Actual source code: theta.c
1: /*
2: Code for timestepping with implicit Theta method
3: */
4: #include <petsc/private/tsimpl.h>
5: #include <petscsnes.h>
6: #include <petscdm.h>
7: #include <petscmat.h>
9: typedef struct {
10: /* context for time stepping */
11: PetscReal stage_time;
12: Vec Stages[2]; /* Storage for stage solutions */
13: Vec X0, X, Xdot; /* Storage for u^n, u^n + dt a_{11} k_1, and time derivative u^{n+1}_t */
14: Vec affine; /* Affine vector needed for residual at beginning of step in endpoint formulation */
15: PetscReal Theta;
16: PetscReal shift; /* Shift parameter for SNES Jacobian, used by forward, TLM and adjoint */
17: PetscInt order;
18: PetscBool endpoint;
19: PetscBool extrapolate;
20: TSStepStatus status;
21: Vec VecCostIntegral0; /* Backup for roll-backs due to events, used by cost integral */
22: PetscReal ptime0; /* Backup for ts->ptime, the start time of current time step, used by TLM and cost integral */
23: PetscReal time_step0; /* Backup for ts->timestep, the step size of current time step, used by TLM and cost integral*/
25: /* context for sensitivity analysis */
26: PetscInt num_tlm; /* Total number of tangent linear equations */
27: Vec *VecsDeltaLam; /* Increment of the adjoint sensitivity w.r.t IC at stage */
28: Vec *VecsDeltaMu; /* Increment of the adjoint sensitivity w.r.t P at stage */
29: Vec *VecsSensiTemp; /* Vector to be multiplied with Jacobian transpose */
30: Mat MatFwdStages[2]; /* TLM Stages */
31: Mat MatDeltaFwdSensip; /* Increment of the forward sensitivity at stage */
32: Vec VecDeltaFwdSensipCol; /* Working vector for holding one column of the sensitivity matrix */
33: Mat MatFwdSensip0; /* backup for roll-backs due to events */
34: Mat MatIntegralSensipTemp; /* Working vector for forward integral sensitivity */
35: Mat MatIntegralSensip0; /* backup for roll-backs due to events */
36: Vec *VecsDeltaLam2; /* Increment of the 2nd-order adjoint sensitivity w.r.t IC at stage */
37: Vec *VecsDeltaMu2; /* Increment of the 2nd-order adjoint sensitivity w.r.t P at stage */
38: Vec *VecsSensi2Temp; /* Working vectors that holds the residual for the second-order adjoint */
39: Vec *VecsAffine; /* Working vectors to store residuals */
40: /* context for error estimation */
41: Vec vec_sol_prev;
42: Vec vec_lte_work;
43: } TS_Theta;
45: static PetscErrorCode TSThetaGetX0AndXdot(TS ts, DM dm, Vec *X0, Vec *Xdot)
46: {
47: TS_Theta *th = (TS_Theta *)ts->data;
49: PetscFunctionBegin;
50: if (X0) {
51: if (dm && dm != ts->dm) PetscCall(DMGetNamedGlobalVector(dm, "TSTheta_X0", X0));
52: else *X0 = ts->vec_sol;
53: }
54: if (Xdot) {
55: if (dm && dm != ts->dm) PetscCall(DMGetNamedGlobalVector(dm, "TSTheta_Xdot", Xdot));
56: else *Xdot = th->Xdot;
57: }
58: PetscFunctionReturn(PETSC_SUCCESS);
59: }
61: static PetscErrorCode TSThetaRestoreX0AndXdot(TS ts, DM dm, Vec *X0, Vec *Xdot)
62: {
63: PetscFunctionBegin;
64: if (X0) {
65: if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSTheta_X0", X0));
66: }
67: if (Xdot) {
68: if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSTheta_Xdot", Xdot));
69: }
70: PetscFunctionReturn(PETSC_SUCCESS);
71: }
73: static PetscErrorCode DMCoarsenHook_TSTheta(DM fine, DM coarse, PetscCtx ctx)
74: {
75: PetscFunctionBegin;
76: PetscFunctionReturn(PETSC_SUCCESS);
77: }
79: static PetscErrorCode DMRestrictHook_TSTheta(DM fine, Mat restrct, Vec rscale, Mat inject, DM coarse, PetscCtx ctx)
80: {
81: TS ts = (TS)ctx;
82: Vec X0, Xdot, X0_c, Xdot_c;
84: PetscFunctionBegin;
85: PetscCall(TSThetaGetX0AndXdot(ts, fine, &X0, &Xdot));
86: PetscCall(TSThetaGetX0AndXdot(ts, coarse, &X0_c, &Xdot_c));
87: PetscCall(MatRestrict(restrct, X0, X0_c));
88: PetscCall(MatRestrict(restrct, Xdot, Xdot_c));
89: PetscCall(VecPointwiseMult(X0_c, rscale, X0_c));
90: PetscCall(VecPointwiseMult(Xdot_c, rscale, Xdot_c));
91: PetscCall(TSThetaRestoreX0AndXdot(ts, fine, &X0, &Xdot));
92: PetscCall(TSThetaRestoreX0AndXdot(ts, coarse, &X0_c, &Xdot_c));
93: PetscFunctionReturn(PETSC_SUCCESS);
94: }
96: static PetscErrorCode DMSubDomainHook_TSTheta(DM dm, DM subdm, PetscCtx ctx)
97: {
98: PetscFunctionBegin;
99: PetscFunctionReturn(PETSC_SUCCESS);
100: }
102: static PetscErrorCode DMSubDomainRestrictHook_TSTheta(DM dm, VecScatter gscat, VecScatter lscat, DM subdm, PetscCtx ctx)
103: {
104: TS ts = (TS)ctx;
105: Vec X0, Xdot, X0_sub, Xdot_sub;
107: PetscFunctionBegin;
108: PetscCall(TSThetaGetX0AndXdot(ts, dm, &X0, &Xdot));
109: PetscCall(TSThetaGetX0AndXdot(ts, subdm, &X0_sub, &Xdot_sub));
111: PetscCall(VecScatterBegin(gscat, X0, X0_sub, INSERT_VALUES, SCATTER_FORWARD));
112: PetscCall(VecScatterEnd(gscat, X0, X0_sub, INSERT_VALUES, SCATTER_FORWARD));
114: PetscCall(VecScatterBegin(gscat, Xdot, Xdot_sub, INSERT_VALUES, SCATTER_FORWARD));
115: PetscCall(VecScatterEnd(gscat, Xdot, Xdot_sub, INSERT_VALUES, SCATTER_FORWARD));
117: PetscCall(TSThetaRestoreX0AndXdot(ts, dm, &X0, &Xdot));
118: PetscCall(TSThetaRestoreX0AndXdot(ts, subdm, &X0_sub, &Xdot_sub));
119: PetscFunctionReturn(PETSC_SUCCESS);
120: }
122: static PetscErrorCode TSThetaEvaluateCostIntegral(TS ts)
123: {
124: TS_Theta *th = (TS_Theta *)ts->data;
125: TS quadts = ts->quadraturets;
127: PetscFunctionBegin;
128: if (th->endpoint) {
129: /* Evolve ts->vec_costintegral to compute integrals */
130: if (th->Theta != 1.0) {
131: PetscCall(TSComputeRHSFunction(quadts, th->ptime0, th->X0, ts->vec_costintegrand));
132: PetscCall(VecAXPY(quadts->vec_sol, th->time_step0 * (1.0 - th->Theta), ts->vec_costintegrand));
133: }
134: PetscCall(TSComputeRHSFunction(quadts, ts->ptime, ts->vec_sol, ts->vec_costintegrand));
135: PetscCall(VecAXPY(quadts->vec_sol, th->time_step0 * th->Theta, ts->vec_costintegrand));
136: } else {
137: PetscCall(TSComputeRHSFunction(quadts, th->stage_time, th->X, ts->vec_costintegrand));
138: PetscCall(VecAXPY(quadts->vec_sol, th->time_step0, ts->vec_costintegrand));
139: }
140: PetscFunctionReturn(PETSC_SUCCESS);
141: }
143: static PetscErrorCode TSForwardCostIntegral_Theta(TS ts)
144: {
145: TS_Theta *th = (TS_Theta *)ts->data;
146: TS quadts = ts->quadraturets;
148: PetscFunctionBegin;
149: /* backup cost integral */
150: PetscCall(VecCopy(quadts->vec_sol, th->VecCostIntegral0));
151: PetscCall(TSThetaEvaluateCostIntegral(ts));
152: PetscFunctionReturn(PETSC_SUCCESS);
153: }
155: static PetscErrorCode TSAdjointCostIntegral_Theta(TS ts)
156: {
157: TS_Theta *th = (TS_Theta *)ts->data;
159: PetscFunctionBegin;
160: /* Like TSForwardCostIntegral(), the adjoint cost integral evaluation relies on ptime0 and time_step0. */
161: th->ptime0 = ts->ptime + ts->time_step;
162: th->time_step0 = -ts->time_step;
163: PetscCall(TSThetaEvaluateCostIntegral(ts));
164: PetscFunctionReturn(PETSC_SUCCESS);
165: }
167: static PetscErrorCode TSTheta_SNESSolve(TS ts, Vec b, Vec x)
168: {
169: PetscInt nits, lits;
171: PetscFunctionBegin;
172: PetscCall(SNESSolve(ts->snes, b, x));
173: PetscCall(SNESGetIterationNumber(ts->snes, &nits));
174: PetscCall(SNESGetLinearSolveIterations(ts->snes, &lits));
175: ts->snes_its += nits;
176: ts->ksp_its += lits;
177: PetscFunctionReturn(PETSC_SUCCESS);
178: }
180: static PetscErrorCode TSResizeRegister_Theta(TS ts, PetscBool reg)
181: {
182: TS_Theta *th = (TS_Theta *)ts->data;
184: PetscFunctionBegin;
185: if (reg) {
186: PetscCall(TSResizeRegisterVec(ts, "ts:theta:sol_prev", th->vec_sol_prev));
187: PetscCall(TSResizeRegisterVec(ts, "ts:theta:X0", th->X0));
188: } else {
189: PetscCall(TSResizeRetrieveVec(ts, "ts:theta:sol_prev", &th->vec_sol_prev));
190: PetscCall(PetscObjectReference((PetscObject)th->vec_sol_prev));
191: PetscCall(TSResizeRetrieveVec(ts, "ts:theta:X0", &th->X0));
192: PetscCall(PetscObjectReference((PetscObject)th->X0));
193: }
194: PetscFunctionReturn(PETSC_SUCCESS);
195: }
197: static PetscErrorCode TSStep_Theta(TS ts)
198: {
199: TS_Theta *th = (TS_Theta *)ts->data;
200: PetscInt rejections = 0;
201: PetscBool stageok, accept = PETSC_TRUE;
202: PetscReal next_time_step = ts->time_step;
204: PetscFunctionBegin;
205: if (!ts->steprollback) {
206: if (th->vec_sol_prev) PetscCall(VecCopy(th->X0, th->vec_sol_prev));
207: PetscCall(VecCopy(ts->vec_sol, th->X0));
208: }
210: th->status = TS_STEP_INCOMPLETE;
211: while (!ts->reason && th->status != TS_STEP_COMPLETE) {
212: th->shift = 1 / (th->Theta * ts->time_step);
213: th->stage_time = ts->ptime + (th->endpoint ? (PetscReal)1 : th->Theta) * ts->time_step;
214: PetscCall(VecCopy(th->X0, th->X));
215: if (th->extrapolate && !ts->steprestart) PetscCall(VecAXPY(th->X, 1 / th->shift, th->Xdot));
216: if (th->endpoint) { /* This formulation assumes linear time-independent mass matrix */
217: if (!th->affine) PetscCall(VecDuplicate(ts->vec_sol, &th->affine));
218: PetscCall(VecZeroEntries(th->Xdot));
219: PetscCall(TSComputeIFunction(ts, ts->ptime, th->X0, th->Xdot, th->affine, PETSC_FALSE));
220: PetscCall(VecScale(th->affine, (th->Theta - 1) / th->Theta));
221: }
222: PetscCall(TSPreStage(ts, th->stage_time));
223: PetscCall(TSTheta_SNESSolve(ts, th->endpoint ? th->affine : NULL, th->X));
224: PetscCall(TSPostStage(ts, th->stage_time, 0, &th->X));
225: PetscCall(TSAdaptCheckStage(ts->adapt, ts, th->stage_time, th->X, &stageok));
226: if (!stageok) goto reject_step;
228: if (th->endpoint) PetscCall(VecCopy(th->X, ts->vec_sol));
229: else {
230: PetscCall(VecAXPBYPCZ(th->Xdot, -th->shift, th->shift, 0, th->X0, th->X)); /* th->Xdot is needed by TSInterpolate_Theta */
231: if (th->Theta == 1.0) PetscCall(VecCopy(th->X, ts->vec_sol)); /* BEULER, stage already checked */
232: else {
233: PetscCall(VecAXPY(ts->vec_sol, ts->time_step, th->Xdot));
234: PetscCall(TSAdaptCheckStage(ts->adapt, ts, ts->ptime + ts->time_step, ts->vec_sol, &stageok));
235: if (!stageok) {
236: PetscCall(VecCopy(th->X0, ts->vec_sol));
237: goto reject_step;
238: }
239: }
240: }
242: th->status = TS_STEP_PENDING;
243: PetscCall(TSAdaptChoose(ts->adapt, ts, ts->time_step, NULL, &next_time_step, &accept));
244: th->status = accept ? TS_STEP_COMPLETE : TS_STEP_INCOMPLETE;
245: if (!accept) {
246: PetscCall(VecCopy(th->X0, ts->vec_sol));
247: ts->time_step = next_time_step;
248: goto reject_step;
249: }
251: if (ts->forward_solve || ts->costintegralfwd) { /* Save the info for the later use in cost integral evaluation */
252: th->ptime0 = ts->ptime;
253: th->time_step0 = ts->time_step;
254: }
255: ts->ptime += ts->time_step;
256: ts->time_step = next_time_step;
257: break;
259: reject_step:
260: ts->reject++;
261: accept = PETSC_FALSE;
262: if (!ts->reason && ++rejections > ts->max_reject && ts->max_reject >= 0) {
263: ts->reason = TS_DIVERGED_STEP_REJECTED;
264: PetscCall(PetscInfo(ts, "Step=%" PetscInt_FMT ", step rejections %" PetscInt_FMT " greater than current TS allowed, stopping solve\n", ts->steps, rejections));
265: }
266: }
267: PetscFunctionReturn(PETSC_SUCCESS);
268: }
270: static PetscErrorCode TSAdjointStepBEuler_Private(TS ts)
271: {
272: TS_Theta *th = (TS_Theta *)ts->data;
273: TS quadts = ts->quadraturets;
274: Vec *VecsDeltaLam = th->VecsDeltaLam, *VecsDeltaMu = th->VecsDeltaMu, *VecsSensiTemp = th->VecsSensiTemp;
275: Vec *VecsDeltaLam2 = th->VecsDeltaLam2, *VecsDeltaMu2 = th->VecsDeltaMu2, *VecsSensi2Temp = th->VecsSensi2Temp;
276: Mat J, Jpre, quadJ = NULL, quadJp = NULL;
277: KSP ksp;
278: PetscScalar *xarr;
279: TSEquationType eqtype;
280: PetscBool isexplicitode = PETSC_FALSE;
281: PetscReal adjoint_time_step;
283: PetscFunctionBegin;
284: PetscCall(TSGetEquationType(ts, &eqtype));
285: if (eqtype == TS_EQ_ODE_EXPLICIT) {
286: isexplicitode = PETSC_TRUE;
287: VecsDeltaLam = ts->vecs_sensi;
288: VecsDeltaLam2 = ts->vecs_sensi2;
289: }
290: th->status = TS_STEP_INCOMPLETE;
291: PetscCall(SNESGetKSP(ts->snes, &ksp));
292: PetscCall(TSGetIJacobian(ts, &J, &Jpre, NULL, NULL));
293: if (quadts) {
294: PetscCall(TSGetRHSJacobian(quadts, &quadJ, NULL, NULL, NULL));
295: PetscCall(TSGetRHSJacobianP(quadts, &quadJp, NULL, NULL));
296: }
298: th->stage_time = ts->ptime;
299: adjoint_time_step = -ts->time_step; /* always positive since time_step is negative */
301: /* Build RHS for first-order adjoint lambda_{n+1}/h + r_u^T(n+1) */
302: if (quadts) PetscCall(TSComputeRHSJacobian(quadts, th->stage_time, ts->vec_sol, quadJ, NULL));
304: for (PetscInt nadj = 0; nadj < ts->numcost; nadj++) {
305: PetscCall(VecCopy(ts->vecs_sensi[nadj], VecsSensiTemp[nadj]));
306: PetscCall(VecScale(VecsSensiTemp[nadj], 1. / adjoint_time_step)); /* lambda_{n+1}/h */
307: if (quadJ) {
308: PetscCall(MatDenseGetColumn(quadJ, nadj, &xarr));
309: PetscCall(VecPlaceArray(ts->vec_drdu_col, xarr));
310: PetscCall(VecAXPY(VecsSensiTemp[nadj], 1., ts->vec_drdu_col));
311: PetscCall(VecResetArray(ts->vec_drdu_col));
312: PetscCall(MatDenseRestoreColumn(quadJ, &xarr));
313: }
314: }
316: /* Build LHS for first-order adjoint */
317: th->shift = 1. / adjoint_time_step;
318: PetscCall(TSComputeSNESJacobian(ts, ts->vec_sol, J, Jpre));
319: PetscCall(KSPSetOperators(ksp, J, Jpre));
321: /* Solve stage equation LHS*lambda_s = RHS for first-order adjoint */
322: for (PetscInt nadj = 0; nadj < ts->numcost; nadj++) {
323: KSPConvergedReason kspreason;
324: PetscCall(KSPSolveTranspose(ksp, VecsSensiTemp[nadj], VecsDeltaLam[nadj]));
325: PetscCall(KSPGetConvergedReason(ksp, &kspreason));
326: if (kspreason < 0) {
327: ts->reason = TSADJOINT_DIVERGED_LINEAR_SOLVE;
328: PetscCall(PetscInfo(ts, "Step=%" PetscInt_FMT ", %" PetscInt_FMT "th cost function, transposed linear solve fails, stopping 1st-order adjoint solve\n", ts->steps, nadj));
329: }
330: }
332: if (ts->vecs_sensi2) { /* U_{n+1} */
333: /* Get w1 at t_{n+1} from TLM matrix */
334: PetscCall(MatDenseGetColumn(ts->mat_sensip, 0, &xarr));
335: PetscCall(VecPlaceArray(ts->vec_sensip_col, xarr));
336: /* lambda_s^T F_UU w_1 */
337: PetscCall(TSComputeIHessianProductFunctionUU(ts, th->stage_time, ts->vec_sol, VecsDeltaLam, ts->vec_sensip_col, ts->vecs_fuu));
338: /* lambda_s^T F_UP w_2 */
339: PetscCall(TSComputeIHessianProductFunctionUP(ts, th->stage_time, ts->vec_sol, VecsDeltaLam, ts->vec_dir, ts->vecs_fup));
340: for (PetscInt nadj = 0; nadj < ts->numcost; nadj++) { /* compute the residual */
341: PetscCall(VecCopy(ts->vecs_sensi2[nadj], VecsSensi2Temp[nadj]));
342: PetscCall(VecScale(VecsSensi2Temp[nadj], 1. / adjoint_time_step));
343: PetscCall(VecAXPY(VecsSensi2Temp[nadj], -1., ts->vecs_fuu[nadj]));
344: if (ts->vecs_fup) PetscCall(VecAXPY(VecsSensi2Temp[nadj], -1., ts->vecs_fup[nadj]));
345: }
346: /* Solve stage equation LHS X = RHS for second-order adjoint */
347: for (PetscInt nadj = 0; nadj < ts->numcost; nadj++) {
348: KSPConvergedReason kspreason;
349: PetscCall(KSPSolveTranspose(ksp, VecsSensi2Temp[nadj], VecsDeltaLam2[nadj]));
350: PetscCall(KSPGetConvergedReason(ksp, &kspreason));
351: if (kspreason < 0) {
352: ts->reason = TSADJOINT_DIVERGED_LINEAR_SOLVE;
353: PetscCall(PetscInfo(ts, "Step=%" PetscInt_FMT ", %" PetscInt_FMT "th cost function, transposed linear solve fails, stopping 2nd-order adjoint solve\n", ts->steps, nadj));
354: }
355: }
356: }
358: /* Update sensitivities, and evaluate integrals if there is any */
359: if (!isexplicitode) {
360: th->shift = 0.0;
361: PetscCall(TSComputeSNESJacobian(ts, ts->vec_sol, J, Jpre));
362: PetscCall(KSPSetOperators(ksp, J, Jpre));
363: for (PetscInt nadj = 0; nadj < ts->numcost; nadj++) {
364: /* Add f_U \lambda_s to the original RHS */
365: PetscCall(VecScale(VecsSensiTemp[nadj], -1.));
366: PetscCall(MatMultTransposeAdd(J, VecsDeltaLam[nadj], VecsSensiTemp[nadj], VecsSensiTemp[nadj]));
367: PetscCall(VecScale(VecsSensiTemp[nadj], -adjoint_time_step));
368: PetscCall(VecCopy(VecsSensiTemp[nadj], ts->vecs_sensi[nadj]));
369: if (ts->vecs_sensi2) {
370: PetscCall(MatMultTransposeAdd(J, VecsDeltaLam2[nadj], VecsSensi2Temp[nadj], VecsSensi2Temp[nadj]));
371: PetscCall(VecScale(VecsSensi2Temp[nadj], -adjoint_time_step));
372: PetscCall(VecCopy(VecsSensi2Temp[nadj], ts->vecs_sensi2[nadj]));
373: }
374: }
375: }
376: if (ts->vecs_sensip) {
377: PetscCall(VecAXPBYPCZ(th->Xdot, -1. / adjoint_time_step, 1.0 / adjoint_time_step, 0, th->X0, ts->vec_sol));
378: PetscCall(TSComputeIJacobianP(ts, th->stage_time, ts->vec_sol, th->Xdot, 1. / adjoint_time_step, ts->Jacp, PETSC_FALSE)); /* get -f_p */
379: if (quadts) PetscCall(TSComputeRHSJacobianP(quadts, th->stage_time, ts->vec_sol, quadJp));
380: if (ts->vecs_sensi2p) {
381: /* lambda_s^T F_PU w_1 */
382: PetscCall(TSComputeIHessianProductFunctionPU(ts, th->stage_time, ts->vec_sol, VecsDeltaLam, ts->vec_sensip_col, ts->vecs_fpu));
383: /* lambda_s^T F_PP w_2 */
384: PetscCall(TSComputeIHessianProductFunctionPP(ts, th->stage_time, ts->vec_sol, VecsDeltaLam, ts->vec_dir, ts->vecs_fpp));
385: }
387: for (PetscInt nadj = 0; nadj < ts->numcost; nadj++) {
388: PetscCall(MatMultTranspose(ts->Jacp, VecsDeltaLam[nadj], VecsDeltaMu[nadj]));
389: PetscCall(VecAXPY(ts->vecs_sensip[nadj], -adjoint_time_step, VecsDeltaMu[nadj]));
390: if (quadJp) {
391: PetscCall(MatDenseGetColumn(quadJp, nadj, &xarr));
392: PetscCall(VecPlaceArray(ts->vec_drdp_col, xarr));
393: PetscCall(VecAXPY(ts->vecs_sensip[nadj], adjoint_time_step, ts->vec_drdp_col));
394: PetscCall(VecResetArray(ts->vec_drdp_col));
395: PetscCall(MatDenseRestoreColumn(quadJp, &xarr));
396: }
397: if (ts->vecs_sensi2p) {
398: PetscCall(MatMultTranspose(ts->Jacp, VecsDeltaLam2[nadj], VecsDeltaMu2[nadj]));
399: PetscCall(VecAXPY(ts->vecs_sensi2p[nadj], -adjoint_time_step, VecsDeltaMu2[nadj]));
400: if (ts->vecs_fpu) PetscCall(VecAXPY(ts->vecs_sensi2p[nadj], -adjoint_time_step, ts->vecs_fpu[nadj]));
401: if (ts->vecs_fpp) PetscCall(VecAXPY(ts->vecs_sensi2p[nadj], -adjoint_time_step, ts->vecs_fpp[nadj]));
402: }
403: }
404: }
406: if (ts->vecs_sensi2) {
407: PetscCall(VecResetArray(ts->vec_sensip_col));
408: PetscCall(MatDenseRestoreColumn(ts->mat_sensip, &xarr));
409: }
410: th->status = TS_STEP_COMPLETE;
411: PetscFunctionReturn(PETSC_SUCCESS);
412: }
414: static PetscErrorCode TSAdjointStep_Theta(TS ts)
415: {
416: TS_Theta *th = (TS_Theta *)ts->data;
417: TS quadts = ts->quadraturets;
418: Vec *VecsDeltaLam = th->VecsDeltaLam, *VecsDeltaMu = th->VecsDeltaMu, *VecsSensiTemp = th->VecsSensiTemp;
419: Vec *VecsDeltaLam2 = th->VecsDeltaLam2, *VecsDeltaMu2 = th->VecsDeltaMu2, *VecsSensi2Temp = th->VecsSensi2Temp;
420: Mat J, Jpre, quadJ = NULL, quadJp = NULL;
421: KSP ksp;
422: PetscScalar *xarr;
423: PetscReal adjoint_time_step;
424: PetscReal adjoint_ptime; /* end time of the adjoint time step (ts->ptime is the start time, usually ts->ptime is larger than adjoint_ptime) */
426: PetscFunctionBegin;
427: if (th->Theta == 1.) {
428: PetscCall(TSAdjointStepBEuler_Private(ts));
429: PetscFunctionReturn(PETSC_SUCCESS);
430: }
431: th->status = TS_STEP_INCOMPLETE;
432: PetscCall(SNESGetKSP(ts->snes, &ksp));
433: PetscCall(TSGetIJacobian(ts, &J, &Jpre, NULL, NULL));
434: if (quadts) {
435: PetscCall(TSGetRHSJacobian(quadts, &quadJ, NULL, NULL, NULL));
436: PetscCall(TSGetRHSJacobianP(quadts, &quadJp, NULL, NULL));
437: }
438: /* If endpoint=1, th->ptime and th->X0 will be used; if endpoint=0, th->stage_time and th->X will be used. */
439: th->stage_time = th->endpoint ? ts->ptime : (ts->ptime + (1. - th->Theta) * ts->time_step);
440: adjoint_ptime = ts->ptime + ts->time_step;
441: adjoint_time_step = -ts->time_step; /* always positive since time_step is negative */
443: if (!th->endpoint) {
444: /* recover th->X0 using vec_sol and the stage value th->X */
445: PetscCall(VecAXPBYPCZ(th->X0, 1.0 / (1.0 - th->Theta), th->Theta / (th->Theta - 1.0), 0, th->X, ts->vec_sol));
446: }
448: /* Build RHS for first-order adjoint */
449: /* Cost function has an integral term */
450: if (quadts) {
451: if (th->endpoint) PetscCall(TSComputeRHSJacobian(quadts, th->stage_time, ts->vec_sol, quadJ, NULL));
452: else PetscCall(TSComputeRHSJacobian(quadts, th->stage_time, th->X, quadJ, NULL));
453: }
455: for (PetscInt nadj = 0; nadj < ts->numcost; nadj++) {
456: PetscCall(VecCopy(ts->vecs_sensi[nadj], VecsSensiTemp[nadj]));
457: PetscCall(VecScale(VecsSensiTemp[nadj], 1. / (th->Theta * adjoint_time_step)));
458: if (quadJ) {
459: PetscCall(MatDenseGetColumn(quadJ, nadj, &xarr));
460: PetscCall(VecPlaceArray(ts->vec_drdu_col, xarr));
461: PetscCall(VecAXPY(VecsSensiTemp[nadj], 1., ts->vec_drdu_col));
462: PetscCall(VecResetArray(ts->vec_drdu_col));
463: PetscCall(MatDenseRestoreColumn(quadJ, &xarr));
464: }
465: }
467: /* Build LHS for first-order adjoint */
468: th->shift = 1. / (th->Theta * adjoint_time_step);
469: if (th->endpoint) {
470: PetscCall(TSComputeSNESJacobian(ts, ts->vec_sol, J, Jpre));
471: } else {
472: PetscCall(TSComputeSNESJacobian(ts, th->X, J, Jpre));
473: }
474: PetscCall(KSPSetOperators(ksp, J, Jpre));
476: /* Solve stage equation LHS*lambda_s = RHS for first-order adjoint */
477: for (PetscInt nadj = 0; nadj < ts->numcost; nadj++) {
478: KSPConvergedReason kspreason;
479: PetscCall(KSPSolveTranspose(ksp, VecsSensiTemp[nadj], VecsDeltaLam[nadj]));
480: PetscCall(KSPGetConvergedReason(ksp, &kspreason));
481: if (kspreason < 0) {
482: ts->reason = TSADJOINT_DIVERGED_LINEAR_SOLVE;
483: PetscCall(PetscInfo(ts, "Step=%" PetscInt_FMT ", %" PetscInt_FMT "th cost function, transposed linear solve fails, stopping 1st-order adjoint solve\n", ts->steps, nadj));
484: }
485: }
487: /* Second-order adjoint */
488: if (ts->vecs_sensi2) { /* U_{n+1} */
489: PetscCheck(th->endpoint, PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "Operation not implemented in TS_Theta");
490: /* Get w1 at t_{n+1} from TLM matrix */
491: PetscCall(MatDenseGetColumn(ts->mat_sensip, 0, &xarr));
492: PetscCall(VecPlaceArray(ts->vec_sensip_col, xarr));
493: /* lambda_s^T F_UU w_1 */
494: PetscCall(TSComputeIHessianProductFunctionUU(ts, th->stage_time, ts->vec_sol, VecsDeltaLam, ts->vec_sensip_col, ts->vecs_fuu));
495: PetscCall(VecResetArray(ts->vec_sensip_col));
496: PetscCall(MatDenseRestoreColumn(ts->mat_sensip, &xarr));
497: /* lambda_s^T F_UP w_2 */
498: PetscCall(TSComputeIHessianProductFunctionUP(ts, th->stage_time, ts->vec_sol, VecsDeltaLam, ts->vec_dir, ts->vecs_fup));
499: for (PetscInt nadj = 0; nadj < ts->numcost; nadj++) { /* compute the residual */
500: PetscCall(VecCopy(ts->vecs_sensi2[nadj], VecsSensi2Temp[nadj]));
501: PetscCall(VecScale(VecsSensi2Temp[nadj], th->shift));
502: PetscCall(VecAXPY(VecsSensi2Temp[nadj], -1., ts->vecs_fuu[nadj]));
503: if (ts->vecs_fup) PetscCall(VecAXPY(VecsSensi2Temp[nadj], -1., ts->vecs_fup[nadj]));
504: }
505: /* Solve stage equation LHS X = RHS for second-order adjoint */
506: for (PetscInt nadj = 0; nadj < ts->numcost; nadj++) {
507: KSPConvergedReason kspreason;
508: PetscCall(KSPSolveTranspose(ksp, VecsSensi2Temp[nadj], VecsDeltaLam2[nadj]));
509: PetscCall(KSPGetConvergedReason(ksp, &kspreason));
510: if (kspreason < 0) {
511: ts->reason = TSADJOINT_DIVERGED_LINEAR_SOLVE;
512: PetscCall(PetscInfo(ts, "Step=%" PetscInt_FMT ", %" PetscInt_FMT "th cost function, transposed linear solve fails, stopping 2nd-order adjoint solve\n", ts->steps, nadj));
513: }
514: }
515: }
517: /* Update sensitivities, and evaluate integrals if there is any */
518: if (th->endpoint) { /* two-stage Theta methods with th->Theta!=1, th->Theta==1 leads to BEuler */
519: th->shift = 1. / ((th->Theta - 1.) * adjoint_time_step);
520: th->stage_time = adjoint_ptime;
521: PetscCall(TSComputeSNESJacobian(ts, th->X0, J, Jpre));
522: PetscCall(KSPSetOperators(ksp, J, Jpre));
523: /* R_U at t_n */
524: if (quadts) PetscCall(TSComputeRHSJacobian(quadts, adjoint_ptime, th->X0, quadJ, NULL));
525: for (PetscInt nadj = 0; nadj < ts->numcost; nadj++) {
526: PetscCall(MatMultTranspose(J, VecsDeltaLam[nadj], ts->vecs_sensi[nadj]));
527: if (quadJ) {
528: PetscCall(MatDenseGetColumn(quadJ, nadj, &xarr));
529: PetscCall(VecPlaceArray(ts->vec_drdu_col, xarr));
530: PetscCall(VecAXPY(ts->vecs_sensi[nadj], -1., ts->vec_drdu_col));
531: PetscCall(VecResetArray(ts->vec_drdu_col));
532: PetscCall(MatDenseRestoreColumn(quadJ, &xarr));
533: }
534: PetscCall(VecScale(ts->vecs_sensi[nadj], 1. / th->shift));
535: }
537: /* Second-order adjoint */
538: if (ts->vecs_sensi2) { /* U_n */
539: /* Get w1 at t_n from TLM matrix */
540: PetscCall(MatDenseGetColumn(th->MatFwdSensip0, 0, &xarr));
541: PetscCall(VecPlaceArray(ts->vec_sensip_col, xarr));
542: /* lambda_s^T F_UU w_1 */
543: PetscCall(TSComputeIHessianProductFunctionUU(ts, adjoint_ptime, th->X0, VecsDeltaLam, ts->vec_sensip_col, ts->vecs_fuu));
544: PetscCall(VecResetArray(ts->vec_sensip_col));
545: PetscCall(MatDenseRestoreColumn(th->MatFwdSensip0, &xarr));
546: /* lambda_s^T F_UU w_2 */
547: PetscCall(TSComputeIHessianProductFunctionUP(ts, adjoint_ptime, th->X0, VecsDeltaLam, ts->vec_dir, ts->vecs_fup));
548: for (PetscInt nadj = 0; nadj < ts->numcost; nadj++) {
549: /* M^T Lambda_s + h(1-theta) F_U^T Lambda_s + h(1-theta) lambda_s^T F_UU w_1 + lambda_s^T F_UP w_2 */
550: PetscCall(MatMultTranspose(J, VecsDeltaLam2[nadj], ts->vecs_sensi2[nadj]));
551: PetscCall(VecAXPY(ts->vecs_sensi2[nadj], 1., ts->vecs_fuu[nadj]));
552: if (ts->vecs_fup) PetscCall(VecAXPY(ts->vecs_sensi2[nadj], 1., ts->vecs_fup[nadj]));
553: PetscCall(VecScale(ts->vecs_sensi2[nadj], 1. / th->shift));
554: }
555: }
557: th->stage_time = ts->ptime; /* recover the old value */
559: if (ts->vecs_sensip) { /* sensitivities wrt parameters */
560: /* U_{n+1} */
561: th->shift = 1.0 / (adjoint_time_step * th->Theta);
562: PetscCall(VecAXPBYPCZ(th->Xdot, -th->shift, th->shift, 0, th->X0, ts->vec_sol));
563: PetscCall(TSComputeIJacobianP(ts, th->stage_time, ts->vec_sol, th->Xdot, -1. / (th->Theta * adjoint_time_step), ts->Jacp, PETSC_FALSE));
564: if (quadts) PetscCall(TSComputeRHSJacobianP(quadts, th->stage_time, ts->vec_sol, quadJp));
565: for (PetscInt nadj = 0; nadj < ts->numcost; nadj++) {
566: PetscCall(MatMultTranspose(ts->Jacp, VecsDeltaLam[nadj], VecsDeltaMu[nadj]));
567: PetscCall(VecAXPY(ts->vecs_sensip[nadj], -adjoint_time_step * th->Theta, VecsDeltaMu[nadj]));
568: if (quadJp) {
569: PetscCall(MatDenseGetColumn(quadJp, nadj, &xarr));
570: PetscCall(VecPlaceArray(ts->vec_drdp_col, xarr));
571: PetscCall(VecAXPY(ts->vecs_sensip[nadj], adjoint_time_step * th->Theta, ts->vec_drdp_col));
572: PetscCall(VecResetArray(ts->vec_drdp_col));
573: PetscCall(MatDenseRestoreColumn(quadJp, &xarr));
574: }
575: }
576: if (ts->vecs_sensi2p) { /* second-order */
577: /* Get w1 at t_{n+1} from TLM matrix */
578: PetscCall(MatDenseGetColumn(ts->mat_sensip, 0, &xarr));
579: PetscCall(VecPlaceArray(ts->vec_sensip_col, xarr));
580: /* lambda_s^T F_PU w_1 */
581: PetscCall(TSComputeIHessianProductFunctionPU(ts, th->stage_time, ts->vec_sol, VecsDeltaLam, ts->vec_sensip_col, ts->vecs_fpu));
582: PetscCall(VecResetArray(ts->vec_sensip_col));
583: PetscCall(MatDenseRestoreColumn(ts->mat_sensip, &xarr));
585: /* lambda_s^T F_PP w_2 */
586: PetscCall(TSComputeIHessianProductFunctionPP(ts, th->stage_time, ts->vec_sol, VecsDeltaLam, ts->vec_dir, ts->vecs_fpp));
587: for (PetscInt nadj = 0; nadj < ts->numcost; nadj++) {
588: /* Mu2 <- Mu2 + h theta F_P^T Lambda_s + h theta (lambda_s^T F_UU w_1 + lambda_s^T F_UP w_2) */
589: PetscCall(MatMultTranspose(ts->Jacp, VecsDeltaLam2[nadj], VecsDeltaMu2[nadj]));
590: PetscCall(VecAXPY(ts->vecs_sensi2p[nadj], -adjoint_time_step * th->Theta, VecsDeltaMu2[nadj]));
591: if (ts->vecs_fpu) PetscCall(VecAXPY(ts->vecs_sensi2p[nadj], -adjoint_time_step * th->Theta, ts->vecs_fpu[nadj]));
592: if (ts->vecs_fpp) PetscCall(VecAXPY(ts->vecs_sensi2p[nadj], -adjoint_time_step * th->Theta, ts->vecs_fpp[nadj]));
593: }
594: }
596: /* U_s */
597: PetscCall(VecZeroEntries(th->Xdot));
598: PetscCall(TSComputeIJacobianP(ts, adjoint_ptime, th->X0, th->Xdot, 1. / ((th->Theta - 1.0) * adjoint_time_step), ts->Jacp, PETSC_FALSE));
599: if (quadts) PetscCall(TSComputeRHSJacobianP(quadts, adjoint_ptime, th->X0, quadJp));
600: for (PetscInt nadj = 0; nadj < ts->numcost; nadj++) {
601: PetscCall(MatMultTranspose(ts->Jacp, VecsDeltaLam[nadj], VecsDeltaMu[nadj]));
602: PetscCall(VecAXPY(ts->vecs_sensip[nadj], -adjoint_time_step * (1.0 - th->Theta), VecsDeltaMu[nadj]));
603: if (quadJp) {
604: PetscCall(MatDenseGetColumn(quadJp, nadj, &xarr));
605: PetscCall(VecPlaceArray(ts->vec_drdp_col, xarr));
606: PetscCall(VecAXPY(ts->vecs_sensip[nadj], adjoint_time_step * (1.0 - th->Theta), ts->vec_drdp_col));
607: PetscCall(VecResetArray(ts->vec_drdp_col));
608: PetscCall(MatDenseRestoreColumn(quadJp, &xarr));
609: }
610: if (ts->vecs_sensi2p) { /* second-order */
611: /* Get w1 at t_n from TLM matrix */
612: PetscCall(MatDenseGetColumn(th->MatFwdSensip0, 0, &xarr));
613: PetscCall(VecPlaceArray(ts->vec_sensip_col, xarr));
614: /* lambda_s^T F_PU w_1 */
615: PetscCall(TSComputeIHessianProductFunctionPU(ts, adjoint_ptime, th->X0, VecsDeltaLam, ts->vec_sensip_col, ts->vecs_fpu));
616: PetscCall(VecResetArray(ts->vec_sensip_col));
617: PetscCall(MatDenseRestoreColumn(th->MatFwdSensip0, &xarr));
618: /* lambda_s^T F_PP w_2 */
619: PetscCall(TSComputeIHessianProductFunctionPP(ts, adjoint_ptime, th->X0, VecsDeltaLam, ts->vec_dir, ts->vecs_fpp));
620: for (PetscInt nadj = 0; nadj < ts->numcost; nadj++) {
621: /* Mu2 <- Mu2 + h(1-theta) F_P^T Lambda_s + h(1-theta) (lambda_s^T F_UU w_1 + lambda_s^T F_UP w_2) */
622: PetscCall(MatMultTranspose(ts->Jacp, VecsDeltaLam2[nadj], VecsDeltaMu2[nadj]));
623: PetscCall(VecAXPY(ts->vecs_sensi2p[nadj], -adjoint_time_step * (1.0 - th->Theta), VecsDeltaMu2[nadj]));
624: if (ts->vecs_fpu) PetscCall(VecAXPY(ts->vecs_sensi2p[nadj], -adjoint_time_step * (1.0 - th->Theta), ts->vecs_fpu[nadj]));
625: if (ts->vecs_fpp) PetscCall(VecAXPY(ts->vecs_sensi2p[nadj], -adjoint_time_step * (1.0 - th->Theta), ts->vecs_fpp[nadj]));
626: }
627: }
628: }
629: }
630: } else { /* one-stage case */
631: th->shift = 0.0;
632: PetscCall(TSComputeSNESJacobian(ts, th->X, J, Jpre)); /* get -f_y */
633: PetscCall(KSPSetOperators(ksp, J, Jpre));
634: if (quadts) PetscCall(TSComputeRHSJacobian(quadts, th->stage_time, th->X, quadJ, NULL));
635: for (PetscInt nadj = 0; nadj < ts->numcost; nadj++) {
636: PetscCall(MatMultTranspose(J, VecsDeltaLam[nadj], VecsSensiTemp[nadj]));
637: PetscCall(VecAXPY(ts->vecs_sensi[nadj], -adjoint_time_step, VecsSensiTemp[nadj]));
638: if (quadJ) {
639: PetscCall(MatDenseGetColumn(quadJ, nadj, &xarr));
640: PetscCall(VecPlaceArray(ts->vec_drdu_col, xarr));
641: PetscCall(VecAXPY(ts->vecs_sensi[nadj], adjoint_time_step, ts->vec_drdu_col));
642: PetscCall(VecResetArray(ts->vec_drdu_col));
643: PetscCall(MatDenseRestoreColumn(quadJ, &xarr));
644: }
645: }
646: if (ts->vecs_sensip) {
647: th->shift = 1.0 / (adjoint_time_step * th->Theta);
648: PetscCall(VecAXPBYPCZ(th->Xdot, -th->shift, th->shift, 0, th->X0, th->X));
649: PetscCall(TSComputeIJacobianP(ts, th->stage_time, th->X, th->Xdot, th->shift, ts->Jacp, PETSC_FALSE));
650: if (quadts) PetscCall(TSComputeRHSJacobianP(quadts, th->stage_time, th->X, quadJp));
651: for (PetscInt nadj = 0; nadj < ts->numcost; nadj++) {
652: PetscCall(MatMultTranspose(ts->Jacp, VecsDeltaLam[nadj], VecsDeltaMu[nadj]));
653: PetscCall(VecAXPY(ts->vecs_sensip[nadj], -adjoint_time_step, VecsDeltaMu[nadj]));
654: if (quadJp) {
655: PetscCall(MatDenseGetColumn(quadJp, nadj, &xarr));
656: PetscCall(VecPlaceArray(ts->vec_drdp_col, xarr));
657: PetscCall(VecAXPY(ts->vecs_sensip[nadj], adjoint_time_step, ts->vec_drdp_col));
658: PetscCall(VecResetArray(ts->vec_drdp_col));
659: PetscCall(MatDenseRestoreColumn(quadJp, &xarr));
660: }
661: }
662: }
663: }
665: th->status = TS_STEP_COMPLETE;
666: PetscFunctionReturn(PETSC_SUCCESS);
667: }
669: static PetscErrorCode TSInterpolate_Theta(TS ts, PetscReal t, Vec X)
670: {
671: TS_Theta *th = (TS_Theta *)ts->data;
672: PetscReal dt = t - ts->ptime;
674: PetscFunctionBegin;
675: PetscCall(VecCopy(ts->vec_sol, th->X));
676: if (th->endpoint) dt *= th->Theta;
677: PetscCall(VecWAXPY(X, dt, th->Xdot, th->X));
678: PetscFunctionReturn(PETSC_SUCCESS);
679: }
681: static PetscErrorCode TSEvaluateWLTE_Theta(TS ts, NormType wnormtype, PetscInt *order, PetscReal *wlte)
682: {
683: TS_Theta *th = (TS_Theta *)ts->data;
684: Vec X = ts->vec_sol; /* X = solution */
685: Vec Y = th->vec_lte_work; /* Y = X + LTE */
686: PetscReal wltea, wlter;
688: PetscFunctionBegin;
689: if (!th->vec_sol_prev) {
690: *wlte = -1;
691: PetscFunctionReturn(PETSC_SUCCESS);
692: }
693: /* Cannot compute LTE in first step or in restart after event */
694: if (ts->steprestart) {
695: *wlte = -1;
696: PetscFunctionReturn(PETSC_SUCCESS);
697: }
698: /* Compute LTE using backward differences with non-constant time step */
699: {
700: PetscReal h = ts->time_step, h_prev = ts->ptime - ts->ptime_prev;
701: PetscReal a = 1 + h_prev / h;
702: PetscScalar scal[3];
703: Vec vecs[3];
705: scal[0] = -1 / a;
706: scal[1] = +1 / (a - 1);
707: scal[2] = -1 / (a * (a - 1));
708: vecs[0] = X;
709: vecs[1] = th->X0;
710: vecs[2] = th->vec_sol_prev;
711: PetscCall(VecCopy(X, Y));
712: PetscCall(VecMAXPY(Y, 3, scal, vecs));
713: PetscCall(TSErrorWeightedNorm(ts, X, Y, wnormtype, wlte, &wltea, &wlter));
714: }
715: if (order) *order = 2;
716: PetscFunctionReturn(PETSC_SUCCESS);
717: }
719: static PetscErrorCode TSRollBack_Theta(TS ts)
720: {
721: TS_Theta *th = (TS_Theta *)ts->data;
722: TS quadts = ts->quadraturets;
724: PetscFunctionBegin;
725: if (quadts && ts->costintegralfwd) PetscCall(VecCopy(th->VecCostIntegral0, quadts->vec_sol));
726: th->status = TS_STEP_INCOMPLETE;
727: if (ts->mat_sensip) PetscCall(MatCopy(th->MatFwdSensip0, ts->mat_sensip, SAME_NONZERO_PATTERN));
728: if (quadts && quadts->mat_sensip) PetscCall(MatCopy(th->MatIntegralSensip0, quadts->mat_sensip, SAME_NONZERO_PATTERN));
729: PetscFunctionReturn(PETSC_SUCCESS);
730: }
732: static PetscErrorCode TSForwardStep_Theta(TS ts)
733: {
734: TS_Theta *th = (TS_Theta *)ts->data;
735: TS quadts = ts->quadraturets;
736: Mat MatDeltaFwdSensip = th->MatDeltaFwdSensip;
737: Vec VecDeltaFwdSensipCol = th->VecDeltaFwdSensipCol;
738: KSP ksp;
739: Mat J, Jpre, quadJ = NULL, quadJp = NULL;
740: PetscScalar *barr, *xarr;
741: PetscReal previous_shift;
743: PetscFunctionBegin;
744: previous_shift = th->shift;
745: PetscCall(MatCopy(ts->mat_sensip, th->MatFwdSensip0, SAME_NONZERO_PATTERN));
747: if (quadts && quadts->mat_sensip) PetscCall(MatCopy(quadts->mat_sensip, th->MatIntegralSensip0, SAME_NONZERO_PATTERN));
748: PetscCall(SNESGetKSP(ts->snes, &ksp));
749: PetscCall(TSGetIJacobian(ts, &J, &Jpre, NULL, NULL));
750: if (quadts) {
751: PetscCall(TSGetRHSJacobian(quadts, &quadJ, NULL, NULL, NULL));
752: PetscCall(TSGetRHSJacobianP(quadts, &quadJp, NULL, NULL));
753: }
755: /* Build RHS */
756: if (th->endpoint) { /* 2-stage method*/
757: th->shift = 1. / ((th->Theta - 1.) * th->time_step0);
758: PetscCall(TSComputeIJacobian(ts, th->ptime0, th->X0, th->Xdot, th->shift, J, Jpre, PETSC_FALSE));
759: PetscCall(MatMatMult(J, ts->mat_sensip, MAT_REUSE_MATRIX, PETSC_DETERMINE, &MatDeltaFwdSensip));
760: PetscCall(MatScale(MatDeltaFwdSensip, (th->Theta - 1.) / th->Theta));
762: /* Add the f_p forcing terms */
763: if (ts->Jacp) {
764: PetscCall(VecZeroEntries(th->Xdot));
765: PetscCall(TSComputeIJacobianP(ts, th->ptime0, th->X0, th->Xdot, th->shift, ts->Jacp, PETSC_FALSE));
766: PetscCall(MatAXPY(MatDeltaFwdSensip, (th->Theta - 1.) / th->Theta, ts->Jacp, SUBSET_NONZERO_PATTERN));
767: th->shift = previous_shift;
768: PetscCall(VecAXPBYPCZ(th->Xdot, -th->shift, th->shift, 0, th->X0, ts->vec_sol));
769: PetscCall(TSComputeIJacobianP(ts, th->stage_time, ts->vec_sol, th->Xdot, th->shift, ts->Jacp, PETSC_FALSE));
770: PetscCall(MatAXPY(MatDeltaFwdSensip, -1., ts->Jacp, SUBSET_NONZERO_PATTERN));
771: }
772: } else { /* 1-stage method */
773: th->shift = 0.0;
774: PetscCall(TSComputeIJacobian(ts, th->stage_time, th->X, th->Xdot, th->shift, J, Jpre, PETSC_FALSE));
775: PetscCall(MatMatMult(J, ts->mat_sensip, MAT_REUSE_MATRIX, PETSC_DETERMINE, &MatDeltaFwdSensip));
776: PetscCall(MatScale(MatDeltaFwdSensip, -1.));
778: /* Add the f_p forcing terms */
779: if (ts->Jacp) {
780: th->shift = previous_shift;
781: PetscCall(VecAXPBYPCZ(th->Xdot, -th->shift, th->shift, 0, th->X0, th->X));
782: PetscCall(TSComputeIJacobianP(ts, th->stage_time, th->X, th->Xdot, th->shift, ts->Jacp, PETSC_FALSE));
783: PetscCall(MatAXPY(MatDeltaFwdSensip, -1., ts->Jacp, SUBSET_NONZERO_PATTERN));
784: }
785: }
787: /* Build LHS */
788: th->shift = previous_shift; /* recover the previous shift used in TSStep_Theta() */
789: if (th->endpoint) {
790: PetscCall(TSComputeIJacobian(ts, th->stage_time, ts->vec_sol, th->Xdot, th->shift, J, Jpre, PETSC_FALSE));
791: } else {
792: PetscCall(TSComputeIJacobian(ts, th->stage_time, th->X, th->Xdot, th->shift, J, Jpre, PETSC_FALSE));
793: }
794: PetscCall(KSPSetOperators(ksp, J, Jpre));
796: /*
797: Evaluate the first stage of integral gradients with the 2-stage method:
798: drdu|t_n*S(t_n) + drdp|t_n
799: This is done before the linear solve because the sensitivity variable S(t_n) will be propagated to S(t_{n+1})
800: */
801: if (th->endpoint) { /* 2-stage method only */
802: if (quadts && quadts->mat_sensip) {
803: PetscCall(TSComputeRHSJacobian(quadts, th->ptime0, th->X0, quadJ, NULL));
804: PetscCall(TSComputeRHSJacobianP(quadts, th->ptime0, th->X0, quadJp));
805: PetscCall(MatTransposeMatMult(ts->mat_sensip, quadJ, MAT_REUSE_MATRIX, PETSC_DETERMINE, &th->MatIntegralSensipTemp));
806: PetscCall(MatAXPY(th->MatIntegralSensipTemp, 1, quadJp, SAME_NONZERO_PATTERN));
807: PetscCall(MatAXPY(quadts->mat_sensip, th->time_step0 * (1. - th->Theta), th->MatIntegralSensipTemp, SAME_NONZERO_PATTERN));
808: }
809: }
811: /* Solve the tangent linear equation for forward sensitivities to parameters */
812: for (PetscInt ntlm = 0; ntlm < th->num_tlm; ntlm++) {
813: KSPConvergedReason kspreason;
814: PetscCall(MatDenseGetColumn(MatDeltaFwdSensip, ntlm, &barr));
815: PetscCall(VecPlaceArray(VecDeltaFwdSensipCol, barr));
816: if (th->endpoint) {
817: PetscCall(MatDenseGetColumn(ts->mat_sensip, ntlm, &xarr));
818: PetscCall(VecPlaceArray(ts->vec_sensip_col, xarr));
819: PetscCall(KSPSolve(ksp, VecDeltaFwdSensipCol, ts->vec_sensip_col));
820: PetscCall(VecResetArray(ts->vec_sensip_col));
821: PetscCall(MatDenseRestoreColumn(ts->mat_sensip, &xarr));
822: } else {
823: PetscCall(KSPSolve(ksp, VecDeltaFwdSensipCol, VecDeltaFwdSensipCol));
824: }
825: PetscCall(KSPGetConvergedReason(ksp, &kspreason));
826: if (kspreason < 0) {
827: ts->reason = TSFORWARD_DIVERGED_LINEAR_SOLVE;
828: PetscCall(PetscInfo(ts, "Step=%" PetscInt_FMT ", %" PetscInt_FMT "th tangent linear solve, linear solve fails, stopping tangent linear solve\n", ts->steps, ntlm));
829: }
830: PetscCall(VecResetArray(VecDeltaFwdSensipCol));
831: PetscCall(MatDenseRestoreColumn(MatDeltaFwdSensip, &barr));
832: }
834: /*
835: Evaluate the second stage of integral gradients with the 2-stage method:
836: drdu|t_{n+1}*S(t_{n+1}) + drdp|t_{n+1}
837: */
838: if (quadts && quadts->mat_sensip) {
839: if (!th->endpoint) {
840: PetscCall(MatAXPY(ts->mat_sensip, 1, MatDeltaFwdSensip, SAME_NONZERO_PATTERN)); /* stage sensitivity */
841: PetscCall(TSComputeRHSJacobian(quadts, th->stage_time, th->X, quadJ, NULL));
842: PetscCall(TSComputeRHSJacobianP(quadts, th->stage_time, th->X, quadJp));
843: PetscCall(MatTransposeMatMult(ts->mat_sensip, quadJ, MAT_REUSE_MATRIX, PETSC_DETERMINE, &th->MatIntegralSensipTemp));
844: PetscCall(MatAXPY(th->MatIntegralSensipTemp, 1, quadJp, SAME_NONZERO_PATTERN));
845: PetscCall(MatAXPY(quadts->mat_sensip, th->time_step0, th->MatIntegralSensipTemp, SAME_NONZERO_PATTERN));
846: PetscCall(MatAXPY(ts->mat_sensip, (1. - th->Theta) / th->Theta, MatDeltaFwdSensip, SAME_NONZERO_PATTERN));
847: } else {
848: PetscCall(TSComputeRHSJacobian(quadts, th->stage_time, ts->vec_sol, quadJ, NULL));
849: PetscCall(TSComputeRHSJacobianP(quadts, th->stage_time, ts->vec_sol, quadJp));
850: PetscCall(MatTransposeMatMult(ts->mat_sensip, quadJ, MAT_REUSE_MATRIX, PETSC_DETERMINE, &th->MatIntegralSensipTemp));
851: PetscCall(MatAXPY(th->MatIntegralSensipTemp, 1, quadJp, SAME_NONZERO_PATTERN));
852: PetscCall(MatAXPY(quadts->mat_sensip, th->time_step0 * th->Theta, th->MatIntegralSensipTemp, SAME_NONZERO_PATTERN));
853: }
854: } else {
855: if (!th->endpoint) PetscCall(MatAXPY(ts->mat_sensip, 1. / th->Theta, MatDeltaFwdSensip, SAME_NONZERO_PATTERN));
856: }
857: PetscFunctionReturn(PETSC_SUCCESS);
858: }
860: static PetscErrorCode TSForwardGetStages_Theta(TS ts, PetscInt *ns, Mat *stagesensip[])
861: {
862: TS_Theta *th = (TS_Theta *)ts->data;
864: PetscFunctionBegin;
865: if (ns) {
866: if (!th->endpoint && th->Theta != 1.0) *ns = 1; /* midpoint form */
867: else *ns = 2; /* endpoint form */
868: }
869: if (stagesensip) {
870: if (!th->endpoint && th->Theta != 1.0) {
871: th->MatFwdStages[0] = th->MatDeltaFwdSensip;
872: } else {
873: th->MatFwdStages[0] = th->MatFwdSensip0;
874: th->MatFwdStages[1] = ts->mat_sensip; /* stiffly accurate */
875: }
876: *stagesensip = th->MatFwdStages;
877: }
878: PetscFunctionReturn(PETSC_SUCCESS);
879: }
881: static PetscErrorCode TSReset_Theta(TS ts)
882: {
883: TS_Theta *th = (TS_Theta *)ts->data;
885: PetscFunctionBegin;
886: PetscCall(VecDestroy(&th->X));
887: PetscCall(VecDestroy(&th->Xdot));
888: PetscCall(VecDestroy(&th->X0));
889: PetscCall(VecDestroy(&th->affine));
891: PetscCall(VecDestroy(&th->vec_sol_prev));
892: PetscCall(VecDestroy(&th->vec_lte_work));
894: PetscCall(VecDestroy(&th->VecCostIntegral0));
895: PetscFunctionReturn(PETSC_SUCCESS);
896: }
898: static PetscErrorCode TSAdjointReset_Theta(TS ts)
899: {
900: TS_Theta *th = (TS_Theta *)ts->data;
902: PetscFunctionBegin;
903: PetscCall(VecDestroyVecs(ts->numcost, &th->VecsDeltaLam));
904: PetscCall(VecDestroyVecs(ts->numcost, &th->VecsDeltaMu));
905: PetscCall(VecDestroyVecs(ts->numcost, &th->VecsDeltaLam2));
906: PetscCall(VecDestroyVecs(ts->numcost, &th->VecsDeltaMu2));
907: PetscCall(VecDestroyVecs(ts->numcost, &th->VecsSensiTemp));
908: PetscCall(VecDestroyVecs(ts->numcost, &th->VecsSensi2Temp));
909: PetscFunctionReturn(PETSC_SUCCESS);
910: }
912: static PetscErrorCode TSDestroy_Theta(TS ts)
913: {
914: PetscFunctionBegin;
915: PetscCall(TSReset_Theta(ts));
916: if (ts->dm) {
917: PetscCall(DMCoarsenHookRemove(ts->dm, DMCoarsenHook_TSTheta, DMRestrictHook_TSTheta, ts));
918: PetscCall(DMSubDomainHookRemove(ts->dm, DMSubDomainHook_TSTheta, DMSubDomainRestrictHook_TSTheta, ts));
919: }
920: PetscCall(PetscFree(ts->data));
921: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSThetaGetTheta_C", NULL));
922: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSThetaSetTheta_C", NULL));
923: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSThetaGetEndpoint_C", NULL));
924: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSThetaSetEndpoint_C", NULL));
925: PetscFunctionReturn(PETSC_SUCCESS);
926: }
928: /*
929: This defines the nonlinear equation that is to be solved with SNES
930: G(U) = F[t0+Theta*dt, U, (U-U0)*shift] = 0
932: Note that U here is the stage argument. This means that U = U_{n+1} only if endpoint = true,
933: otherwise U = theta U_{n+1} + (1 - theta) U0, which for the case of implicit midpoint is
934: U = (U_{n+1} + U0)/2
935: */
936: static PetscErrorCode SNESTSFormFunction_Theta(SNES snes, Vec x, Vec y, TS ts)
937: {
938: TS_Theta *th = (TS_Theta *)ts->data;
939: Vec X0, Xdot;
940: DM dm, dmsave;
941: PetscReal shift = th->shift;
943: PetscFunctionBegin;
944: PetscCall(SNESGetDM(snes, &dm));
945: /* When using the endpoint variant, this is actually 1/Theta * Xdot */
946: PetscCall(TSThetaGetX0AndXdot(ts, dm, &X0, &Xdot));
947: if (x != X0) PetscCall(VecAXPBYPCZ(Xdot, -shift, shift, 0, X0, x));
948: else PetscCall(VecZeroEntries(Xdot));
949: /* DM monkey-business allows user code to call TSGetDM() inside of functions evaluated on levels of FAS */
950: dmsave = ts->dm;
951: ts->dm = dm;
952: PetscCall(TSComputeIFunction(ts, th->stage_time, x, Xdot, y, PETSC_FALSE));
953: ts->dm = dmsave;
954: PetscCall(TSThetaRestoreX0AndXdot(ts, dm, &X0, &Xdot));
955: PetscFunctionReturn(PETSC_SUCCESS);
956: }
958: static PetscErrorCode SNESTSFormJacobian_Theta(SNES snes, Vec x, Mat A, Mat B, TS ts)
959: {
960: TS_Theta *th = (TS_Theta *)ts->data;
961: Vec Xdot;
962: DM dm, dmsave;
963: PetscReal shift = th->shift;
965: PetscFunctionBegin;
966: PetscCall(SNESGetDM(snes, &dm));
967: /* Xdot has already been computed in SNESTSFormFunction_Theta (SNES guarantees this) */
968: PetscCall(TSThetaGetX0AndXdot(ts, dm, NULL, &Xdot));
970: dmsave = ts->dm;
971: ts->dm = dm;
972: PetscCall(TSComputeIJacobian(ts, th->stage_time, x, Xdot, shift, A, B, PETSC_FALSE));
973: ts->dm = dmsave;
974: PetscCall(TSThetaRestoreX0AndXdot(ts, dm, NULL, &Xdot));
975: PetscFunctionReturn(PETSC_SUCCESS);
976: }
978: static PetscErrorCode TSForwardSetUp_Theta(TS ts)
979: {
980: TS_Theta *th = (TS_Theta *)ts->data;
981: TS quadts = ts->quadraturets;
983: PetscFunctionBegin;
984: /* combine sensitivities to parameters and sensitivities to initial values into one array */
985: th->num_tlm = ts->num_parameters;
986: PetscCall(MatDuplicate(ts->mat_sensip, MAT_DO_NOT_COPY_VALUES, &th->MatDeltaFwdSensip));
987: if (quadts && quadts->mat_sensip) {
988: PetscCall(MatDuplicate(quadts->mat_sensip, MAT_DO_NOT_COPY_VALUES, &th->MatIntegralSensipTemp));
989: PetscCall(MatDuplicate(quadts->mat_sensip, MAT_DO_NOT_COPY_VALUES, &th->MatIntegralSensip0));
990: }
991: /* backup sensitivity results for roll-backs */
992: PetscCall(MatDuplicate(ts->mat_sensip, MAT_DO_NOT_COPY_VALUES, &th->MatFwdSensip0));
994: PetscCall(VecDuplicate(ts->vec_sol, &th->VecDeltaFwdSensipCol));
995: PetscFunctionReturn(PETSC_SUCCESS);
996: }
998: static PetscErrorCode TSForwardReset_Theta(TS ts)
999: {
1000: TS_Theta *th = (TS_Theta *)ts->data;
1001: TS quadts = ts->quadraturets;
1003: PetscFunctionBegin;
1004: if (quadts && quadts->mat_sensip) {
1005: PetscCall(MatDestroy(&th->MatIntegralSensipTemp));
1006: PetscCall(MatDestroy(&th->MatIntegralSensip0));
1007: }
1008: PetscCall(VecDestroy(&th->VecDeltaFwdSensipCol));
1009: PetscCall(MatDestroy(&th->MatDeltaFwdSensip));
1010: PetscCall(MatDestroy(&th->MatFwdSensip0));
1011: PetscFunctionReturn(PETSC_SUCCESS);
1012: }
1014: static PetscErrorCode TSSetUp_Theta(TS ts)
1015: {
1016: TS_Theta *th = (TS_Theta *)ts->data;
1017: TS quadts = ts->quadraturets;
1018: PetscBool match;
1020: PetscFunctionBegin;
1021: if (!th->VecCostIntegral0 && quadts && ts->costintegralfwd) { /* back up cost integral */
1022: PetscCall(VecDuplicate(quadts->vec_sol, &th->VecCostIntegral0));
1023: }
1024: if (!th->X) PetscCall(VecDuplicate(ts->vec_sol, &th->X));
1025: if (!th->Xdot) PetscCall(VecDuplicate(ts->vec_sol, &th->Xdot));
1026: if (!th->X0) PetscCall(VecDuplicate(ts->vec_sol, &th->X0));
1027: if (th->endpoint) PetscCall(VecDuplicate(ts->vec_sol, &th->affine));
1029: th->order = (th->Theta == 0.5) ? 2 : 1;
1030: th->shift = 1 / (th->Theta * ts->time_step);
1032: PetscCall(TSGetDM(ts, &ts->dm));
1033: PetscCall(DMCoarsenHookAdd(ts->dm, DMCoarsenHook_TSTheta, DMRestrictHook_TSTheta, ts));
1034: PetscCall(DMSubDomainHookAdd(ts->dm, DMSubDomainHook_TSTheta, DMSubDomainRestrictHook_TSTheta, ts));
1036: PetscCall(TSGetAdapt(ts, &ts->adapt));
1037: PetscCall(TSAdaptCandidatesClear(ts->adapt));
1038: PetscCall(PetscObjectTypeCompare((PetscObject)ts->adapt, TSADAPTNONE, &match));
1039: if (!match) {
1040: if (!th->vec_sol_prev) PetscCall(VecDuplicate(ts->vec_sol, &th->vec_sol_prev));
1041: if (!th->vec_lte_work) PetscCall(VecDuplicate(ts->vec_sol, &th->vec_lte_work));
1042: }
1043: PetscCall(TSGetSNES(ts, &ts->snes));
1045: ts->stifflyaccurate = (!th->endpoint && th->Theta != 1.0) ? PETSC_FALSE : PETSC_TRUE;
1046: PetscFunctionReturn(PETSC_SUCCESS);
1047: }
1049: static PetscErrorCode TSAdjointSetUp_Theta(TS ts)
1050: {
1051: TS_Theta *th = (TS_Theta *)ts->data;
1053: PetscFunctionBegin;
1054: PetscCall(VecDuplicateVecs(ts->vecs_sensi[0], ts->numcost, &th->VecsDeltaLam));
1055: PetscCall(VecDuplicateVecs(ts->vecs_sensi[0], ts->numcost, &th->VecsSensiTemp));
1056: if (ts->vecs_sensip) PetscCall(VecDuplicateVecs(ts->vecs_sensip[0], ts->numcost, &th->VecsDeltaMu));
1057: if (ts->vecs_sensi2) {
1058: PetscCall(VecDuplicateVecs(ts->vecs_sensi[0], ts->numcost, &th->VecsDeltaLam2));
1059: PetscCall(VecDuplicateVecs(ts->vecs_sensi2[0], ts->numcost, &th->VecsSensi2Temp));
1060: /* hack ts to make implicit TS solver work when users provide only explicit versions of callbacks (RHSFunction,RHSJacobian,RHSHessian etc.) */
1061: if (!ts->ihessianproduct_fuu) ts->vecs_fuu = ts->vecs_guu;
1062: if (!ts->ihessianproduct_fup) ts->vecs_fup = ts->vecs_gup;
1063: }
1064: if (ts->vecs_sensi2p) {
1065: PetscCall(VecDuplicateVecs(ts->vecs_sensi2p[0], ts->numcost, &th->VecsDeltaMu2));
1066: /* hack ts to make implicit TS solver work when users provide only explicit versions of callbacks (RHSFunction,RHSJacobian,RHSHessian etc.) */
1067: if (!ts->ihessianproduct_fpu) ts->vecs_fpu = ts->vecs_gpu;
1068: if (!ts->ihessianproduct_fpp) ts->vecs_fpp = ts->vecs_gpp;
1069: }
1070: PetscFunctionReturn(PETSC_SUCCESS);
1071: }
1073: static PetscErrorCode TSSetFromOptions_Theta(TS ts, PetscOptionItems PetscOptionsObject)
1074: {
1075: TS_Theta *th = (TS_Theta *)ts->data;
1077: PetscFunctionBegin;
1078: PetscOptionsHeadBegin(PetscOptionsObject, "Theta ODE solver options");
1079: {
1080: PetscCall(PetscOptionsReal("-ts_theta_theta", "Location of stage (0<Theta<=1)", "TSThetaSetTheta", th->Theta, &th->Theta, NULL));
1081: PetscCall(PetscOptionsBool("-ts_theta_endpoint", "Use the endpoint instead of midpoint form of the Theta method", "TSThetaSetEndpoint", th->endpoint, &th->endpoint, NULL));
1082: PetscCall(PetscOptionsBool("-ts_theta_initial_guess_extrapolate", "Extrapolate stage initial guess from previous solution (sometimes unstable)", "TSThetaSetExtrapolate", th->extrapolate, &th->extrapolate, NULL));
1083: }
1084: PetscOptionsHeadEnd();
1085: PetscFunctionReturn(PETSC_SUCCESS);
1086: }
1088: static PetscErrorCode TSView_Theta(TS ts, PetscViewer viewer)
1089: {
1090: TS_Theta *th = (TS_Theta *)ts->data;
1091: PetscBool isascii;
1093: PetscFunctionBegin;
1094: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
1095: if (isascii) {
1096: PetscCall(PetscViewerASCIIPrintf(viewer, " Theta=%g\n", (double)th->Theta));
1097: PetscCall(PetscViewerASCIIPrintf(viewer, " Extrapolation=%s\n", th->extrapolate ? "yes" : "no"));
1098: }
1099: PetscFunctionReturn(PETSC_SUCCESS);
1100: }
1102: static PetscErrorCode TSThetaGetTheta_Theta(TS ts, PetscReal *theta)
1103: {
1104: TS_Theta *th = (TS_Theta *)ts->data;
1106: PetscFunctionBegin;
1107: *theta = th->Theta;
1108: PetscFunctionReturn(PETSC_SUCCESS);
1109: }
1111: static PetscErrorCode TSThetaSetTheta_Theta(TS ts, PetscReal theta)
1112: {
1113: TS_Theta *th = (TS_Theta *)ts->data;
1115: PetscFunctionBegin;
1116: PetscCheck(theta > 0 && theta <= 1, PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_OUTOFRANGE, "Theta %g not in range (0,1]", (double)theta);
1117: th->Theta = theta;
1118: th->order = (th->Theta == 0.5) ? 2 : 1;
1119: PetscFunctionReturn(PETSC_SUCCESS);
1120: }
1122: static PetscErrorCode TSThetaGetEndpoint_Theta(TS ts, PetscBool *endpoint)
1123: {
1124: TS_Theta *th = (TS_Theta *)ts->data;
1126: PetscFunctionBegin;
1127: *endpoint = th->endpoint;
1128: PetscFunctionReturn(PETSC_SUCCESS);
1129: }
1131: static PetscErrorCode TSThetaSetEndpoint_Theta(TS ts, PetscBool flg)
1132: {
1133: TS_Theta *th = (TS_Theta *)ts->data;
1135: PetscFunctionBegin;
1136: th->endpoint = flg;
1137: PetscFunctionReturn(PETSC_SUCCESS);
1138: }
1140: #if defined(PETSC_HAVE_COMPLEX)
1141: static PetscErrorCode TSComputeLinearStability_Theta(TS ts, PetscReal xr, PetscReal xi, PetscReal *yr, PetscReal *yi)
1142: {
1143: PetscComplex z = xr + xi * PETSC_i, f;
1144: TS_Theta *th = (TS_Theta *)ts->data;
1146: PetscFunctionBegin;
1147: f = (1.0 + (1.0 - th->Theta) * z) / (1.0 - th->Theta * z);
1148: *yr = PetscRealPartComplex(f);
1149: *yi = PetscImaginaryPartComplex(f);
1150: PetscFunctionReturn(PETSC_SUCCESS);
1151: }
1152: #endif
1154: static PetscErrorCode TSGetStages_Theta(TS ts, PetscInt *ns, Vec *Y[])
1155: {
1156: TS_Theta *th = (TS_Theta *)ts->data;
1158: PetscFunctionBegin;
1159: if (ns) {
1160: if (!th->endpoint && th->Theta != 1.0) *ns = 1; /* midpoint form */
1161: else *ns = 2; /* endpoint form */
1162: }
1163: if (Y) {
1164: if (!th->endpoint && th->Theta != 1.0) {
1165: th->Stages[0] = th->X;
1166: } else {
1167: th->Stages[0] = th->X0;
1168: th->Stages[1] = ts->vec_sol; /* stiffly accurate */
1169: }
1170: *Y = th->Stages;
1171: }
1172: PetscFunctionReturn(PETSC_SUCCESS);
1173: }
1175: /*MC
1176: TSTHETA - DAE solver using the implicit Theta method
1178: Level: beginner
1180: Options Database Keys:
1181: + -ts_theta_theta Theta - Location of stage (0<Theta<=1)
1182: . -ts_theta_endpoint flag - Use the endpoint (like Crank-Nicholson) instead of midpoint form of the Theta method
1183: - -ts_theta_initial_guess_extrapolate flg - Extrapolate stage initial guess from previous solution (sometimes unstable)
1185: Notes:
1186: .vb
1187: -ts_type theta -ts_theta_theta 1.0 corresponds to backward Euler (TSBEULER)
1188: -ts_type theta -ts_theta_theta 0.5 corresponds to the implicit midpoint rule
1189: -ts_type theta -ts_theta_theta 0.5 -ts_theta_endpoint corresponds to Crank-Nicholson (TSCN)
1190: .ve
1192: The endpoint variant of the Theta method and backward Euler can be applied to DAE. The midpoint variant is not suitable for DAEs because it is not stiffly accurate.
1194: The midpoint variant is cast as a 1-stage implicit Runge-Kutta method.
1196: .vb
1197: Theta | Theta
1198: -------------
1199: | 1
1200: .ve
1202: For the default Theta=0.5, this is also known as the implicit midpoint rule.
1204: When the endpoint variant is chosen, the method becomes a 2-stage method with first stage explicit:
1206: .vb
1207: 0 | 0 0
1208: 1 | 1-Theta Theta
1209: -------------------
1210: | 1-Theta Theta
1211: .ve
1213: For the default Theta=0.5, this is the trapezoid rule (also known as Crank-Nicolson, see TSCN).
1215: To apply a diagonally implicit RK method to DAE, the stage formula
1216: .vb
1217: Y_i = X + h sum_j a_ij Y'_j
1218: .ve
1219: is interpreted as a formula for Y'_i in terms of Y_i and known values (Y'_j, j<i)
1221: .seealso: [](ch_ts), `TSCreate()`, `TS`, `TSSetType()`, `TSCN`, `TSBEULER`, `TSThetaSetTheta()`, `TSThetaSetEndpoint()`
1222: M*/
1223: PETSC_EXTERN PetscErrorCode TSCreate_Theta(TS ts)
1224: {
1225: TS_Theta *th;
1227: PetscFunctionBegin;
1228: ts->ops->reset = TSReset_Theta;
1229: ts->ops->adjointreset = TSAdjointReset_Theta;
1230: ts->ops->destroy = TSDestroy_Theta;
1231: ts->ops->view = TSView_Theta;
1232: ts->ops->setup = TSSetUp_Theta;
1233: ts->ops->adjointsetup = TSAdjointSetUp_Theta;
1234: ts->ops->adjointreset = TSAdjointReset_Theta;
1235: ts->ops->step = TSStep_Theta;
1236: ts->ops->interpolate = TSInterpolate_Theta;
1237: ts->ops->evaluatewlte = TSEvaluateWLTE_Theta;
1238: ts->ops->rollback = TSRollBack_Theta;
1239: ts->ops->resizeregister = TSResizeRegister_Theta;
1240: ts->ops->setfromoptions = TSSetFromOptions_Theta;
1241: ts->ops->snesfunction = SNESTSFormFunction_Theta;
1242: ts->ops->snesjacobian = SNESTSFormJacobian_Theta;
1243: #if defined(PETSC_HAVE_COMPLEX)
1244: ts->ops->linearstability = TSComputeLinearStability_Theta;
1245: #endif
1246: ts->ops->getstages = TSGetStages_Theta;
1247: ts->ops->adjointstep = TSAdjointStep_Theta;
1248: ts->ops->adjointintegral = TSAdjointCostIntegral_Theta;
1249: ts->ops->forwardintegral = TSForwardCostIntegral_Theta;
1250: ts->default_adapt_type = TSADAPTNONE;
1252: ts->ops->forwardsetup = TSForwardSetUp_Theta;
1253: ts->ops->forwardreset = TSForwardReset_Theta;
1254: ts->ops->forwardstep = TSForwardStep_Theta;
1255: ts->ops->forwardgetstages = TSForwardGetStages_Theta;
1257: ts->usessnes = PETSC_TRUE;
1259: PetscCall(PetscNew(&th));
1260: ts->data = (void *)th;
1262: th->VecsDeltaLam = NULL;
1263: th->VecsDeltaMu = NULL;
1264: th->VecsSensiTemp = NULL;
1265: th->VecsSensi2Temp = NULL;
1267: th->extrapolate = PETSC_FALSE;
1268: th->Theta = 0.5;
1269: th->order = 2;
1270: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSThetaGetTheta_C", TSThetaGetTheta_Theta));
1271: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSThetaSetTheta_C", TSThetaSetTheta_Theta));
1272: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSThetaGetEndpoint_C", TSThetaGetEndpoint_Theta));
1273: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSThetaSetEndpoint_C", TSThetaSetEndpoint_Theta));
1274: PetscFunctionReturn(PETSC_SUCCESS);
1275: }
1277: /*@
1278: TSThetaGetTheta - Get the abscissa of the stage in (0,1] for `TSTHETA`
1280: Not Collective
1282: Input Parameter:
1283: . ts - timestepping context
1285: Output Parameter:
1286: . theta - stage abscissa
1288: Level: advanced
1290: Note:
1291: Use of this function is normally only required to hack `TSTHETA` to use a modified integration scheme.
1293: .seealso: [](ch_ts), `TSThetaSetTheta()`, `TSTHETA`
1294: @*/
1295: PetscErrorCode TSThetaGetTheta(TS ts, PetscReal *theta)
1296: {
1297: PetscFunctionBegin;
1299: PetscAssertPointer(theta, 2);
1300: PetscUseMethod(ts, "TSThetaGetTheta_C", (TS, PetscReal *), (ts, theta));
1301: PetscFunctionReturn(PETSC_SUCCESS);
1302: }
1304: /*@
1305: TSThetaSetTheta - Set the abscissa of the stage in (0,1] for `TSTHETA`
1307: Not Collective
1309: Input Parameters:
1310: + ts - timestepping context
1311: - theta - stage abscissa
1313: Options Database Key:
1314: . -ts_theta_theta theta - set theta
1316: Level: intermediate
1318: .seealso: [](ch_ts), `TSThetaGetTheta()`, `TSTHETA`, `TSCN`
1319: @*/
1320: PetscErrorCode TSThetaSetTheta(TS ts, PetscReal theta)
1321: {
1322: PetscFunctionBegin;
1324: PetscTryMethod(ts, "TSThetaSetTheta_C", (TS, PetscReal), (ts, theta));
1325: PetscFunctionReturn(PETSC_SUCCESS);
1326: }
1328: /*@
1329: TSThetaGetEndpoint - Gets whether to use the endpoint variant of the method (e.g. trapezoid/Crank-Nicolson instead of midpoint rule) for `TSTHETA`
1331: Not Collective
1333: Input Parameter:
1334: . ts - timestepping context
1336: Output Parameter:
1337: . endpoint - `PETSC_TRUE` when using the endpoint variant
1339: Level: advanced
1341: .seealso: [](ch_ts), `TSThetaSetEndpoint()`, `TSTHETA`, `TSCN`
1342: @*/
1343: PetscErrorCode TSThetaGetEndpoint(TS ts, PetscBool *endpoint)
1344: {
1345: PetscFunctionBegin;
1347: PetscAssertPointer(endpoint, 2);
1348: PetscUseMethod(ts, "TSThetaGetEndpoint_C", (TS, PetscBool *), (ts, endpoint));
1349: PetscFunctionReturn(PETSC_SUCCESS);
1350: }
1352: /*@
1353: TSThetaSetEndpoint - Sets whether to use the endpoint variant of the method (e.g. trapezoid/Crank-Nicolson instead of midpoint rule) for `TSTHETA`
1355: Not Collective
1357: Input Parameters:
1358: + ts - timestepping context
1359: - flg - `PETSC_TRUE` to use the endpoint variant
1361: Options Database Key:
1362: . -ts_theta_endpoint flg - use the endpoint variant
1364: Level: intermediate
1366: .seealso: [](ch_ts), `TSTHETA`, `TSCN`
1367: @*/
1368: PetscErrorCode TSThetaSetEndpoint(TS ts, PetscBool flg)
1369: {
1370: PetscFunctionBegin;
1372: PetscTryMethod(ts, "TSThetaSetEndpoint_C", (TS, PetscBool), (ts, flg));
1373: PetscFunctionReturn(PETSC_SUCCESS);
1374: }
1376: /*
1377: * TSBEULER and TSCN are straightforward specializations of TSTHETA.
1378: * The creation functions for these specializations are below.
1379: */
1381: static PetscErrorCode TSSetUp_BEuler(TS ts)
1382: {
1383: TS_Theta *th = (TS_Theta *)ts->data;
1385: PetscFunctionBegin;
1386: PetscCheck(th->Theta == 1.0, PetscObjectComm((PetscObject)ts), PETSC_ERR_OPT_OVERWRITE, "Can not change the default value (1) of theta when using backward Euler");
1387: PetscCheck(!th->endpoint, PetscObjectComm((PetscObject)ts), PETSC_ERR_OPT_OVERWRITE, "Can not change to the endpoint form of the Theta methods when using backward Euler");
1388: PetscCall(TSSetUp_Theta(ts));
1389: PetscFunctionReturn(PETSC_SUCCESS);
1390: }
1392: static PetscErrorCode TSView_BEuler(TS ts, PetscViewer viewer)
1393: {
1394: PetscFunctionBegin;
1395: PetscFunctionReturn(PETSC_SUCCESS);
1396: }
1398: /*MC
1399: TSBEULER - ODE solver using the implicit backward Euler method
1401: Level: beginner
1403: Note:
1404: `TSBEULER` is equivalent to `TSTHETA` with Theta=1.0 or `-ts_type theta -ts_theta_theta 1.0`
1406: .seealso: [](ch_ts), `TSCreate()`, `TS`, `TSSetType()`, `TSEULER`, `TSCN`, `TSTHETA`
1407: M*/
1408: PETSC_EXTERN PetscErrorCode TSCreate_BEuler(TS ts)
1409: {
1410: PetscFunctionBegin;
1411: PetscCall(TSCreate_Theta(ts));
1412: PetscCall(TSThetaSetTheta(ts, 1.0));
1413: PetscCall(TSThetaSetEndpoint(ts, PETSC_FALSE));
1414: ts->ops->setup = TSSetUp_BEuler;
1415: ts->ops->view = TSView_BEuler;
1416: PetscFunctionReturn(PETSC_SUCCESS);
1417: }
1419: static PetscErrorCode TSSetUp_CN(TS ts)
1420: {
1421: TS_Theta *th = (TS_Theta *)ts->data;
1423: PetscFunctionBegin;
1424: PetscCheck(th->Theta == 0.5, PetscObjectComm((PetscObject)ts), PETSC_ERR_OPT_OVERWRITE, "Can not change the default value (0.5) of theta when using Crank-Nicolson");
1425: PetscCheck(th->endpoint, PetscObjectComm((PetscObject)ts), PETSC_ERR_OPT_OVERWRITE, "Can not change to the midpoint form of the Theta methods when using Crank-Nicolson");
1426: PetscCall(TSSetUp_Theta(ts));
1427: PetscFunctionReturn(PETSC_SUCCESS);
1428: }
1430: static PetscErrorCode TSView_CN(TS ts, PetscViewer viewer)
1431: {
1432: PetscFunctionBegin;
1433: PetscFunctionReturn(PETSC_SUCCESS);
1434: }
1436: /*MC
1437: TSCN - ODE solver using the implicit Crank-Nicolson method.
1439: Level: beginner
1441: Notes:
1442: `TSCN` is equivalent to `TSTHETA` with Theta=0.5 and the "endpoint" option set. I.e.
1443: .vb
1444: -ts_type theta
1445: -ts_theta_theta 0.5
1446: -ts_theta_endpoint
1447: .ve
1449: .seealso: [](ch_ts), `TSCreate()`, `TS`, `TSSetType()`, `TSBEULER`, `TSTHETA`, `TSType`
1450: M*/
1451: PETSC_EXTERN PetscErrorCode TSCreate_CN(TS ts)
1452: {
1453: PetscFunctionBegin;
1454: PetscCall(TSCreate_Theta(ts));
1455: PetscCall(TSThetaSetTheta(ts, 0.5));
1456: PetscCall(TSThetaSetEndpoint(ts, PETSC_TRUE));
1457: ts->ops->setup = TSSetUp_CN;
1458: ts->ops->view = TSView_CN;
1459: PetscFunctionReturn(PETSC_SUCCESS);
1460: }