtx *user)
897: {
899: PetscInt n,i,j,linear_index,istart,iend,iblock,lo,hi;
900: Vec XX,YY,XXwork,YYwork,yi,uxi,ui,bc;
901: PetscReal h,sum;
902: PetscScalar hinv,neg_hinv,quarter=0.25,one=1.0,half_hinv,neg_half_hinv;
903: PetscScalar vx,vy;
904: IS is_from_y,is_to_yi,is_from_u,is_to_uxi,is_to_uyi;
907: user->jformed = PETSC_FALSE;
908: user->c_formed = PETSC_FALSE;
910: user->ksp_its = 0;
911: user->ksp_its_initial = 0;
913: n = user->mx * user->mx;
915: h = 1.0/user->mx;
916: hinv = user->mx;
917: neg_hinv = -hinv;
918: half_hinv = hinv / 2.0;
919: neg_half_hinv = neg_hinv / 2.0;
921: /* Generate Grad matrix */
922: MatCreate(PETSC_COMM_WORLD,&user->Grad);
923: MatSetSizes(user->Grad,PETSC_DECIDE,PETSC_DECIDE,2*n,n);
924: MatSetFromOptions(user->Grad);
925: MatMPIAIJSetPreallocation(user->Grad,2,PETSC_NULL,2,PETSC_NULL);
926: MatSeqAIJSetPreallocation(user->Grad,2,PETSC_NULL);
927: MatGetOwnershipRange(user->Grad,&istart,&iend);
929: for (i=istart; i<iend; i++){
930: if (i<n){
931: iblock = i / user->mx;
932: j = iblock*user->mx + ((i+user->mx-1) % user->mx);
933: MatSetValues(user->Grad,1,&i,1,&j,&half_hinv,INSERT_VALUES);
934: j = iblock*user->mx + ((i+1) % user->mx);
935: MatSetValues(user->Grad,1,&i,1,&j,&neg_half_hinv,INSERT_VALUES);
936: }
937: if (i>=n){
938: j = (i - user->mx) % n;
939: MatSetValues(user->Grad,1,&i,1,&j,&half_hinv,INSERT_VALUES);
940: j = (j + 2*user->mx) % n;
941: MatSetValues(user->Grad,1,&i,1,&j,&neg_half_hinv,INSERT_VALUES);
942: }
943: }
945: MatAssemblyBegin(user->Grad,MAT_FINAL_ASSEMBLY);
946: MatAssemblyEnd(user->Grad,MAT_FINAL_ASSEMBLY);
948: MatCreate(PETSC_COMM_WORLD,&user->Gradxy[0]);
949: MatSetSizes(user->Gradxy[0],PETSC_DECIDE,PETSC_DECIDE,n,n);
950: MatSetFromOptions(user->Gradxy[0]);
951: MatMPIAIJSetPreallocation(user->Gradxy[0],2,PETSC_NULL,2,PETSC_NULL);
952: MatSeqAIJSetPreallocation(user->Gradxy[0],2,PETSC_NULL);
953: MatGetOwnershipRange(user->Gradxy[0],&istart,&iend);
954:
955: for (i=istart; i<iend; i++){
956: iblock = i / user->mx;
957: j = iblock*user->mx + ((i+user->mx-1) % user->mx);
958: MatSetValues(user->Gradxy[0],1,&i,1,&j,&half_hinv,INSERT_VALUES);
959: j = iblock*user->mx + ((i+1) % user->mx);
960: MatSetValues(user->Gradxy[0],1,&i,1,&j,&neg_half_hinv,INSERT_VALUES);
961: }
962: MatAssemblyBegin(user->Gradxy[0],MAT_FINAL_ASSEMBLY);
963: MatAssemblyEnd(user->Gradxy[0],MAT_FINAL_ASSEMBLY);
965: MatCreate(PETSC_COMM_WORLD,&user->Gradxy[1]);
966: MatSetSizes(user->Gradxy[1],PETSC_DECIDE,PETSC_DECIDE,n,n);
967: MatSetFromOptions(user->Gradxy[1]);
968: MatMPIAIJSetPreallocation(user->Gradxy[1],2,PETSC_NULL,2,PETSC_NULL);
969: MatSeqAIJSetPreallocation(user->Gradxy[1],2,PETSC_NULL);
970: MatGetOwnershipRange(user->Gradxy[1],&istart,&iend);
972: for (i=istart; i<iend; i++){
973: j = (i + n - user->mx) % n;
974: MatSetValues(user->Gradxy[1],1,&i,1,&j,&half_hinv,INSERT_VALUES);
975: j = (j + 2*user->mx) % n;
976: MatSetValues(user->Gradxy[1],1,&i,1,&j,&neg_half_hinv,INSERT_VALUES);
977: }
978: MatAssemblyBegin(user->Gradxy[1],MAT_FINAL_ASSEMBLY);
979: MatAssemblyEnd(user->Gradxy[1],MAT_FINAL_ASSEMBLY);
981: /* Generate Div matrix */
982: MatTranspose(user->Grad,MAT_INITIAL_MATRIX,&user->Div);
983: MatTranspose(user->Gradxy[0],MAT_INITIAL_MATRIX,&user->Divxy[0]);
984: MatTranspose(user->Gradxy[1],MAT_INITIAL_MATRIX,&user->Divxy[1]);
986: /* Off-diagonal averaging matrix */
987: MatCreate(PETSC_COMM_WORLD,&user->M);
988: MatSetSizes(user->M,PETSC_DECIDE,PETSC_DECIDE,n,n);
989: MatSetFromOptions(user->M);
990: MatMPIAIJSetPreallocation(user->M,4,PETSC_NULL,4,PETSC_NULL);
991: MatSeqAIJSetPreallocation(user->M,4,PETSC_NULL);
992: MatGetOwnershipRange(user->M,&istart,&iend);
994: for (i=istart; i<iend; i++){
995: /* kron(Id,Av) */
996: iblock = i / user->mx;
997: j = iblock*user->mx + ((i+user->mx-1) % user->mx);
998: MatSetValues(user->M,1,&i,1,&j,&quarter,INSERT_VALUES);
999: j = iblock*user->mx + ((i+1) % user->mx);
1000: MatSetValues(user->M,1,&i,1,&j,&quarter,INSERT_VALUES);
1001:
1002: /* kron(Av,Id) */
1003: j = (i + user->mx) % n;
1004: MatSetValues(user->M,1,&i,1,&j,&quarter,INSERT_VALUES);
1005: j = (i + n - user->mx) % n;
1006: MatSetValues(user->M,1,&i,1,&j,&quarter,INSERT_VALUES);
1007: }
1009: MatAssemblyBegin(user->M,MAT_FINAL_ASSEMBLY);
1010: MatAssemblyEnd(user->M,MAT_FINAL_ASSEMBLY);
1012: /* Generate 2D grid */
1013: VecCreate(PETSC_COMM_WORLD,&XX);
1014: VecCreate(PETSC_COMM_WORLD,&user->q);
1015: VecSetSizes(XX,PETSC_DECIDE,n);
1016: VecSetSizes(user->q,PETSC_DECIDE,n*user->nt);
1017: VecSetFromOptions(XX);
1018: VecSetFromOptions(user->q);
1020: VecDuplicate(XX,&YY);
1021: VecDuplicate(XX,&XXwork);
1022: VecDuplicate(XX,&YYwork);
1023: VecDuplicate(XX,&user->d);
1024: VecDuplicate(XX,&user->dwork);
1026: VecGetOwnershipRange(XX,&istart,&iend);
1027: for (linear_index=istart; linear_index<iend; linear_index++){
1028: i = linear_index % user->mx;
1029: j = (linear_index-i)/user->mx;
1030: vx = h*(i+0.5);
1031: vy = h*(j+0.5);
1032: VecSetValues(XX,1,&linear_index,&vx,INSERT_VALUES);
1033: VecSetValues(YY,1,&linear_index,&vy,INSERT_VALUES);
1034: }
1036: VecAssemblyBegin(XX);
1037: VecAssemblyEnd(XX);
1038: VecAssemblyBegin(YY);
1039: VecAssemblyEnd(YY);
1041: /* Compute final density function yT
1042: yT = 1.0 + exp(-30*((x-0.25)^2+(y-0.25)^2)) + exp(-30*((x-0.75)^2+(y-0.75)^2))
1043: yT = yT / (h^2*sum(yT)) */
1044: VecCopy(XX,XXwork);
1045: VecCopy(YY,YYwork);
1047: VecShift(XXwork,-0.25);
1048: VecShift(YYwork,-0.25);
1050: VecPointwiseMult(XXwork,XXwork,XXwork);
1051: VecPointwiseMult(YYwork,YYwork,YYwork);
1053: VecCopy(XXwork,user->dwork);
1054: VecAXPY(user->dwork,1.0,YYwork);
1055: VecScale(user->dwork,-30.0);
1056: VecExp(user->dwork);
1057: VecCopy(user->dwork,user->d);
1059: VecCopy(XX,XXwork);
1060: VecCopy(YY,YYwork);
1062: VecShift(XXwork,-0.75);
1063: VecShift(YYwork,-0.75);
1065: VecPointwiseMult(XXwork,XXwork,XXwork);
1066: VecPointwiseMult(YYwork,YYwork,YYwork);
1068: VecCopy(XXwork,user->dwork);
1069: VecAXPY(user->dwork,1.0,YYwork);
1070: VecScale(user->dwork,-30.0);
1071: VecExp(user->dwork);
1073: VecAXPY(user->d,1.0,user->dwork);
1074: VecShift(user->d,1.0);
1075: VecSum(user->d,&sum);
1076: VecScale(user->d,1.0/(h*h*sum));
1078: /* Initial conditions of forward problem */
1079: VecDuplicate(XX,&bc);
1080: VecCopy(XX,XXwork);
1081: VecCopy(YY,YYwork);
1083: VecShift(XXwork,-0.5);
1084: VecShift(YYwork,-0.5);
1086: VecPointwiseMult(XXwork,XXwork,XXwork);
1087: VecPointwiseMult(YYwork,YYwork,YYwork);
1089: VecWAXPY(bc,1.0,XXwork,YYwork);
1090: VecScale(bc,-50.0);
1091: VecExp(bc);
1092: VecShift(bc,1.0);
1093: VecSum(bc,&sum);
1094: VecScale(bc,1.0/(h*h*sum));
1096: /* Create scatter from y to y_1,y_2,...,y_nt */
1097: /* TODO: Reorder for better parallelism. (This will require reordering Q and L as well.) */
1098: PetscMalloc(user->nt*user->mx*user->mx*sizeof(PetscInt),&user->yi_scatter);
1099: VecCreate(PETSC_COMM_WORLD,&yi);
1100: VecSetSizes(yi,PETSC_DECIDE,user->mx*user->mx);
1101: VecSetFromOptions(yi);
1102: VecDuplicateVecs(yi,user->nt,&user->yi);
1103: VecDuplicateVecs(yi,user->nt,&user->yiwork);
1104: VecDuplicateVecs(yi,user->nt,&user->ziwork);
1105: for (i=0; i<user->nt; i++){
1106: VecGetOwnershipRange(user->yi[i],&lo,&hi);
1107: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_yi);
1108: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+i*user->mx*user->mx,1,&is_from_y);
1109: VecScatterCreate(user->y,is_from_y,user->yi[i],is_to_yi,&user->yi_scatter[i]);
1110: ISDestroy(&is_to_yi);
1111: ISDestroy(&is_from_y);
1112: }
1114: /* Create scatter from u to ux_1,uy_1,ux_2,uy_2,...,ux_nt,uy_nt */
1115: /* TODO: reorder for better parallelism */
1116: PetscMalloc(user->nt*user->mx*user->mx*sizeof(PetscInt),&user->uxi_scatter);
1117: PetscMalloc(user->nt*user->mx*user->mx*sizeof(PetscInt),&user->uyi_scatter);
1118: PetscMalloc(user->nt*user->mx*user->mx*sizeof(PetscInt),&user->ux_scatter);
1119: PetscMalloc(user->nt*user->mx*user->mx*sizeof(PetscInt),&user->uy_scatter);
1120: PetscMalloc(2*user->nt*user->mx*user->mx*sizeof(PetscInt),&user->ui_scatter);
1121: VecCreate(PETSC_COMM_WORLD,&uxi);
1122: VecCreate(PETSC_COMM_WORLD,&ui);
1123: VecSetSizes(uxi,PETSC_DECIDE,user->mx*user->mx);
1124: VecSetSizes(ui,PETSC_DECIDE,2*user->mx*user->mx);
1125: VecSetFromOptions(uxi);
1126: VecSetFromOptions(ui);
1127: VecDuplicateVecs(uxi,user->nt,&user->uxi);
1128: VecDuplicateVecs(uxi,user->nt,&user->uyi);
1129: VecDuplicateVecs(uxi,user->nt,&user->uxiwork);
1130: VecDuplicateVecs(uxi,user->nt,&user->uyiwork);
1131: VecDuplicateVecs(ui,user->nt,&user->ui);
1132: VecDuplicateVecs(ui,user->nt,&user->uiwork);
1133: for (i=0; i<user->nt; i++){
1134: VecGetOwnershipRange(user->uxi[i],&lo,&hi);
1135: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_uxi);
1136: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+2*i*user->mx*user->mx,1,&is_from_u);
1137: VecScatterCreate(user->u,is_from_u,user->uxi[i],is_to_uxi,&user->uxi_scatter[i]);
1139: ISDestroy(&is_to_uxi);
1140: ISDestroy(&is_from_u);
1142: VecGetOwnershipRange(user->uyi[i],&lo,&hi);
1143: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_uyi);
1144: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+(2*i+1)*user->mx*user->mx,1,&is_from_u);
1145: VecScatterCreate(user->u,is_from_u,user->uyi[i],is_to_uyi,&user->uyi_scatter[i]);
1147: ISDestroy(&is_to_uyi);
1148: ISDestroy(&is_from_u);
1150: VecGetOwnershipRange(user->uxi[i],&lo,&hi);
1151: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_uxi);
1152: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_from_u);
1153: VecScatterCreate(user->ui[i],is_from_u,user->uxi[i],is_to_uxi,&user->ux_scatter[i]);
1155: ISDestroy(&is_to_uxi);
1156: ISDestroy(&is_from_u);
1158: VecGetOwnershipRange(user->uyi[i],&lo,&hi);
1159: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_uyi);
1160: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+user->mx*user->mx,1,&is_from_u);
1161: VecScatterCreate(user->ui[i],is_from_u,user->uyi[i],is_to_uyi,&user->uy_scatter[i]);
1163: ISDestroy(&is_to_uyi);
1164: ISDestroy(&is_from_u);
1166: VecGetOwnershipRange(user->ui[i],&lo,&hi);
1167: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo,1,&is_to_uxi);
1168: ISCreateStride(PETSC_COMM_SELF,hi-lo,lo+2*i*user->mx*user->mx,1,&is_from_u);
1169: VecScatterCreate(user->u,is_from_u,user->ui[i],is_to_uxi,&user->ui_scatter[i]);
1171: ISDestroy(&is_to_uxi);
1172: ISDestroy(&is_from_u);
1173: }
1175: /* RHS of forward problem */
1176: MatMult(user->M,bc,user->yiwork[0]);
1177: for (i=1; i<user->nt; i++){
1178: VecSet(user->yiwork[i],0.0);
1179: }
1180: Gather_yi(user->q,user->yiwork,user->yi_scatter,user->nt);
1182: /* Compute true velocity field utrue */
1183: VecDuplicate(user->u,&user->utrue);
1184: for (i=0; i<user->nt; i++){
1185: VecCopy(YY,user->uxi[i]);
1186: VecScale(user->uxi[i],150.0*i*user->ht);
1187: VecCopy(XX,user->uyi[i]);
1188: VecShift(user->uyi[i],-10.0);
1189: VecScale(user->uyi[i],15.0*i*user->ht);
1190: }
1191: Gather_uxi_uyi(user->utrue,user->uxi,user->uxi_scatter,user->uyi,user->uyi_scatter,user->nt);
1192:
1193: /* Initial guess and reference model */
1194: VecDuplicate(user->utrue,&user->ur);
1195: for (i=0; i<user->nt; i++){
1196: VecCopy(XX,user->uxi[i]);
1197: VecShift(user->uxi[i],i*user->ht);
1198: VecCopy(YY,user->uyi[i]);
1199: VecShift(user->uyi[i],-i*user->ht);
1200: }
1201: Gather_uxi_uyi(user->ur,user->uxi,user->uxi_scatter,user->uyi,user->uyi_scatter,user->nt);
1203: /* Generate regularization matrix L */
1204: MatCreate(PETSC_COMM_WORLD,&user->LT);
1205: MatSetSizes(user->LT,PETSC_DECIDE,PETSC_DECIDE,2*n*user->nt,n*user->nt);
1206: MatSetFromOptions(user->LT);
1207: MatMPIAIJSetPreallocation(user->LT,1,PETSC_NULL,1,PETSC_NULL);
1208: MatSeqAIJSetPreallocation(user->LT,1,PETSC_NULL);
1209: MatGetOwnershipRange(user->LT,&istart,&iend);
1211: for (i=istart; i<iend; i++){
1212: iblock = (i+n) / (2*n);
1213: j = i - iblock*n;
1214: MatSetValues(user->LT,1,&i,1,&j,&user->gamma,INSERT_VALUES);
1215: }
1217: MatAssemblyBegin(user->LT,MAT_FINAL_ASSEMBLY);
1218: MatAssemblyEnd(user->LT,MAT_FINAL_ASSEMBLY);
1220: MatTranspose(user->LT,MAT_INITIAL_MATRIX,&user->L);
1222: /* Build work vectors and matrices */
1223: VecCreate(PETSC_COMM_WORLD,&user->lwork);
1224: VecSetType(user->lwork,VECMPI);
1225: VecSetSizes(user->lwork,PETSC_DECIDE,user->m);
1226: VecSetFromOptions(user->lwork);
1228: MatDuplicate(user->Div,MAT_SHARE_NONZERO_PATTERN,&user->Divwork);
1230: VecDuplicate(user->y,&user->ywork);
1231: VecDuplicate(user->u,&user->uwork);
1232: VecDuplicate(user->u,&user->vwork);
1233: VecDuplicate(user->u,&user->js_diag);
1234: VecDuplicate(user->c,&user->cwork);
1236: /* Create matrix-free shell user->Js for computing A*x */
1237: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,&user->Js);
1238: MatShellSetOperation(user->Js,MATOP_MULT,(void(*)(void))StateMatMult);
1239: MatShellSetOperation(user->Js,MATOP_DUPLICATE,(void(*)(void))StateMatDuplicate);
1240: MatShellSetOperation(user->Js,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatMultTranspose);
1241: MatShellSetOperation(user->Js,MATOP_GET_DIAGONAL,(void(*)(void))StateMatGetDiagonal);
1243: /* Diagonal blocks of user->Js */
1244: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,n,n,user,&user->JsBlock);
1245: MatShellSetOperation(user->JsBlock,MATOP_MULT,(void(*)(void))StateMatBlockMult);
1246: MatShellSetOperation(user->JsBlock,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatBlockMultTranspose);
1248: /* Create a matrix-free shell user->JsBlockPrec for computing (U+D)\D*(L+D)\x, where JsBlock = L+D+U,
1249: D is diagonal, L is strictly lower triangular, and U is strictly upper triangular.
1250: This is an SOR preconditioner for user->JsBlock. */
1251: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,n,n,user,&user->JsBlockPrec);
1252: MatShellSetOperation(user->JsBlockPrec,MATOP_MULT,(void(*)(void))StateMatBlockPrecMult);
1253: MatShellSetOperation(user->JsBlockPrec,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatBlockPrecMultTranspose);
1254:
1255: /* Create a matrix-free shell user->Jd for computing B*x */
1256: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->n-user->m,user,&user->Jd);
1257: MatShellSetOperation(user->Jd,MATOP_MULT,(void(*)(void))DesignMatMult);
1258: MatShellSetOperation(user->Jd,MATOP_MULT_TRANSPOSE,(void(*)(void))DesignMatMultTranspose);
1260: /* User-defined routines for computing user->Js\x and user->Js^T\x*/
1261: MatCreateShell(PETSC_COMM_WORLD,PETSC_DETERMINE,PETSC_DETERMINE,user->m,user->m,user,&user->JsInv);
1262: MatShellSetOperation(user->JsInv,MATOP_MULT,(void(*)(void))StateMatInvMult);
1263: MatShellSetOperation(user->JsInv,MATOP_MULT_TRANSPOSE,(void(*)(void))StateMatInvTransposeMult);
1266: /* Build matrices for SOR preconditioner */
1267: Scatter_uxi_uyi(user->u,user->uxi,user->uxi_scatter,user->uyi,user->uyi_scatter,user->nt);
1268: MatShift(user->Divxy[0],0.0); /* Force C[i] and Divxy[0] to share same nonzero pattern */
1269: MatAXPY(user->Divxy[0],0.0,user->Divxy[1],DIFFERENT_NONZERO_PATTERN);
1270: PetscMalloc(5*n*sizeof(PetscReal),&user->C);
1271: PetscMalloc(2*n*sizeof(PetscReal),&user->Cwork);
1272: for (i=0; i<user->nt; i++){
1273: MatDuplicate(user->Divxy[0],MAT_COPY_VALUES,&user->C[i]);
1274: MatDuplicate(user->Divxy[1],MAT_COPY_VALUES,&user->Cwork[i]);
1276: MatDiagonalScale(user->C[i],PETSC_NULL,user->uxi[i]);
1277: MatDiagonalScale(user->Cwork[i],PETSC_NULL,user->uyi[i]);
1278: MatAXPY(user->C[i],1.0,user->Cwork[i],SUBSET_NONZERO_PATTERN);
1279: MatScale(user->C[i],user->ht);
1280: MatShift(user->C[i],1.0);
1281: }
1283: /* Solver options and tolerances */
1284: KSPCreate(PETSC_COMM_WORLD,&user->solver);
1285: KSPSetType(user->solver,KSPGMRES);
1286: KSPSetOperators(user->solver,user->JsBlock,user->JsBlockPrec,DIFFERENT_NONZERO_PATTERN);
1287: KSPSetInitialGuessNonzero(user->solver,PETSC_FALSE); /* TODO: why is true slower? */
1288: KSPSetTolerances(user->solver,1e-4,1e-20,1e3,500);
1289: /* KSPSetTolerances(user->solver,1e-8,1e-16,1e3,500); */
1290: KSPGetPC(user->solver,&user->prec);
1291: PCSetType(user->prec,PCSHELL);
1293: PCShellSetApply(user->prec,StateMatBlockPrecMult);
1294: PCShellSetApplyTranspose(user->prec,StateMatBlockPrecMultTranspose);
1295: PCShellSetContext(user->prec,user);
1297: /* Compute true state function yt given ut */
1298: VecCreate(PETSC_COMM_WORLD,&user->ytrue);
1299: VecSetSizes(user->ytrue,PETSC_DECIDE,n*user->nt);
1300: VecSetFromOptions(user->ytrue);
1301: user->c_formed = PETSC_TRUE;
1302: VecCopy(user->utrue,user->u); /* Set u=utrue temporarily for StateMatInv */
1303: VecSet(user->ytrue,0.0); /* Initial guess */
1304: StateMatInvMult(user->Js,user->q,user->ytrue);
1305: VecCopy(user->ur,user->u); /* Reset u=ur */
1307: /* Initial guess y0 for state given u0 */
1308: user->lcl->solve_type = LCL_FORWARD1;
1309: StateMatInvMult(user->Js,user->q,user->y);
1311: /* Data discretization */
1312: MatCreate(PETSC_COMM_WORLD,&user->Q);
1313: MatSetSizes(user->Q,PETSC_DECIDE,PETSC_DECIDE,user->mx*user->mx,user->m);
1314: MatSetFromOptions(user->Q);
1315: MatMPIAIJSetPreallocation(user->Q,0,PETSC_NULL,1,PETSC_NULL);
1316: MatSeqAIJSetPreallocation(user->Q,1,PETSC_NULL);
1318: MatGetOwnershipRange(user->Q,&istart,&iend);
1320: for (i=istart; i<iend; i++){
1321: j = i + user->m - user->mx*user->mx;
1322: MatSetValues(user->Q,1,&i,1,&j,&one,INSERT_VALUES);
1323: }
1325: MatAssemblyBegin(user->Q,MAT_FINAL_ASSEMBLY);
1326: MatAssemblyEnd(user->Q,MAT_FINAL_ASSEMBLY);
1328: MatTranspose(user->Q,MAT_INITIAL_MATRIX,&user->QT);
1330: VecDestroy(&XX);
1331: VecDestroy(&YY);
1332: VecDestroy(&XXwork);
1333: VecDestroy(&YYwork);
1334: VecDestroy(&yi);
1335: VecDestroy(&uxi);
1336: VecDestroy(&ui);
1337: VecDestroy(&bc);
1339: /* Now that initial conditions have been set, let the user pass tolerance options to the KSP solver */
1340: KSPSetFromOptions(user->solver);
1343: return(0);
1344: }
1348: PetscErrorCode HyperbolicDestroy(AppCtx *user)
1349: {
1351: PetscInt i;
1353: MatDestroy(&user->Q);
1354: MatDestroy(&user->QT);
1355: MatDestroy(&user->Div);
1356: MatDestroy(&user->Divwork);
1357: MatDestroy(&user->Grad);
1358: MatDestroy(&user->L);
1359: MatDestroy(&user->LT);
1360: KSPDestroy(&user->solver);
1361: MatDestroy(&user->Js);
1362: MatDestroy(&user->Jd);
1363: MatDestroy(&user->JsBlockPrec);
1364: MatDestroy(&user->JsInv);
1365: MatDestroy(&user->JsBlock);
1366: MatDestroy(&user->Divxy[0]);
1367: MatDestroy(&user->Divxy[1]);
1368: MatDestroy(&user->Gradxy[0]);
1369: MatDestroy(&user->Gradxy[1]);
1370: MatDestroy(&user->M);
1371: for (i=0; i<user->nt; i++){
1372: MatDestroy(&user->C[i]);
1373: MatDestroy(&user->Cwork[i]);
1374: }
1375: PetscFree(user->C);
1376: PetscFree(user->Cwork);
1377: VecDestroy(&user->u);
1378: VecDestroy(&user->uwork);
1379: VecDestroy(&user->vwork);
1380: VecDestroy(&user->utrue);
1381: VecDestroy(&user->y);
1382: VecDestroy(&user->ywork);
1383: VecDestroy(&user->ytrue);
1384: VecDestroyVecs(user->nt,&user->yi);
1385: VecDestroyVecs(user->nt,&user->yiwork);
1386: VecDestroyVecs(user->nt,&user->ziwork);
1387: VecDestroyVecs(user->nt,&user->uxi);
1388: VecDestroyVecs(user->nt,&user->uyi);
1389: VecDestroyVecs(user->nt,&user->uxiwork);
1390: VecDestroyVecs(user->nt,&user->uyiwork);
1391: VecDestroyVecs(user->nt,&user->ui);
1392: VecDestroyVecs(user->nt,&user->uiwork);
1393: VecDestroy(&user->c);
1394: VecDestroy(&user->cwork);
1395: VecDestroy(&user->ur);
1396: VecDestroy(&user->q);
1397: VecDestroy(&user->d);
1398: VecDestroy(&user->dwork);
1399: VecDestroy(&user->lwork);
1400: VecDestroy(&user->js_diag);
1401: ISDestroy(&user->s_is);
1402: ISDestroy(&user->d_is);
1403: VecScatterDestroy(&user->state_scatter);
1404: VecScatterDestroy(&user->design_scatter);
1405: for (i=0; i<user->nt; i++){
1406: VecScatterDestroy(&user->uxi_scatter[i]);
1407: VecScatterDestroy(&user->uyi_scatter[i]);
1408: VecScatterDestroy(&user->ux_scatter[i]);
1409: VecScatterDestroy(&user->uy_scatter[i]);
1410: VecScatterDestroy(&user->ui_scatter[i]);
1411: VecScatterDestroy(&user->yi_scatter[i]);
1412: }
1413: PetscFree(user->uxi_scatter);
1414: PetscFree(user->uyi_scatter);
1415: PetscFree(user->ux_scatter);
1416: PetscFree(user->uy_scatter);
1417: PetscFree(user->ui_scatter);
1418: PetscFree(user->yi_scatter);
1419: return(0);
1420: }
1424: PetscErrorCode HyperbolicMonitor(TaoSolver tao, void *ptr)
1425: {
1427: Vec X;
1428: PetscReal unorm,ynorm;
1429: AppCtx *user = (AppCtx*)ptr;
1431: TaoGetSolutionVector(tao,&X);
1432: Scatter(X,user->ywork,user->state_scatter,user->uwork,user->design_scatter);
1433: VecAXPY(user->ywork,-1.0,user->ytrue);
1434: VecAXPY(user->uwork,-1.0,user->utrue);
1435: VecNorm(user->uwork,NORM_2,&unorm);
1436: VecNorm(user->ywork,NORM_2,&ynorm);
1437: PetscPrintf(MPI_COMM_WORLD, "||u-ut||=%G ||y-yt||=%G\n",unorm,ynorm);
1438: return(0);
1439: }