1
2 static char help[] = "Basic equation for generator stability analysis.\n";
3
4 /*F
5
6 \begin{eqnarray}
7 \frac{d \theta}{dt} = \omega_b (\omega - \omega_s)
8 \frac{2 H}{\omega_s}\frac{d \omega}{dt} & = & P_m - P_max \sin(\theta) -D(\omega - \omega_s)\\
9 \end{eqnarray}
10
11
12
13 Ensemble of initial conditions
14 ./ex2 -ensemble -ts_monitor_draw_solution_phase -1,-3,3,3 -ts_adapt_dt_max .01 -ts_monitor -ts_type rosw -pc_type lu -ksp_type preonly
15
16 Fault at .1 seconds
17 ./ex2 -ts_monitor_draw_solution_phase .42,.95,.6,1.05 -ts_adapt_dt_max .01 -ts_monitor -ts_type rosw -pc_type lu -ksp_type preonly
18
19 Initial conditions same as when fault is ended
20 ./ex2 -u 0.496792,1.00932 -ts_monitor_draw_solution_phase .42,.95,.6,1.05 -ts_adapt_dt_max .01 -ts_monitor -ts_type rosw -pc_type lu -ksp_type preonly
21
22
23 F*/
24
25 /*
26 Include "petscts.h" so that we can use TS solvers. Note that this
27 file automatically includes:
28 petscsys.h - base PETSc routines petscvec.h - vectors
29 petscmat.h - matrices
30 petscis.h - index sets petscksp.h - Krylov subspace methods
31 petscviewer.h - viewers petscpc.h - preconditioners
32 petscksp.h - linear solvers
33 */
34
35 #include <petsctao.h>
36 #include <petscts.h>
37
38 typedef struct {
39 TS ts;
40 PetscScalar H,D,omega_b,omega_s,Pmax,Pm,E,V,X,u_s,c;
41 PetscInt beta;
42 PetscReal tf,tcl,dt;
43 } AppCtx;
44
45 PetscErrorCode FormFunction(Tao,Vec,PetscReal*,void*);
46 PetscErrorCode FormGradient(Tao,Vec,Vec,void*);
47
48 /*
49 Defines the ODE passed to the ODE solver
50 */
RHSFunction(TS ts,PetscReal t,Vec U,Vec F,AppCtx * ctx)51 static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec U,Vec F,AppCtx *ctx)
52 {
53 PetscErrorCode ierr;
54 PetscScalar *f,Pmax;
55 const PetscScalar *u;
56
57 PetscFunctionBegin;
58 /* The next three lines allow us to access the entries of the vectors directly */
59 ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr);
60 ierr = VecGetArray(F,&f);CHKERRQ(ierr);
61 if ((t > ctx->tf) && (t < ctx->tcl)) Pmax = 0.0; /* A short-circuit on the generator terminal that drives the electrical power output (Pmax*sin(delta)) to 0 */
62 else Pmax = ctx->Pmax;
63
64 f[0] = ctx->omega_b*(u[1] - ctx->omega_s);
65 f[1] = (-Pmax*PetscSinScalar(u[0]) - ctx->D*(u[1] - ctx->omega_s) + ctx->Pm)*ctx->omega_s/(2.0*ctx->H);
66
67 ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr);
68 ierr = VecRestoreArray(F,&f);CHKERRQ(ierr);
69 PetscFunctionReturn(0);
70 }
71
72 /*
73 Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
74 */
RHSJacobian(TS ts,PetscReal t,Vec U,Mat A,Mat B,AppCtx * ctx)75 static PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec U,Mat A,Mat B,AppCtx *ctx)
76 {
77 PetscErrorCode ierr;
78 PetscInt rowcol[] = {0,1};
79 PetscScalar J[2][2],Pmax;
80 const PetscScalar *u;
81
82 PetscFunctionBegin;
83 ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr);
84 if ((t > ctx->tf) && (t < ctx->tcl)) Pmax = 0.0; /* A short-circuit on the generator terminal that drives the electrical power output (Pmax*sin(delta)) to 0 */
85 else Pmax = ctx->Pmax;
86
87 J[0][0] = 0; J[0][1] = ctx->omega_b;
88 J[1][1] = -ctx->D*ctx->omega_s/(2.0*ctx->H); J[1][0] = -Pmax*PetscCosScalar(u[0])*ctx->omega_s/(2.0*ctx->H);
89
90 ierr = MatSetValues(A,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);CHKERRQ(ierr);
91 ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr);
92
93 ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
94 ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
95 if (A != B) {
96 ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
97 ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
98 }
99 PetscFunctionReturn(0);
100 }
101
RHSJacobianP(TS ts,PetscReal t,Vec X,Mat A,void * ctx0)102 static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec X,Mat A,void *ctx0)
103 {
104 PetscErrorCode ierr;
105 PetscInt row[] = {0,1},col[]={0};
106 PetscScalar J[2][1];
107 AppCtx *ctx=(AppCtx*)ctx0;
108
109 PetscFunctionBeginUser;
110 J[0][0] = 0;
111 J[1][0] = ctx->omega_s/(2.0*ctx->H);
112 ierr = MatSetValues(A,2,row,1,col,&J[0][0],INSERT_VALUES);CHKERRQ(ierr);
113 ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
114 ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
115 PetscFunctionReturn(0);
116 }
117
CostIntegrand(TS ts,PetscReal t,Vec U,Vec R,AppCtx * ctx)118 static PetscErrorCode CostIntegrand(TS ts,PetscReal t,Vec U,Vec R,AppCtx *ctx)
119 {
120 PetscErrorCode ierr;
121 PetscScalar *r;
122 const PetscScalar *u;
123
124 PetscFunctionBegin;
125 ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr);
126 ierr = VecGetArray(R,&r);CHKERRQ(ierr);
127 r[0] = ctx->c*PetscPowScalarInt(PetscMax(0., u[0]-ctx->u_s),ctx->beta);CHKERRQ(ierr);
128 ierr = VecRestoreArray(R,&r);CHKERRQ(ierr);
129 ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr);
130 PetscFunctionReturn(0);
131 }
132
DRDUJacobianTranspose(TS ts,PetscReal t,Vec U,Mat DRDU,Mat B,AppCtx * ctx)133 static PetscErrorCode DRDUJacobianTranspose(TS ts,PetscReal t,Vec U,Mat DRDU,Mat B,AppCtx *ctx)
134 {
135 PetscErrorCode ierr;
136 PetscScalar ru[1];
137 const PetscScalar *u;
138 PetscInt row[] = {0},col[] = {0};
139
140 PetscFunctionBegin;
141 ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr);
142 ru[0] = ctx->c*ctx->beta*PetscPowScalarInt(PetscMax(0., u[0]-ctx->u_s),ctx->beta-1);CHKERRQ(ierr);
143 ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr);
144 ierr = MatSetValues(DRDU,1,row,1,col,ru,INSERT_VALUES);CHKERRQ(ierr);
145 ierr = MatAssemblyBegin(DRDU,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
146 ierr = MatAssemblyEnd(DRDU,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
147 PetscFunctionReturn(0);
148 }
149
DRDPJacobianTranspose(TS ts,PetscReal t,Vec U,Mat DRDP,AppCtx * ctx)150 static PetscErrorCode DRDPJacobianTranspose(TS ts,PetscReal t,Vec U,Mat DRDP,AppCtx *ctx)
151 {
152 PetscErrorCode ierr;
153
154 PetscFunctionBegin;
155 ierr = MatZeroEntries(DRDP);CHKERRQ(ierr);
156 ierr = MatAssemblyBegin(DRDP,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
157 ierr = MatAssemblyEnd(DRDP,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
158 PetscFunctionReturn(0);
159 }
160
ComputeSensiP(Vec lambda,Vec mu,AppCtx * ctx)161 PetscErrorCode ComputeSensiP(Vec lambda,Vec mu,AppCtx *ctx)
162 {
163 PetscErrorCode ierr;
164 PetscScalar *y,sensip;
165 const PetscScalar *x;
166
167 PetscFunctionBegin;
168 ierr = VecGetArrayRead(lambda,&x);CHKERRQ(ierr);
169 ierr = VecGetArray(mu,&y);CHKERRQ(ierr);
170 sensip = 1./PetscSqrtScalar(1.-(ctx->Pm/ctx->Pmax)*(ctx->Pm/ctx->Pmax))/ctx->Pmax*x[0]+y[0];
171 y[0] = sensip;
172 ierr = VecRestoreArray(mu,&y);CHKERRQ(ierr);
173 ierr = VecRestoreArrayRead(lambda,&x);CHKERRQ(ierr);
174 PetscFunctionReturn(0);
175 }
176
main(int argc,char ** argv)177 int main(int argc,char **argv)
178 {
179 Vec p;
180 PetscScalar *x_ptr;
181 PetscErrorCode ierr;
182 PetscMPIInt size;
183 AppCtx ctx;
184 Vec lowerb,upperb;
185 Tao tao;
186 KSP ksp;
187 PC pc;
188 Vec U,lambda[1],mu[1];
189 Mat A; /* Jacobian matrix */
190 Mat Jacp; /* Jacobian matrix */
191 Mat DRDU,DRDP;
192 PetscInt n = 2;
193 TS quadts;
194
195 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
196 Initialize program
197 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
198 ierr = PetscInitialize(&argc,&argv,NULL,help);if (ierr) return ierr;
199 PetscFunctionBeginUser;
200 ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
201 if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only!");
202
203 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
204 Set runtime options
205 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
206 ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");CHKERRQ(ierr);
207 {
208 ctx.beta = 2;
209 ctx.c = PetscRealConstant(10000.0);
210 ctx.u_s = PetscRealConstant(1.0);
211 ctx.omega_s = PetscRealConstant(1.0);
212 ctx.omega_b = PetscRealConstant(120.0)*PETSC_PI;
213 ctx.H = PetscRealConstant(5.0);
214 ierr = PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);CHKERRQ(ierr);
215 ctx.D = PetscRealConstant(5.0);
216 ierr = PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);CHKERRQ(ierr);
217 ctx.E = PetscRealConstant(1.1378);
218 ctx.V = PetscRealConstant(1.0);
219 ctx.X = PetscRealConstant(0.545);
220 ctx.Pmax = ctx.E*ctx.V/ctx.X;
221 ierr = PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);CHKERRQ(ierr);
222 ctx.Pm = PetscRealConstant(1.0194);
223 ierr = PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);CHKERRQ(ierr);
224 ctx.tf = PetscRealConstant(0.1);
225 ctx.tcl = PetscRealConstant(0.2);
226 ierr = PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);CHKERRQ(ierr);
227 ierr = PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);CHKERRQ(ierr);
228
229 }
230 ierr = PetscOptionsEnd();CHKERRQ(ierr);
231
232 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
233 Create necessary matrix and vectors
234 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
235 ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
236 ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
237 ierr = MatSetType(A,MATDENSE);CHKERRQ(ierr);
238 ierr = MatSetFromOptions(A);CHKERRQ(ierr);
239 ierr = MatSetUp(A);CHKERRQ(ierr);
240
241 ierr = MatCreateVecs(A,&U,NULL);CHKERRQ(ierr);
242
243 ierr = MatCreate(PETSC_COMM_WORLD,&Jacp);CHKERRQ(ierr);
244 ierr = MatSetSizes(Jacp,PETSC_DECIDE,PETSC_DECIDE,2,1);CHKERRQ(ierr);
245 ierr = MatSetFromOptions(Jacp);CHKERRQ(ierr);
246 ierr = MatSetUp(Jacp);CHKERRQ(ierr);
247 ierr = MatCreateDense(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,&DRDP);CHKERRQ(ierr);
248 ierr = MatSetUp(DRDP);CHKERRQ(ierr);
249 ierr = MatCreateDense(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,1,2,NULL,&DRDU);CHKERRQ(ierr);
250 ierr = MatSetUp(DRDU);CHKERRQ(ierr);
251
252 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
253 Create timestepping solver context
254 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
255 ierr = TSCreate(PETSC_COMM_WORLD,&ctx.ts);CHKERRQ(ierr);
256 ierr = TSSetProblemType(ctx.ts,TS_NONLINEAR);CHKERRQ(ierr);
257 ierr = TSSetEquationType(ctx.ts,TS_EQ_ODE_EXPLICIT);CHKERRQ(ierr); /* less Jacobian evaluations when adjoint BEuler is used, otherwise no effect */
258 ierr = TSSetType(ctx.ts,TSRK);CHKERRQ(ierr);
259 ierr = TSSetRHSFunction(ctx.ts,NULL,(TSRHSFunction)RHSFunction,&ctx);CHKERRQ(ierr);
260 ierr = TSSetRHSJacobian(ctx.ts,A,A,(TSRHSJacobian)RHSJacobian,&ctx);CHKERRQ(ierr);
261 ierr = TSSetExactFinalTime(ctx.ts,TS_EXACTFINALTIME_MATCHSTEP);CHKERRQ(ierr);
262
263 ierr = MatCreateVecs(A,&lambda[0],NULL);CHKERRQ(ierr);
264 ierr = MatCreateVecs(Jacp,&mu[0],NULL);CHKERRQ(ierr);
265 ierr = TSSetCostGradients(ctx.ts,1,lambda,mu);CHKERRQ(ierr);
266 ierr = TSSetRHSJacobianP(ctx.ts,Jacp,RHSJacobianP,&ctx);CHKERRQ(ierr);
267
268 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
269 Set solver options
270 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
271 ierr = TSSetMaxTime(ctx.ts,PetscRealConstant(1.0));CHKERRQ(ierr);
272 ierr = TSSetTimeStep(ctx.ts,PetscRealConstant(0.01));CHKERRQ(ierr);
273 ierr = TSSetFromOptions(ctx.ts);CHKERRQ(ierr);
274
275 ierr = TSGetTimeStep(ctx.ts,&ctx.dt);CHKERRQ(ierr); /* save the stepsize */
276
277 ierr = TSCreateQuadratureTS(ctx.ts,PETSC_TRUE,&quadts);CHKERRQ(ierr);
278 ierr = TSSetRHSFunction(quadts,NULL,(TSRHSFunction)CostIntegrand,&ctx);CHKERRQ(ierr);
279 ierr = TSSetRHSJacobian(quadts,DRDU,DRDU,(TSRHSJacobian)DRDUJacobianTranspose,&ctx);CHKERRQ(ierr);
280 ierr = TSSetRHSJacobianP(quadts,DRDP,(TSRHSJacobianP)DRDPJacobianTranspose,&ctx);CHKERRQ(ierr);
281 ierr = TSSetSolution(ctx.ts,U);CHKERRQ(ierr);
282
283 /* Create TAO solver and set desired solution method */
284 ierr = TaoCreate(PETSC_COMM_WORLD,&tao);CHKERRQ(ierr);
285 ierr = TaoSetType(tao,TAOBLMVM);CHKERRQ(ierr);
286
287 /*
288 Optimization starts
289 */
290 /* Set initial solution guess */
291 ierr = VecCreateSeq(PETSC_COMM_WORLD,1,&p);CHKERRQ(ierr);
292 ierr = VecGetArray(p,&x_ptr);CHKERRQ(ierr);
293 x_ptr[0] = ctx.Pm;
294 ierr = VecRestoreArray(p,&x_ptr);CHKERRQ(ierr);
295
296 ierr = TaoSetInitialVector(tao,p);CHKERRQ(ierr);
297 /* Set routine for function and gradient evaluation */
298 ierr = TaoSetObjectiveRoutine(tao,FormFunction,(void *)&ctx);CHKERRQ(ierr);
299 ierr = TaoSetGradientRoutine(tao,FormGradient,(void *)&ctx);CHKERRQ(ierr);
300
301 /* Set bounds for the optimization */
302 ierr = VecDuplicate(p,&lowerb);CHKERRQ(ierr);
303 ierr = VecDuplicate(p,&upperb);CHKERRQ(ierr);
304 ierr = VecGetArray(lowerb,&x_ptr);CHKERRQ(ierr);
305 x_ptr[0] = 0.;
306 ierr = VecRestoreArray(lowerb,&x_ptr);CHKERRQ(ierr);
307 ierr = VecGetArray(upperb,&x_ptr);CHKERRQ(ierr);
308 x_ptr[0] = PetscRealConstant(1.1);
309 ierr = VecRestoreArray(upperb,&x_ptr);CHKERRQ(ierr);
310 ierr = TaoSetVariableBounds(tao,lowerb,upperb);CHKERRQ(ierr);
311
312 /* Check for any TAO command line options */
313 ierr = TaoSetFromOptions(tao);CHKERRQ(ierr);
314 ierr = TaoGetKSP(tao,&ksp);CHKERRQ(ierr);
315 if (ksp) {
316 ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
317 ierr = PCSetType(pc,PCNONE);CHKERRQ(ierr);
318 }
319
320 /* SOLVE THE APPLICATION */
321 ierr = TaoSolve(tao);CHKERRQ(ierr);
322
323 ierr = VecView(p,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
324 /* Free TAO data structures */
325 ierr = TaoDestroy(&tao);CHKERRQ(ierr);
326 ierr = VecDestroy(&p);CHKERRQ(ierr);
327 ierr = VecDestroy(&lowerb);CHKERRQ(ierr);
328 ierr = VecDestroy(&upperb);CHKERRQ(ierr);
329
330 ierr = TSDestroy(&ctx.ts);CHKERRQ(ierr);
331 ierr = VecDestroy(&U);CHKERRQ(ierr);
332 ierr = MatDestroy(&A);CHKERRQ(ierr);
333 ierr = MatDestroy(&Jacp);CHKERRQ(ierr);
334 ierr = MatDestroy(&DRDU);CHKERRQ(ierr);
335 ierr = MatDestroy(&DRDP);CHKERRQ(ierr);
336 ierr = VecDestroy(&lambda[0]);CHKERRQ(ierr);
337 ierr = VecDestroy(&mu[0]);CHKERRQ(ierr);
338 ierr = PetscFinalize();
339 return ierr;
340 }
341
342 /* ------------------------------------------------------------------ */
343 /*
344 FormFunction - Evaluates the function
345
346 Input Parameters:
347 tao - the Tao context
348 X - the input vector
349 ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()
350
351 Output Parameters:
352 f - the newly evaluated function
353 */
FormFunction(Tao tao,Vec P,PetscReal * f,void * ctx0)354 PetscErrorCode FormFunction(Tao tao,Vec P,PetscReal *f,void *ctx0)
355 {
356 AppCtx *ctx = (AppCtx*)ctx0;
357 TS ts = ctx->ts;
358 Vec U; /* solution will be stored here */
359 PetscErrorCode ierr;
360 PetscScalar *u;
361 PetscScalar *x_ptr;
362 Vec q;
363
364 ierr = VecGetArrayRead(P,(const PetscScalar**)&x_ptr);CHKERRQ(ierr);
365 ctx->Pm = x_ptr[0];
366 ierr = VecRestoreArrayRead(P,(const PetscScalar**)&x_ptr);CHKERRQ(ierr);
367
368 /* reset time */
369 ierr = TSSetTime(ts,0.0);CHKERRQ(ierr);
370 /* reset step counter, this is critical for adjoint solver */
371 ierr = TSSetStepNumber(ts,0);CHKERRQ(ierr);
372 /* reset step size, the step size becomes negative after TSAdjointSolve */
373 ierr = TSSetTimeStep(ts,ctx->dt);CHKERRQ(ierr);
374 /* reinitialize the integral value */
375 ierr = TSGetCostIntegral(ts,&q);CHKERRQ(ierr);
376 ierr = VecSet(q,0.0);CHKERRQ(ierr);
377
378 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
379 Set initial conditions
380 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
381 ierr = TSGetSolution(ts,&U);CHKERRQ(ierr);
382 ierr = VecGetArray(U,&u);CHKERRQ(ierr);
383 u[0] = PetscAsinScalar(ctx->Pm/ctx->Pmax);
384 u[1] = PetscRealConstant(1.0);
385 ierr = VecRestoreArray(U,&u);CHKERRQ(ierr);
386
387 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
388 Solve nonlinear system
389 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
390 ierr = TSSolve(ts,U);CHKERRQ(ierr);
391 ierr = TSGetCostIntegral(ts,&q);CHKERRQ(ierr);
392 ierr = VecGetArray(q,&x_ptr);CHKERRQ(ierr);
393 *f = -ctx->Pm + x_ptr[0];
394 ierr = VecRestoreArray(q,&x_ptr);CHKERRQ(ierr);
395 return 0;
396 }
397
FormGradient(Tao tao,Vec P,Vec G,void * ctx0)398 PetscErrorCode FormGradient(Tao tao,Vec P,Vec G,void *ctx0)
399 {
400 AppCtx *ctx = (AppCtx*)ctx0;
401 TS ts = ctx->ts;
402 Vec U; /* solution will be stored here */
403 PetscErrorCode ierr;
404 PetscReal ftime;
405 PetscInt steps;
406 PetscScalar *u;
407 PetscScalar *x_ptr,*y_ptr;
408 Vec *lambda,q,*mu;
409
410 ierr = VecGetArrayRead(P,(const PetscScalar**)&x_ptr);CHKERRQ(ierr);
411 ctx->Pm = x_ptr[0];
412 ierr = VecRestoreArrayRead(P,(const PetscScalar**)&x_ptr);CHKERRQ(ierr);
413
414 /* reset time */
415 ierr = TSSetTime(ts,0.0);CHKERRQ(ierr);
416 /* reset step counter, this is critical for adjoint solver */
417 ierr = TSSetStepNumber(ts,0);CHKERRQ(ierr);
418 /* reset step size, the step size becomes negative after TSAdjointSolve */
419 ierr = TSSetTimeStep(ts,ctx->dt);CHKERRQ(ierr);
420 /* reinitialize the integral value */
421 ierr = TSGetCostIntegral(ts,&q);CHKERRQ(ierr);
422 ierr = VecSet(q,0.0);CHKERRQ(ierr);
423
424 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
425 Set initial conditions
426 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
427 ierr = TSGetSolution(ts,&U);CHKERRQ(ierr);
428 ierr = VecGetArray(U,&u);CHKERRQ(ierr);
429 u[0] = PetscAsinScalar(ctx->Pm/ctx->Pmax);
430 u[1] = PetscRealConstant(1.0);
431 ierr = VecRestoreArray(U,&u);CHKERRQ(ierr);
432
433 /* Set up to save trajectory before TSSetFromOptions() so that TSTrajectory options can be captured */
434 ierr = TSSetSaveTrajectory(ts);CHKERRQ(ierr);
435 ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
436
437 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
438 Solve nonlinear system
439 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
440 ierr = TSSolve(ts,U);CHKERRQ(ierr);
441
442 ierr = TSGetSolveTime(ts,&ftime);CHKERRQ(ierr);
443 ierr = TSGetStepNumber(ts,&steps);CHKERRQ(ierr);
444
445 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
446 Adjoint model starts here
447 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
448 ierr = TSGetCostGradients(ts,NULL,&lambda,&mu);CHKERRQ(ierr);
449 /* Set initial conditions for the adjoint integration */
450 ierr = VecGetArray(lambda[0],&y_ptr);CHKERRQ(ierr);
451 y_ptr[0] = 0.0; y_ptr[1] = 0.0;
452 ierr = VecRestoreArray(lambda[0],&y_ptr);CHKERRQ(ierr);
453 ierr = VecGetArray(mu[0],&x_ptr);CHKERRQ(ierr);
454 x_ptr[0] = PetscRealConstant(-1.0);
455 ierr = VecRestoreArray(mu[0],&x_ptr);CHKERRQ(ierr);
456
457 ierr = TSAdjointSolve(ts);CHKERRQ(ierr);
458 ierr = TSGetCostIntegral(ts,&q);CHKERRQ(ierr);
459 ierr = ComputeSensiP(lambda[0],mu[0],ctx);CHKERRQ(ierr);
460 ierr = VecCopy(mu[0],G);CHKERRQ(ierr);
461 return 0;
462 }
463
464
465 /*TEST
466
467 build:
468 requires: !complex
469
470 test:
471 args: -viewer_binary_skip_info -ts_adapt_type none -tao_monitor -tao_gatol 0.0 -tao_grtol 1.e-3 -tao_converged_reason
472
473 test:
474 suffix: 2
475 args: -viewer_binary_skip_info -ts_adapt_type none -tao_monitor -tao_gatol 0.0 -tao_grtol 1.e-3 -tao_converged_reason -tao_test_gradient
476
477 TEST*/
478