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: PetscInt nadj;
277: Mat J, Jpre, quadJ = NULL, quadJp = NULL;
278: KSP ksp;
279: PetscScalar *xarr;
280: TSEquationType eqtype;
281: PetscBool isexplicitode = PETSC_FALSE;
282: PetscReal adjoint_time_step;
284: PetscFunctionBegin;
285: PetscCall(TSGetEquationType(ts, &eqtype));
286: if (eqtype == TS_EQ_ODE_EXPLICIT) {
287: isexplicitode = PETSC_TRUE;
288: VecsDeltaLam = ts->vecs_sensi;
289: VecsDeltaLam2 = ts->vecs_sensi2;
290: }
291: th->status = TS_STEP_INCOMPLETE;
292: PetscCall(SNESGetKSP(ts->snes, &ksp));
293: PetscCall(TSGetIJacobian(ts, &J, &Jpre, NULL, NULL));
294: if (quadts) {
295: PetscCall(TSGetRHSJacobian(quadts, &quadJ, NULL, NULL, NULL));
296: PetscCall(TSGetRHSJacobianP(quadts, &quadJp, NULL, NULL));
297: }
299: th->stage_time = ts->ptime;
300: adjoint_time_step = -ts->time_step; /* always positive since time_step is negative */
302: /* Build RHS for first-order adjoint lambda_{n+1}/h + r_u^T(n+1) */
303: if (quadts) PetscCall(TSComputeRHSJacobian(quadts, th->stage_time, ts->vec_sol, quadJ, NULL));
305: for (nadj = 0; nadj < ts->numcost; nadj++) {
306: PetscCall(VecCopy(ts->vecs_sensi[nadj], VecsSensiTemp[nadj]));
307: PetscCall(VecScale(VecsSensiTemp[nadj], 1. / adjoint_time_step)); /* lambda_{n+1}/h */
308: if (quadJ) {
309: PetscCall(MatDenseGetColumn(quadJ, nadj, &xarr));
310: PetscCall(VecPlaceArray(ts->vec_drdu_col, xarr));
311: PetscCall(VecAXPY(VecsSensiTemp[nadj], 1., ts->vec_drdu_col));
312: PetscCall(VecResetArray(ts->vec_drdu_col));
313: PetscCall(MatDenseRestoreColumn(quadJ, &xarr));
314: }
315: }
317: /* Build LHS for first-order adjoint */
318: th->shift = 1. / adjoint_time_step;
319: PetscCall(TSComputeSNESJacobian(ts, ts->vec_sol, J, Jpre));
320: PetscCall(KSPSetOperators(ksp, J, Jpre));
322: /* Solve stage equation LHS*lambda_s = RHS for first-order adjoint */
323: for (nadj = 0; nadj < ts->numcost; nadj++) {
324: KSPConvergedReason kspreason;
325: PetscCall(KSPSolveTranspose(ksp, VecsSensiTemp[nadj], VecsDeltaLam[nadj]));
326: PetscCall(KSPGetConvergedReason(ksp, &kspreason));
327: if (kspreason < 0) {
328: ts->reason = TSADJOINT_DIVERGED_LINEAR_SOLVE;
329: PetscCall(PetscInfo(ts, "Step=%" PetscInt_FMT ", %" PetscInt_FMT "th cost function, transposed linear solve fails, stopping 1st-order adjoint solve\n", ts->steps, nadj));
330: }
331: }
333: if (ts->vecs_sensi2) { /* U_{n+1} */
334: /* Get w1 at t_{n+1} from TLM matrix */
335: PetscCall(MatDenseGetColumn(ts->mat_sensip, 0, &xarr));
336: PetscCall(VecPlaceArray(ts->vec_sensip_col, xarr));
337: /* lambda_s^T F_UU w_1 */
338: PetscCall(TSComputeIHessianProductFunctionUU(ts, th->stage_time, ts->vec_sol, VecsDeltaLam, ts->vec_sensip_col, ts->vecs_fuu));
339: /* lambda_s^T F_UP w_2 */
340: PetscCall(TSComputeIHessianProductFunctionUP(ts, th->stage_time, ts->vec_sol, VecsDeltaLam, ts->vec_dir, ts->vecs_fup));
341: for (nadj = 0; nadj < ts->numcost; nadj++) { /* compute the residual */
342: PetscCall(VecCopy(ts->vecs_sensi2[nadj], VecsSensi2Temp[nadj]));
343: PetscCall(VecScale(VecsSensi2Temp[nadj], 1. / adjoint_time_step));
344: PetscCall(VecAXPY(VecsSensi2Temp[nadj], -1., ts->vecs_fuu[nadj]));
345: if (ts->vecs_fup) PetscCall(VecAXPY(VecsSensi2Temp[nadj], -1., ts->vecs_fup[nadj]));
346: }
347: /* Solve stage equation LHS X = RHS for second-order adjoint */
348: for (nadj = 0; nadj < ts->numcost; nadj++) {
349: KSPConvergedReason kspreason;
350: PetscCall(KSPSolveTranspose(ksp, VecsSensi2Temp[nadj], VecsDeltaLam2[nadj]));
351: PetscCall(KSPGetConvergedReason(ksp, &kspreason));
352: if (kspreason < 0) {
353: ts->reason = TSADJOINT_DIVERGED_LINEAR_SOLVE;
354: PetscCall(PetscInfo(ts, "Step=%" PetscInt_FMT ", %" PetscInt_FMT "th cost function, transposed linear solve fails, stopping 2nd-order adjoint solve\n", ts->steps, nadj));
355: }
356: }
357: }
359: /* Update sensitivities, and evaluate integrals if there is any */
360: if (!isexplicitode) {
361: th->shift = 0.0;
362: PetscCall(TSComputeSNESJacobian(ts, ts->vec_sol, J, Jpre));
363: PetscCall(KSPSetOperators(ksp, J, Jpre));
364: for (nadj = 0; nadj < ts->numcost; nadj++) {
365: /* Add f_U \lambda_s to the original RHS */
366: PetscCall(VecScale(VecsSensiTemp[nadj], -1.));
367: PetscCall(MatMultTransposeAdd(J, VecsDeltaLam[nadj], VecsSensiTemp[nadj], VecsSensiTemp[nadj]));
368: PetscCall(VecScale(VecsSensiTemp[nadj], -adjoint_time_step));
369: PetscCall(VecCopy(VecsSensiTemp[nadj], ts->vecs_sensi[nadj]));
370: if (ts->vecs_sensi2) {
371: PetscCall(MatMultTransposeAdd(J, VecsDeltaLam2[nadj], VecsSensi2Temp[nadj], VecsSensi2Temp[nadj]));
372: PetscCall(VecScale(VecsSensi2Temp[nadj], -adjoint_time_step));
373: PetscCall(VecCopy(VecsSensi2Temp[nadj], ts->vecs_sensi2[nadj]));
374: }
375: }
376: }
377: if (ts->vecs_sensip) {
378: PetscCall(VecAXPBYPCZ(th->Xdot, -1. / adjoint_time_step, 1.0 / adjoint_time_step, 0, th->X0, ts->vec_sol));
379: PetscCall(TSComputeIJacobianP(ts, th->stage_time, ts->vec_sol, th->Xdot, 1. / adjoint_time_step, ts->Jacp, PETSC_FALSE)); /* get -f_p */
380: if (quadts) PetscCall(TSComputeRHSJacobianP(quadts, th->stage_time, ts->vec_sol, quadJp));
381: if (ts->vecs_sensi2p) {
382: /* lambda_s^T F_PU w_1 */
383: PetscCall(TSComputeIHessianProductFunctionPU(ts, th->stage_time, ts->vec_sol, VecsDeltaLam, ts->vec_sensip_col, ts->vecs_fpu));
384: /* lambda_s^T F_PP w_2 */
385: PetscCall(TSComputeIHessianProductFunctionPP(ts, th->stage_time, ts->vec_sol, VecsDeltaLam, ts->vec_dir, ts->vecs_fpp));
386: }
388: for (nadj = 0; nadj < ts->numcost; nadj++) {
389: PetscCall(MatMultTranspose(ts->Jacp, VecsDeltaLam[nadj], VecsDeltaMu[nadj]));
390: PetscCall(VecAXPY(ts->vecs_sensip[nadj], -adjoint_time_step, VecsDeltaMu[nadj]));
391: if (quadJp) {
392: PetscCall(MatDenseGetColumn(quadJp, nadj, &xarr));
393: PetscCall(VecPlaceArray(ts->vec_drdp_col, xarr));
394: PetscCall(VecAXPY(ts->vecs_sensip[nadj], adjoint_time_step, ts->vec_drdp_col));
395: PetscCall(VecResetArray(ts->vec_drdp_col));
396: PetscCall(MatDenseRestoreColumn(quadJp, &xarr));
397: }
398: if (ts->vecs_sensi2p) {
399: PetscCall(MatMultTranspose(ts->Jacp, VecsDeltaLam2[nadj], VecsDeltaMu2[nadj]));
400: PetscCall(VecAXPY(ts->vecs_sensi2p[nadj], -adjoint_time_step, VecsDeltaMu2[nadj]));
401: if (ts->vecs_fpu) PetscCall(VecAXPY(ts->vecs_sensi2p[nadj], -adjoint_time_step, ts->vecs_fpu[nadj]));
402: if (ts->vecs_fpp) PetscCall(VecAXPY(ts->vecs_sensi2p[nadj], -adjoint_time_step, ts->vecs_fpp[nadj]));
403: }
404: }
405: }
407: if (ts->vecs_sensi2) {
408: PetscCall(VecResetArray(ts->vec_sensip_col));
409: PetscCall(MatDenseRestoreColumn(ts->mat_sensip, &xarr));
410: }
411: th->status = TS_STEP_COMPLETE;
412: PetscFunctionReturn(PETSC_SUCCESS);
413: }
415: static PetscErrorCode TSAdjointStep_Theta(TS ts)
416: {
417: TS_Theta *th = (TS_Theta *)ts->data;
418: TS quadts = ts->quadraturets;
419: Vec *VecsDeltaLam = th->VecsDeltaLam, *VecsDeltaMu = th->VecsDeltaMu, *VecsSensiTemp = th->VecsSensiTemp;
420: Vec *VecsDeltaLam2 = th->VecsDeltaLam2, *VecsDeltaMu2 = th->VecsDeltaMu2, *VecsSensi2Temp = th->VecsSensi2Temp;
421: PetscInt nadj;
422: Mat J, Jpre, quadJ = NULL, quadJp = NULL;
423: KSP ksp;
424: PetscScalar *xarr;
425: PetscReal adjoint_time_step;
426: PetscReal adjoint_ptime; /* end time of the adjoint time step (ts->ptime is the start time, usually ts->ptime is larger than adjoint_ptime) */
428: PetscFunctionBegin;
429: if (th->Theta == 1.) {
430: PetscCall(TSAdjointStepBEuler_Private(ts));
431: PetscFunctionReturn(PETSC_SUCCESS);
432: }
433: th->status = TS_STEP_INCOMPLETE;
434: PetscCall(SNESGetKSP(ts->snes, &ksp));
435: PetscCall(TSGetIJacobian(ts, &J, &Jpre, NULL, NULL));
436: if (quadts) {
437: PetscCall(TSGetRHSJacobian(quadts, &quadJ, NULL, NULL, NULL));
438: PetscCall(TSGetRHSJacobianP(quadts, &quadJp, NULL, NULL));
439: }
440: /* If endpoint=1, th->ptime and th->X0 will be used; if endpoint=0, th->stage_time and th->X will be used. */
441: th->stage_time = th->endpoint ? ts->ptime : (ts->ptime + (1. - th->Theta) * ts->time_step);
442: adjoint_ptime = ts->ptime + ts->time_step;
443: adjoint_time_step = -ts->time_step; /* always positive since time_step is negative */
445: if (!th->endpoint) {
446: /* recover th->X0 using vec_sol and the stage value th->X */
447: PetscCall(VecAXPBYPCZ(th->X0, 1.0 / (1.0 - th->Theta), th->Theta / (th->Theta - 1.0), 0, th->X, ts->vec_sol));
448: }
450: /* Build RHS for first-order adjoint */
451: /* Cost function has an integral term */
452: if (quadts) {
453: if (th->endpoint) PetscCall(TSComputeRHSJacobian(quadts, th->stage_time, ts->vec_sol, quadJ, NULL));
454: else PetscCall(TSComputeRHSJacobian(quadts, th->stage_time, th->X, quadJ, NULL));
455: }
457: for (nadj = 0; nadj < ts->numcost; nadj++) {
458: PetscCall(VecCopy(ts->vecs_sensi[nadj], VecsSensiTemp[nadj]));
459: PetscCall(VecScale(VecsSensiTemp[nadj], 1. / (th->Theta * adjoint_time_step)));
460: if (quadJ) {
461: PetscCall(MatDenseGetColumn(quadJ, nadj, &xarr));
462: PetscCall(VecPlaceArray(ts->vec_drdu_col, xarr));
463: PetscCall(VecAXPY(VecsSensiTemp[nadj], 1., ts->vec_drdu_col));
464: PetscCall(VecResetArray(ts->vec_drdu_col));
465: PetscCall(MatDenseRestoreColumn(quadJ, &xarr));
466: }
467: }
469: /* Build LHS for first-order adjoint */
470: th->shift = 1. / (th->Theta * adjoint_time_step);
471: if (th->endpoint) {
472: PetscCall(TSComputeSNESJacobian(ts, ts->vec_sol, J, Jpre));
473: } else {
474: PetscCall(TSComputeSNESJacobian(ts, th->X, J, Jpre));
475: }
476: PetscCall(KSPSetOperators(ksp, J, Jpre));
478: /* Solve stage equation LHS*lambda_s = RHS for first-order adjoint */
479: for (nadj = 0; nadj < ts->numcost; nadj++) {
480: KSPConvergedReason kspreason;
481: PetscCall(KSPSolveTranspose(ksp, VecsSensiTemp[nadj], VecsDeltaLam[nadj]));
482: PetscCall(KSPGetConvergedReason(ksp, &kspreason));
483: if (kspreason < 0) {
484: ts->reason = TSADJOINT_DIVERGED_LINEAR_SOLVE;
485: PetscCall(PetscInfo(ts, "Step=%" PetscInt_FMT ", %" PetscInt_FMT "th cost function, transposed linear solve fails, stopping 1st-order adjoint solve\n", ts->steps, nadj));
486: }
487: }
489: /* Second-order adjoint */
490: if (ts->vecs_sensi2) { /* U_{n+1} */
491: PetscCheck(th->endpoint, PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "Operation not implemented in TS_Theta");
492: /* Get w1 at t_{n+1} from TLM matrix */
493: PetscCall(MatDenseGetColumn(ts->mat_sensip, 0, &xarr));
494: PetscCall(VecPlaceArray(ts->vec_sensip_col, xarr));
495: /* lambda_s^T F_UU w_1 */
496: PetscCall(TSComputeIHessianProductFunctionUU(ts, th->stage_time, ts->vec_sol, VecsDeltaLam, ts->vec_sensip_col, ts->vecs_fuu));
497: PetscCall(VecResetArray(ts->vec_sensip_col));
498: PetscCall(MatDenseRestoreColumn(ts->mat_sensip, &xarr));
499: /* lambda_s^T F_UP w_2 */
500: PetscCall(TSComputeIHessianProductFunctionUP(ts, th->stage_time, ts->vec_sol, VecsDeltaLam, ts->vec_dir, ts->vecs_fup));
501: for (nadj = 0; nadj < ts->numcost; nadj++) { /* compute the residual */
502: PetscCall(VecCopy(ts->vecs_sensi2[nadj], VecsSensi2Temp[nadj]));
503: PetscCall(VecScale(VecsSensi2Temp[nadj], th->shift));
504: PetscCall(VecAXPY(VecsSensi2Temp[nadj], -1., ts->vecs_fuu[nadj]));
505: if (ts->vecs_fup) PetscCall(VecAXPY(VecsSensi2Temp[nadj], -1., ts->vecs_fup[nadj]));
506: }
507: /* Solve stage equation LHS X = RHS for second-order adjoint */
508: for (nadj = 0; nadj < ts->numcost; nadj++) {
509: KSPConvergedReason kspreason;
510: PetscCall(KSPSolveTranspose(ksp, VecsSensi2Temp[nadj], VecsDeltaLam2[nadj]));
511: PetscCall(KSPGetConvergedReason(ksp, &kspreason));
512: if (kspreason < 0) {
513: ts->reason = TSADJOINT_DIVERGED_LINEAR_SOLVE;
514: PetscCall(PetscInfo(ts, "Step=%" PetscInt_FMT ", %" PetscInt_FMT "th cost function, transposed linear solve fails, stopping 2nd-order adjoint solve\n", ts->steps, nadj));
515: }
516: }
517: }
519: /* Update sensitivities, and evaluate integrals if there is any */
520: if (th->endpoint) { /* two-stage Theta methods with th->Theta!=1, th->Theta==1 leads to BEuler */
521: th->shift = 1. / ((th->Theta - 1.) * adjoint_time_step);
522: th->stage_time = adjoint_ptime;
523: PetscCall(TSComputeSNESJacobian(ts, th->X0, J, Jpre));
524: PetscCall(KSPSetOperators(ksp, J, Jpre));
525: /* R_U at t_n */
526: if (quadts) PetscCall(TSComputeRHSJacobian(quadts, adjoint_ptime, th->X0, quadJ, NULL));
527: for (nadj = 0; nadj < ts->numcost; nadj++) {
528: PetscCall(MatMultTranspose(J, VecsDeltaLam[nadj], ts->vecs_sensi[nadj]));
529: if (quadJ) {
530: PetscCall(MatDenseGetColumn(quadJ, nadj, &xarr));
531: PetscCall(VecPlaceArray(ts->vec_drdu_col, xarr));
532: PetscCall(VecAXPY(ts->vecs_sensi[nadj], -1., ts->vec_drdu_col));
533: PetscCall(VecResetArray(ts->vec_drdu_col));
534: PetscCall(MatDenseRestoreColumn(quadJ, &xarr));
535: }
536: PetscCall(VecScale(ts->vecs_sensi[nadj], 1. / th->shift));
537: }
539: /* Second-order adjoint */
540: if (ts->vecs_sensi2) { /* U_n */
541: /* Get w1 at t_n from TLM matrix */
542: PetscCall(MatDenseGetColumn(th->MatFwdSensip0, 0, &xarr));
543: PetscCall(VecPlaceArray(ts->vec_sensip_col, xarr));
544: /* lambda_s^T F_UU w_1 */
545: PetscCall(TSComputeIHessianProductFunctionUU(ts, adjoint_ptime, th->X0, VecsDeltaLam, ts->vec_sensip_col, ts->vecs_fuu));
546: PetscCall(VecResetArray(ts->vec_sensip_col));
547: PetscCall(MatDenseRestoreColumn(th->MatFwdSensip0, &xarr));
548: /* lambda_s^T F_UU w_2 */
549: PetscCall(TSComputeIHessianProductFunctionUP(ts, adjoint_ptime, th->X0, VecsDeltaLam, ts->vec_dir, ts->vecs_fup));
550: for (nadj = 0; nadj < ts->numcost; nadj++) {
551: /* 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 */
552: PetscCall(MatMultTranspose(J, VecsDeltaLam2[nadj], ts->vecs_sensi2[nadj]));
553: PetscCall(VecAXPY(ts->vecs_sensi2[nadj], 1., ts->vecs_fuu[nadj]));
554: if (ts->vecs_fup) PetscCall(VecAXPY(ts->vecs_sensi2[nadj], 1., ts->vecs_fup[nadj]));
555: PetscCall(VecScale(ts->vecs_sensi2[nadj], 1. / th->shift));
556: }
557: }
559: th->stage_time = ts->ptime; /* recover the old value */
561: if (ts->vecs_sensip) { /* sensitivities wrt parameters */
562: /* U_{n+1} */
563: th->shift = 1.0 / (adjoint_time_step * th->Theta);
564: PetscCall(VecAXPBYPCZ(th->Xdot, -th->shift, th->shift, 0, th->X0, ts->vec_sol));
565: PetscCall(TSComputeIJacobianP(ts, th->stage_time, ts->vec_sol, th->Xdot, -1. / (th->Theta * adjoint_time_step), ts->Jacp, PETSC_FALSE));
566: if (quadts) PetscCall(TSComputeRHSJacobianP(quadts, th->stage_time, ts->vec_sol, quadJp));
567: for (nadj = 0; nadj < ts->numcost; nadj++) {
568: PetscCall(MatMultTranspose(ts->Jacp, VecsDeltaLam[nadj], VecsDeltaMu[nadj]));
569: PetscCall(VecAXPY(ts->vecs_sensip[nadj], -adjoint_time_step * th->Theta, VecsDeltaMu[nadj]));
570: if (quadJp) {
571: PetscCall(MatDenseGetColumn(quadJp, nadj, &xarr));
572: PetscCall(VecPlaceArray(ts->vec_drdp_col, xarr));
573: PetscCall(VecAXPY(ts->vecs_sensip[nadj], adjoint_time_step * th->Theta, ts->vec_drdp_col));
574: PetscCall(VecResetArray(ts->vec_drdp_col));
575: PetscCall(MatDenseRestoreColumn(quadJp, &xarr));
576: }
577: }
578: if (ts->vecs_sensi2p) { /* second-order */
579: /* Get w1 at t_{n+1} from TLM matrix */
580: PetscCall(MatDenseGetColumn(ts->mat_sensip, 0, &xarr));
581: PetscCall(VecPlaceArray(ts->vec_sensip_col, xarr));
582: /* lambda_s^T F_PU w_1 */
583: PetscCall(TSComputeIHessianProductFunctionPU(ts, th->stage_time, ts->vec_sol, VecsDeltaLam, ts->vec_sensip_col, ts->vecs_fpu));
584: PetscCall(VecResetArray(ts->vec_sensip_col));
585: PetscCall(MatDenseRestoreColumn(ts->mat_sensip, &xarr));
587: /* lambda_s^T F_PP w_2 */
588: PetscCall(TSComputeIHessianProductFunctionPP(ts, th->stage_time, ts->vec_sol, VecsDeltaLam, ts->vec_dir, ts->vecs_fpp));
589: for (nadj = 0; nadj < ts->numcost; nadj++) {
590: /* 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) */
591: PetscCall(MatMultTranspose(ts->Jacp, VecsDeltaLam2[nadj], VecsDeltaMu2[nadj]));
592: PetscCall(VecAXPY(ts->vecs_sensi2p[nadj], -adjoint_time_step * th->Theta, VecsDeltaMu2[nadj]));
593: if (ts->vecs_fpu) PetscCall(VecAXPY(ts->vecs_sensi2p[nadj], -adjoint_time_step * th->Theta, ts->vecs_fpu[nadj]));
594: if (ts->vecs_fpp) PetscCall(VecAXPY(ts->vecs_sensi2p[nadj], -adjoint_time_step * th->Theta, ts->vecs_fpp[nadj]));
595: }
596: }
598: /* U_s */
599: PetscCall(VecZeroEntries(th->Xdot));
600: PetscCall(TSComputeIJacobianP(ts, adjoint_ptime, th->X0, th->Xdot, 1. / ((th->Theta - 1.0) * adjoint_time_step), ts->Jacp, PETSC_FALSE));
601: if (quadts) PetscCall(TSComputeRHSJacobianP(quadts, adjoint_ptime, th->X0, quadJp));
602: for (nadj = 0; nadj < ts->numcost; nadj++) {
603: PetscCall(MatMultTranspose(ts->Jacp, VecsDeltaLam[nadj], VecsDeltaMu[nadj]));
604: PetscCall(VecAXPY(ts->vecs_sensip[nadj], -adjoint_time_step * (1.0 - th->Theta), VecsDeltaMu[nadj]));
605: if (quadJp) {
606: PetscCall(MatDenseGetColumn(quadJp, nadj, &xarr));
607: PetscCall(VecPlaceArray(ts->vec_drdp_col, xarr));
608: PetscCall(VecAXPY(ts->vecs_sensip[nadj], adjoint_time_step * (1.0 - th->Theta), ts->vec_drdp_col));
609: PetscCall(VecResetArray(ts->vec_drdp_col));
610: PetscCall(MatDenseRestoreColumn(quadJp, &xarr));
611: }
612: if (ts->vecs_sensi2p) { /* second-order */
613: /* Get w1 at t_n from TLM matrix */
614: PetscCall(MatDenseGetColumn(th->MatFwdSensip0, 0, &xarr));
615: PetscCall(VecPlaceArray(ts->vec_sensip_col, xarr));
616: /* lambda_s^T F_PU w_1 */
617: PetscCall(TSComputeIHessianProductFunctionPU(ts, adjoint_ptime, th->X0, VecsDeltaLam, ts->vec_sensip_col, ts->vecs_fpu));
618: PetscCall(VecResetArray(ts->vec_sensip_col));
619: PetscCall(MatDenseRestoreColumn(th->MatFwdSensip0, &xarr));
620: /* lambda_s^T F_PP w_2 */
621: PetscCall(TSComputeIHessianProductFunctionPP(ts, adjoint_ptime, th->X0, VecsDeltaLam, ts->vec_dir, ts->vecs_fpp));
622: for (nadj = 0; nadj < ts->numcost; nadj++) {
623: /* 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) */
624: PetscCall(MatMultTranspose(ts->Jacp, VecsDeltaLam2[nadj], VecsDeltaMu2[nadj]));
625: PetscCall(VecAXPY(ts->vecs_sensi2p[nadj], -adjoint_time_step * (1.0 - th->Theta), VecsDeltaMu2[nadj]));
626: if (ts->vecs_fpu) PetscCall(VecAXPY(ts->vecs_sensi2p[nadj], -adjoint_time_step * (1.0 - th->Theta), ts->vecs_fpu[nadj]));
627: if (ts->vecs_fpp) PetscCall(VecAXPY(ts->vecs_sensi2p[nadj], -adjoint_time_step * (1.0 - th->Theta), ts->vecs_fpp[nadj]));
628: }
629: }
630: }
631: }
632: } else { /* one-stage case */
633: th->shift = 0.0;
634: PetscCall(TSComputeSNESJacobian(ts, th->X, J, Jpre)); /* get -f_y */
635: PetscCall(KSPSetOperators(ksp, J, Jpre));
636: if (quadts) PetscCall(TSComputeRHSJacobian(quadts, th->stage_time, th->X, quadJ, NULL));
637: for (nadj = 0; nadj < ts->numcost; nadj++) {
638: PetscCall(MatMultTranspose(J, VecsDeltaLam[nadj], VecsSensiTemp[nadj]));
639: PetscCall(VecAXPY(ts->vecs_sensi[nadj], -adjoint_time_step, VecsSensiTemp[nadj]));
640: if (quadJ) {
641: PetscCall(MatDenseGetColumn(quadJ, nadj, &xarr));
642: PetscCall(VecPlaceArray(ts->vec_drdu_col, xarr));
643: PetscCall(VecAXPY(ts->vecs_sensi[nadj], adjoint_time_step, ts->vec_drdu_col));
644: PetscCall(VecResetArray(ts->vec_drdu_col));
645: PetscCall(MatDenseRestoreColumn(quadJ, &xarr));
646: }
647: }
648: if (ts->vecs_sensip) {
649: th->shift = 1.0 / (adjoint_time_step * th->Theta);
650: PetscCall(VecAXPBYPCZ(th->Xdot, -th->shift, th->shift, 0, th->X0, th->X));
651: PetscCall(TSComputeIJacobianP(ts, th->stage_time, th->X, th->Xdot, th->shift, ts->Jacp, PETSC_FALSE));
652: if (quadts) PetscCall(TSComputeRHSJacobianP(quadts, th->stage_time, th->X, quadJp));
653: for (nadj = 0; nadj < ts->numcost; nadj++) {
654: PetscCall(MatMultTranspose(ts->Jacp, VecsDeltaLam[nadj], VecsDeltaMu[nadj]));
655: PetscCall(VecAXPY(ts->vecs_sensip[nadj], -adjoint_time_step, VecsDeltaMu[nadj]));
656: if (quadJp) {
657: PetscCall(MatDenseGetColumn(quadJp, nadj, &xarr));
658: PetscCall(VecPlaceArray(ts->vec_drdp_col, xarr));
659: PetscCall(VecAXPY(ts->vecs_sensip[nadj], adjoint_time_step, ts->vec_drdp_col));
660: PetscCall(VecResetArray(ts->vec_drdp_col));
661: PetscCall(MatDenseRestoreColumn(quadJp, &xarr));
662: }
663: }
664: }
665: }
667: th->status = TS_STEP_COMPLETE;
668: PetscFunctionReturn(PETSC_SUCCESS);
669: }
671: static PetscErrorCode TSInterpolate_Theta(TS ts, PetscReal t, Vec X)
672: {
673: TS_Theta *th = (TS_Theta *)ts->data;
674: PetscReal dt = t - ts->ptime;
676: PetscFunctionBegin;
677: PetscCall(VecCopy(ts->vec_sol, th->X));
678: if (th->endpoint) dt *= th->Theta;
679: PetscCall(VecWAXPY(X, dt, th->Xdot, th->X));
680: PetscFunctionReturn(PETSC_SUCCESS);
681: }
683: static PetscErrorCode TSEvaluateWLTE_Theta(TS ts, NormType wnormtype, PetscInt *order, PetscReal *wlte)
684: {
685: TS_Theta *th = (TS_Theta *)ts->data;
686: Vec X = ts->vec_sol; /* X = solution */
687: Vec Y = th->vec_lte_work; /* Y = X + LTE */
688: PetscReal wltea, wlter;
690: PetscFunctionBegin;
691: if (!th->vec_sol_prev) {
692: *wlte = -1;
693: PetscFunctionReturn(PETSC_SUCCESS);
694: }
695: /* Cannot compute LTE in first step or in restart after event */
696: if (ts->steprestart) {
697: *wlte = -1;
698: PetscFunctionReturn(PETSC_SUCCESS);
699: }
700: /* Compute LTE using backward differences with non-constant time step */
701: {
702: PetscReal h = ts->time_step, h_prev = ts->ptime - ts->ptime_prev;
703: PetscReal a = 1 + h_prev / h;
704: PetscScalar scal[3];
705: Vec vecs[3];
707: scal[0] = -1 / a;
708: scal[1] = +1 / (a - 1);
709: scal[2] = -1 / (a * (a - 1));
710: vecs[0] = X;
711: vecs[1] = th->X0;
712: vecs[2] = th->vec_sol_prev;
713: PetscCall(VecCopy(X, Y));
714: PetscCall(VecMAXPY(Y, 3, scal, vecs));
715: PetscCall(TSErrorWeightedNorm(ts, X, Y, wnormtype, wlte, &wltea, &wlter));
716: }
717: if (order) *order = 2;
718: PetscFunctionReturn(PETSC_SUCCESS);
719: }
721: static PetscErrorCode TSRollBack_Theta(TS ts)
722: {
723: TS_Theta *th = (TS_Theta *)ts->data;
724: TS quadts = ts->quadraturets;
726: PetscFunctionBegin;
727: if (quadts && ts->costintegralfwd) PetscCall(VecCopy(th->VecCostIntegral0, quadts->vec_sol));
728: th->status = TS_STEP_INCOMPLETE;
729: if (ts->mat_sensip) PetscCall(MatCopy(th->MatFwdSensip0, ts->mat_sensip, SAME_NONZERO_PATTERN));
730: if (quadts && quadts->mat_sensip) PetscCall(MatCopy(th->MatIntegralSensip0, quadts->mat_sensip, SAME_NONZERO_PATTERN));
731: PetscFunctionReturn(PETSC_SUCCESS);
732: }
734: static PetscErrorCode TSForwardStep_Theta(TS ts)
735: {
736: TS_Theta *th = (TS_Theta *)ts->data;
737: TS quadts = ts->quadraturets;
738: Mat MatDeltaFwdSensip = th->MatDeltaFwdSensip;
739: Vec VecDeltaFwdSensipCol = th->VecDeltaFwdSensipCol;
740: PetscInt ntlm;
741: KSP ksp;
742: Mat J, Jpre, quadJ = NULL, quadJp = NULL;
743: PetscScalar *barr, *xarr;
744: PetscReal previous_shift;
746: PetscFunctionBegin;
747: previous_shift = th->shift;
748: PetscCall(MatCopy(ts->mat_sensip, th->MatFwdSensip0, SAME_NONZERO_PATTERN));
750: if (quadts && quadts->mat_sensip) PetscCall(MatCopy(quadts->mat_sensip, th->MatIntegralSensip0, SAME_NONZERO_PATTERN));
751: PetscCall(SNESGetKSP(ts->snes, &ksp));
752: PetscCall(TSGetIJacobian(ts, &J, &Jpre, NULL, NULL));
753: if (quadts) {
754: PetscCall(TSGetRHSJacobian(quadts, &quadJ, NULL, NULL, NULL));
755: PetscCall(TSGetRHSJacobianP(quadts, &quadJp, NULL, NULL));
756: }
758: /* Build RHS */
759: if (th->endpoint) { /* 2-stage method*/
760: th->shift = 1. / ((th->Theta - 1.) * th->time_step0);
761: PetscCall(TSComputeIJacobian(ts, th->ptime0, th->X0, th->Xdot, th->shift, J, Jpre, PETSC_FALSE));
762: PetscCall(MatMatMult(J, ts->mat_sensip, MAT_REUSE_MATRIX, PETSC_DETERMINE, &MatDeltaFwdSensip));
763: PetscCall(MatScale(MatDeltaFwdSensip, (th->Theta - 1.) / th->Theta));
765: /* Add the f_p forcing terms */
766: if (ts->Jacp) {
767: PetscCall(VecZeroEntries(th->Xdot));
768: PetscCall(TSComputeIJacobianP(ts, th->ptime0, th->X0, th->Xdot, th->shift, ts->Jacp, PETSC_FALSE));
769: PetscCall(MatAXPY(MatDeltaFwdSensip, (th->Theta - 1.) / th->Theta, ts->Jacp, SUBSET_NONZERO_PATTERN));
770: th->shift = previous_shift;
771: PetscCall(VecAXPBYPCZ(th->Xdot, -th->shift, th->shift, 0, th->X0, ts->vec_sol));
772: PetscCall(TSComputeIJacobianP(ts, th->stage_time, ts->vec_sol, th->Xdot, th->shift, ts->Jacp, PETSC_FALSE));
773: PetscCall(MatAXPY(MatDeltaFwdSensip, -1., ts->Jacp, SUBSET_NONZERO_PATTERN));
774: }
775: } else { /* 1-stage method */
776: th->shift = 0.0;
777: PetscCall(TSComputeIJacobian(ts, th->stage_time, th->X, th->Xdot, th->shift, J, Jpre, PETSC_FALSE));
778: PetscCall(MatMatMult(J, ts->mat_sensip, MAT_REUSE_MATRIX, PETSC_DETERMINE, &MatDeltaFwdSensip));
779: PetscCall(MatScale(MatDeltaFwdSensip, -1.));
781: /* Add the f_p forcing terms */
782: if (ts->Jacp) {
783: th->shift = previous_shift;
784: PetscCall(VecAXPBYPCZ(th->Xdot, -th->shift, th->shift, 0, th->X0, th->X));
785: PetscCall(TSComputeIJacobianP(ts, th->stage_time, th->X, th->Xdot, th->shift, ts->Jacp, PETSC_FALSE));
786: PetscCall(MatAXPY(MatDeltaFwdSensip, -1., ts->Jacp, SUBSET_NONZERO_PATTERN));
787: }
788: }
790: /* Build LHS */
791: th->shift = previous_shift; /* recover the previous shift used in TSStep_Theta() */
792: if (th->endpoint) {
793: PetscCall(TSComputeIJacobian(ts, th->stage_time, ts->vec_sol, th->Xdot, th->shift, J, Jpre, PETSC_FALSE));
794: } else {
795: PetscCall(TSComputeIJacobian(ts, th->stage_time, th->X, th->Xdot, th->shift, J, Jpre, PETSC_FALSE));
796: }
797: PetscCall(KSPSetOperators(ksp, J, Jpre));
799: /*
800: Evaluate the first stage of integral gradients with the 2-stage method:
801: drdu|t_n*S(t_n) + drdp|t_n
802: This is done before the linear solve because the sensitivity variable S(t_n) will be propagated to S(t_{n+1})
803: */
804: if (th->endpoint) { /* 2-stage method only */
805: if (quadts && quadts->mat_sensip) {
806: PetscCall(TSComputeRHSJacobian(quadts, th->ptime0, th->X0, quadJ, NULL));
807: PetscCall(TSComputeRHSJacobianP(quadts, th->ptime0, th->X0, quadJp));
808: PetscCall(MatTransposeMatMult(ts->mat_sensip, quadJ, MAT_REUSE_MATRIX, PETSC_DETERMINE, &th->MatIntegralSensipTemp));
809: PetscCall(MatAXPY(th->MatIntegralSensipTemp, 1, quadJp, SAME_NONZERO_PATTERN));
810: PetscCall(MatAXPY(quadts->mat_sensip, th->time_step0 * (1. - th->Theta), th->MatIntegralSensipTemp, SAME_NONZERO_PATTERN));
811: }
812: }
814: /* Solve the tangent linear equation for forward sensitivities to parameters */
815: for (ntlm = 0; ntlm < th->num_tlm; ntlm++) {
816: KSPConvergedReason kspreason;
817: PetscCall(MatDenseGetColumn(MatDeltaFwdSensip, ntlm, &barr));
818: PetscCall(VecPlaceArray(VecDeltaFwdSensipCol, barr));
819: if (th->endpoint) {
820: PetscCall(MatDenseGetColumn(ts->mat_sensip, ntlm, &xarr));
821: PetscCall(VecPlaceArray(ts->vec_sensip_col, xarr));
822: PetscCall(KSPSolve(ksp, VecDeltaFwdSensipCol, ts->vec_sensip_col));
823: PetscCall(VecResetArray(ts->vec_sensip_col));
824: PetscCall(MatDenseRestoreColumn(ts->mat_sensip, &xarr));
825: } else {
826: PetscCall(KSPSolve(ksp, VecDeltaFwdSensipCol, VecDeltaFwdSensipCol));
827: }
828: PetscCall(KSPGetConvergedReason(ksp, &kspreason));
829: if (kspreason < 0) {
830: ts->reason = TSFORWARD_DIVERGED_LINEAR_SOLVE;
831: PetscCall(PetscInfo(ts, "Step=%" PetscInt_FMT ", %" PetscInt_FMT "th tangent linear solve, linear solve fails, stopping tangent linear solve\n", ts->steps, ntlm));
832: }
833: PetscCall(VecResetArray(VecDeltaFwdSensipCol));
834: PetscCall(MatDenseRestoreColumn(MatDeltaFwdSensip, &barr));
835: }
837: /*
838: Evaluate the second stage of integral gradients with the 2-stage method:
839: drdu|t_{n+1}*S(t_{n+1}) + drdp|t_{n+1}
840: */
841: if (quadts && quadts->mat_sensip) {
842: if (!th->endpoint) {
843: PetscCall(MatAXPY(ts->mat_sensip, 1, MatDeltaFwdSensip, SAME_NONZERO_PATTERN)); /* stage sensitivity */
844: PetscCall(TSComputeRHSJacobian(quadts, th->stage_time, th->X, quadJ, NULL));
845: PetscCall(TSComputeRHSJacobianP(quadts, th->stage_time, th->X, quadJp));
846: PetscCall(MatTransposeMatMult(ts->mat_sensip, quadJ, MAT_REUSE_MATRIX, PETSC_DETERMINE, &th->MatIntegralSensipTemp));
847: PetscCall(MatAXPY(th->MatIntegralSensipTemp, 1, quadJp, SAME_NONZERO_PATTERN));
848: PetscCall(MatAXPY(quadts->mat_sensip, th->time_step0, th->MatIntegralSensipTemp, SAME_NONZERO_PATTERN));
849: PetscCall(MatAXPY(ts->mat_sensip, (1. - th->Theta) / th->Theta, MatDeltaFwdSensip, SAME_NONZERO_PATTERN));
850: } else {
851: PetscCall(TSComputeRHSJacobian(quadts, th->stage_time, ts->vec_sol, quadJ, NULL));
852: PetscCall(TSComputeRHSJacobianP(quadts, th->stage_time, ts->vec_sol, quadJp));
853: PetscCall(MatTransposeMatMult(ts->mat_sensip, quadJ, MAT_REUSE_MATRIX, PETSC_DETERMINE, &th->MatIntegralSensipTemp));
854: PetscCall(MatAXPY(th->MatIntegralSensipTemp, 1, quadJp, SAME_NONZERO_PATTERN));
855: PetscCall(MatAXPY(quadts->mat_sensip, th->time_step0 * th->Theta, th->MatIntegralSensipTemp, SAME_NONZERO_PATTERN));
856: }
857: } else {
858: if (!th->endpoint) PetscCall(MatAXPY(ts->mat_sensip, 1. / th->Theta, MatDeltaFwdSensip, SAME_NONZERO_PATTERN));
859: }
860: PetscFunctionReturn(PETSC_SUCCESS);
861: }
863: static PetscErrorCode TSForwardGetStages_Theta(TS ts, PetscInt *ns, Mat *stagesensip[])
864: {
865: TS_Theta *th = (TS_Theta *)ts->data;
867: PetscFunctionBegin;
868: if (ns) {
869: if (!th->endpoint && th->Theta != 1.0) *ns = 1; /* midpoint form */
870: else *ns = 2; /* endpoint form */
871: }
872: if (stagesensip) {
873: if (!th->endpoint && th->Theta != 1.0) {
874: th->MatFwdStages[0] = th->MatDeltaFwdSensip;
875: } else {
876: th->MatFwdStages[0] = th->MatFwdSensip0;
877: th->MatFwdStages[1] = ts->mat_sensip; /* stiffly accurate */
878: }
879: *stagesensip = th->MatFwdStages;
880: }
881: PetscFunctionReturn(PETSC_SUCCESS);
882: }
884: static PetscErrorCode TSReset_Theta(TS ts)
885: {
886: TS_Theta *th = (TS_Theta *)ts->data;
888: PetscFunctionBegin;
889: PetscCall(VecDestroy(&th->X));
890: PetscCall(VecDestroy(&th->Xdot));
891: PetscCall(VecDestroy(&th->X0));
892: PetscCall(VecDestroy(&th->affine));
894: PetscCall(VecDestroy(&th->vec_sol_prev));
895: PetscCall(VecDestroy(&th->vec_lte_work));
897: PetscCall(VecDestroy(&th->VecCostIntegral0));
898: PetscFunctionReturn(PETSC_SUCCESS);
899: }
901: static PetscErrorCode TSAdjointReset_Theta(TS ts)
902: {
903: TS_Theta *th = (TS_Theta *)ts->data;
905: PetscFunctionBegin;
906: PetscCall(VecDestroyVecs(ts->numcost, &th->VecsDeltaLam));
907: PetscCall(VecDestroyVecs(ts->numcost, &th->VecsDeltaMu));
908: PetscCall(VecDestroyVecs(ts->numcost, &th->VecsDeltaLam2));
909: PetscCall(VecDestroyVecs(ts->numcost, &th->VecsDeltaMu2));
910: PetscCall(VecDestroyVecs(ts->numcost, &th->VecsSensiTemp));
911: PetscCall(VecDestroyVecs(ts->numcost, &th->VecsSensi2Temp));
912: PetscFunctionReturn(PETSC_SUCCESS);
913: }
915: static PetscErrorCode TSDestroy_Theta(TS ts)
916: {
917: PetscFunctionBegin;
918: PetscCall(TSReset_Theta(ts));
919: if (ts->dm) {
920: PetscCall(DMCoarsenHookRemove(ts->dm, DMCoarsenHook_TSTheta, DMRestrictHook_TSTheta, ts));
921: PetscCall(DMSubDomainHookRemove(ts->dm, DMSubDomainHook_TSTheta, DMSubDomainRestrictHook_TSTheta, ts));
922: }
923: PetscCall(PetscFree(ts->data));
924: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSThetaGetTheta_C", NULL));
925: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSThetaSetTheta_C", NULL));
926: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSThetaGetEndpoint_C", NULL));
927: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSThetaSetEndpoint_C", NULL));
928: PetscFunctionReturn(PETSC_SUCCESS);
929: }
931: /*
932: This defines the nonlinear equation that is to be solved with SNES
933: G(U) = F[t0+Theta*dt, U, (U-U0)*shift] = 0
935: Note that U here is the stage argument. This means that U = U_{n+1} only if endpoint = true,
936: otherwise U = theta U_{n+1} + (1 - theta) U0, which for the case of implicit midpoint is
937: U = (U_{n+1} + U0)/2
938: */
939: static PetscErrorCode SNESTSFormFunction_Theta(SNES snes, Vec x, Vec y, TS ts)
940: {
941: TS_Theta *th = (TS_Theta *)ts->data;
942: Vec X0, Xdot;
943: DM dm, dmsave;
944: PetscReal shift = th->shift;
946: PetscFunctionBegin;
947: PetscCall(SNESGetDM(snes, &dm));
948: /* When using the endpoint variant, this is actually 1/Theta * Xdot */
949: PetscCall(TSThetaGetX0AndXdot(ts, dm, &X0, &Xdot));
950: if (x != X0) PetscCall(VecAXPBYPCZ(Xdot, -shift, shift, 0, X0, x));
951: else PetscCall(VecZeroEntries(Xdot));
952: /* DM monkey-business allows user code to call TSGetDM() inside of functions evaluated on levels of FAS */
953: dmsave = ts->dm;
954: ts->dm = dm;
955: PetscCall(TSComputeIFunction(ts, th->stage_time, x, Xdot, y, PETSC_FALSE));
956: ts->dm = dmsave;
957: PetscCall(TSThetaRestoreX0AndXdot(ts, dm, &X0, &Xdot));
958: PetscFunctionReturn(PETSC_SUCCESS);
959: }
961: static PetscErrorCode SNESTSFormJacobian_Theta(SNES snes, Vec x, Mat A, Mat B, TS ts)
962: {
963: TS_Theta *th = (TS_Theta *)ts->data;
964: Vec Xdot;
965: DM dm, dmsave;
966: PetscReal shift = th->shift;
968: PetscFunctionBegin;
969: PetscCall(SNESGetDM(snes, &dm));
970: /* Xdot has already been computed in SNESTSFormFunction_Theta (SNES guarantees this) */
971: PetscCall(TSThetaGetX0AndXdot(ts, dm, NULL, &Xdot));
973: dmsave = ts->dm;
974: ts->dm = dm;
975: PetscCall(TSComputeIJacobian(ts, th->stage_time, x, Xdot, shift, A, B, PETSC_FALSE));
976: ts->dm = dmsave;
977: PetscCall(TSThetaRestoreX0AndXdot(ts, dm, NULL, &Xdot));
978: PetscFunctionReturn(PETSC_SUCCESS);
979: }
981: static PetscErrorCode TSForwardSetUp_Theta(TS ts)
982: {
983: TS_Theta *th = (TS_Theta *)ts->data;
984: TS quadts = ts->quadraturets;
986: PetscFunctionBegin;
987: /* combine sensitivities to parameters and sensitivities to initial values into one array */
988: th->num_tlm = ts->num_parameters;
989: PetscCall(MatDuplicate(ts->mat_sensip, MAT_DO_NOT_COPY_VALUES, &th->MatDeltaFwdSensip));
990: if (quadts && quadts->mat_sensip) {
991: PetscCall(MatDuplicate(quadts->mat_sensip, MAT_DO_NOT_COPY_VALUES, &th->MatIntegralSensipTemp));
992: PetscCall(MatDuplicate(quadts->mat_sensip, MAT_DO_NOT_COPY_VALUES, &th->MatIntegralSensip0));
993: }
994: /* backup sensitivity results for roll-backs */
995: PetscCall(MatDuplicate(ts->mat_sensip, MAT_DO_NOT_COPY_VALUES, &th->MatFwdSensip0));
997: PetscCall(VecDuplicate(ts->vec_sol, &th->VecDeltaFwdSensipCol));
998: PetscFunctionReturn(PETSC_SUCCESS);
999: }
1001: static PetscErrorCode TSForwardReset_Theta(TS ts)
1002: {
1003: TS_Theta *th = (TS_Theta *)ts->data;
1004: TS quadts = ts->quadraturets;
1006: PetscFunctionBegin;
1007: if (quadts && quadts->mat_sensip) {
1008: PetscCall(MatDestroy(&th->MatIntegralSensipTemp));
1009: PetscCall(MatDestroy(&th->MatIntegralSensip0));
1010: }
1011: PetscCall(VecDestroy(&th->VecDeltaFwdSensipCol));
1012: PetscCall(MatDestroy(&th->MatDeltaFwdSensip));
1013: PetscCall(MatDestroy(&th->MatFwdSensip0));
1014: PetscFunctionReturn(PETSC_SUCCESS);
1015: }
1017: static PetscErrorCode TSSetUp_Theta(TS ts)
1018: {
1019: TS_Theta *th = (TS_Theta *)ts->data;
1020: TS quadts = ts->quadraturets;
1021: PetscBool match;
1023: PetscFunctionBegin;
1024: if (!th->VecCostIntegral0 && quadts && ts->costintegralfwd) { /* back up cost integral */
1025: PetscCall(VecDuplicate(quadts->vec_sol, &th->VecCostIntegral0));
1026: }
1027: if (!th->X) PetscCall(VecDuplicate(ts->vec_sol, &th->X));
1028: if (!th->Xdot) PetscCall(VecDuplicate(ts->vec_sol, &th->Xdot));
1029: if (!th->X0) PetscCall(VecDuplicate(ts->vec_sol, &th->X0));
1030: if (th->endpoint) PetscCall(VecDuplicate(ts->vec_sol, &th->affine));
1032: th->order = (th->Theta == 0.5) ? 2 : 1;
1033: th->shift = 1 / (th->Theta * ts->time_step);
1035: PetscCall(TSGetDM(ts, &ts->dm));
1036: PetscCall(DMCoarsenHookAdd(ts->dm, DMCoarsenHook_TSTheta, DMRestrictHook_TSTheta, ts));
1037: PetscCall(DMSubDomainHookAdd(ts->dm, DMSubDomainHook_TSTheta, DMSubDomainRestrictHook_TSTheta, ts));
1039: PetscCall(TSGetAdapt(ts, &ts->adapt));
1040: PetscCall(TSAdaptCandidatesClear(ts->adapt));
1041: PetscCall(PetscObjectTypeCompare((PetscObject)ts->adapt, TSADAPTNONE, &match));
1042: if (!match) {
1043: if (!th->vec_sol_prev) PetscCall(VecDuplicate(ts->vec_sol, &th->vec_sol_prev));
1044: if (!th->vec_lte_work) PetscCall(VecDuplicate(ts->vec_sol, &th->vec_lte_work));
1045: }
1046: PetscCall(TSGetSNES(ts, &ts->snes));
1048: ts->stifflyaccurate = (!th->endpoint && th->Theta != 1.0) ? PETSC_FALSE : PETSC_TRUE;
1049: PetscFunctionReturn(PETSC_SUCCESS);
1050: }
1052: static PetscErrorCode TSAdjointSetUp_Theta(TS ts)
1053: {
1054: TS_Theta *th = (TS_Theta *)ts->data;
1056: PetscFunctionBegin;
1057: PetscCall(VecDuplicateVecs(ts->vecs_sensi[0], ts->numcost, &th->VecsDeltaLam));
1058: PetscCall(VecDuplicateVecs(ts->vecs_sensi[0], ts->numcost, &th->VecsSensiTemp));
1059: if (ts->vecs_sensip) PetscCall(VecDuplicateVecs(ts->vecs_sensip[0], ts->numcost, &th->VecsDeltaMu));
1060: if (ts->vecs_sensi2) {
1061: PetscCall(VecDuplicateVecs(ts->vecs_sensi[0], ts->numcost, &th->VecsDeltaLam2));
1062: PetscCall(VecDuplicateVecs(ts->vecs_sensi2[0], ts->numcost, &th->VecsSensi2Temp));
1063: /* hack ts to make implicit TS solver work when users provide only explicit versions of callbacks (RHSFunction,RHSJacobian,RHSHessian etc.) */
1064: if (!ts->ihessianproduct_fuu) ts->vecs_fuu = ts->vecs_guu;
1065: if (!ts->ihessianproduct_fup) ts->vecs_fup = ts->vecs_gup;
1066: }
1067: if (ts->vecs_sensi2p) {
1068: PetscCall(VecDuplicateVecs(ts->vecs_sensi2p[0], ts->numcost, &th->VecsDeltaMu2));
1069: /* hack ts to make implicit TS solver work when users provide only explicit versions of callbacks (RHSFunction,RHSJacobian,RHSHessian etc.) */
1070: if (!ts->ihessianproduct_fpu) ts->vecs_fpu = ts->vecs_gpu;
1071: if (!ts->ihessianproduct_fpp) ts->vecs_fpp = ts->vecs_gpp;
1072: }
1073: PetscFunctionReturn(PETSC_SUCCESS);
1074: }
1076: static PetscErrorCode TSSetFromOptions_Theta(TS ts, PetscOptionItems PetscOptionsObject)
1077: {
1078: TS_Theta *th = (TS_Theta *)ts->data;
1080: PetscFunctionBegin;
1081: PetscOptionsHeadBegin(PetscOptionsObject, "Theta ODE solver options");
1082: {
1083: PetscCall(PetscOptionsReal("-ts_theta_theta", "Location of stage (0<Theta<=1)", "TSThetaSetTheta", th->Theta, &th->Theta, NULL));
1084: PetscCall(PetscOptionsBool("-ts_theta_endpoint", "Use the endpoint instead of midpoint form of the Theta method", "TSThetaSetEndpoint", th->endpoint, &th->endpoint, NULL));
1085: PetscCall(PetscOptionsBool("-ts_theta_initial_guess_extrapolate", "Extrapolate stage initial guess from previous solution (sometimes unstable)", "TSThetaSetExtrapolate", th->extrapolate, &th->extrapolate, NULL));
1086: }
1087: PetscOptionsHeadEnd();
1088: PetscFunctionReturn(PETSC_SUCCESS);
1089: }
1091: static PetscErrorCode TSView_Theta(TS ts, PetscViewer viewer)
1092: {
1093: TS_Theta *th = (TS_Theta *)ts->data;
1094: PetscBool isascii;
1096: PetscFunctionBegin;
1097: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
1098: if (isascii) {
1099: PetscCall(PetscViewerASCIIPrintf(viewer, " Theta=%g\n", (double)th->Theta));
1100: PetscCall(PetscViewerASCIIPrintf(viewer, " Extrapolation=%s\n", th->extrapolate ? "yes" : "no"));
1101: }
1102: PetscFunctionReturn(PETSC_SUCCESS);
1103: }
1105: static PetscErrorCode TSThetaGetTheta_Theta(TS ts, PetscReal *theta)
1106: {
1107: TS_Theta *th = (TS_Theta *)ts->data;
1109: PetscFunctionBegin;
1110: *theta = th->Theta;
1111: PetscFunctionReturn(PETSC_SUCCESS);
1112: }
1114: static PetscErrorCode TSThetaSetTheta_Theta(TS ts, PetscReal theta)
1115: {
1116: TS_Theta *th = (TS_Theta *)ts->data;
1118: PetscFunctionBegin;
1119: PetscCheck(theta > 0 && theta <= 1, PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_OUTOFRANGE, "Theta %g not in range (0,1]", (double)theta);
1120: th->Theta = theta;
1121: th->order = (th->Theta == 0.5) ? 2 : 1;
1122: PetscFunctionReturn(PETSC_SUCCESS);
1123: }
1125: static PetscErrorCode TSThetaGetEndpoint_Theta(TS ts, PetscBool *endpoint)
1126: {
1127: TS_Theta *th = (TS_Theta *)ts->data;
1129: PetscFunctionBegin;
1130: *endpoint = th->endpoint;
1131: PetscFunctionReturn(PETSC_SUCCESS);
1132: }
1134: static PetscErrorCode TSThetaSetEndpoint_Theta(TS ts, PetscBool flg)
1135: {
1136: TS_Theta *th = (TS_Theta *)ts->data;
1138: PetscFunctionBegin;
1139: th->endpoint = flg;
1140: PetscFunctionReturn(PETSC_SUCCESS);
1141: }
1143: #if defined(PETSC_HAVE_COMPLEX)
1144: static PetscErrorCode TSComputeLinearStability_Theta(TS ts, PetscReal xr, PetscReal xi, PetscReal *yr, PetscReal *yi)
1145: {
1146: PetscComplex z = xr + xi * PETSC_i, f;
1147: TS_Theta *th = (TS_Theta *)ts->data;
1149: PetscFunctionBegin;
1150: f = (1.0 + (1.0 - th->Theta) * z) / (1.0 - th->Theta * z);
1151: *yr = PetscRealPartComplex(f);
1152: *yi = PetscImaginaryPartComplex(f);
1153: PetscFunctionReturn(PETSC_SUCCESS);
1154: }
1155: #endif
1157: static PetscErrorCode TSGetStages_Theta(TS ts, PetscInt *ns, Vec *Y[])
1158: {
1159: TS_Theta *th = (TS_Theta *)ts->data;
1161: PetscFunctionBegin;
1162: if (ns) {
1163: if (!th->endpoint && th->Theta != 1.0) *ns = 1; /* midpoint form */
1164: else *ns = 2; /* endpoint form */
1165: }
1166: if (Y) {
1167: if (!th->endpoint && th->Theta != 1.0) {
1168: th->Stages[0] = th->X;
1169: } else {
1170: th->Stages[0] = th->X0;
1171: th->Stages[1] = ts->vec_sol; /* stiffly accurate */
1172: }
1173: *Y = th->Stages;
1174: }
1175: PetscFunctionReturn(PETSC_SUCCESS);
1176: }
1178: /*MC
1179: TSTHETA - DAE solver using the implicit Theta method
1181: Level: beginner
1183: Options Database Keys:
1184: + -ts_theta_theta Theta - Location of stage (0<Theta<=1)
1185: . -ts_theta_endpoint flag - Use the endpoint (like Crank-Nicholson) instead of midpoint form of the Theta method
1186: - -ts_theta_initial_guess_extrapolate flg - Extrapolate stage initial guess from previous solution (sometimes unstable)
1188: Notes:
1189: .vb
1190: -ts_type theta -ts_theta_theta 1.0 corresponds to backward Euler (TSBEULER)
1191: -ts_type theta -ts_theta_theta 0.5 corresponds to the implicit midpoint rule
1192: -ts_type theta -ts_theta_theta 0.5 -ts_theta_endpoint corresponds to Crank-Nicholson (TSCN)
1193: .ve
1195: 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.
1197: The midpoint variant is cast as a 1-stage implicit Runge-Kutta method.
1199: .vb
1200: Theta | Theta
1201: -------------
1202: | 1
1203: .ve
1205: For the default Theta=0.5, this is also known as the implicit midpoint rule.
1207: When the endpoint variant is chosen, the method becomes a 2-stage method with first stage explicit:
1209: .vb
1210: 0 | 0 0
1211: 1 | 1-Theta Theta
1212: -------------------
1213: | 1-Theta Theta
1214: .ve
1216: For the default Theta=0.5, this is the trapezoid rule (also known as Crank-Nicolson, see TSCN).
1218: To apply a diagonally implicit RK method to DAE, the stage formula
1219: .vb
1220: Y_i = X + h sum_j a_ij Y'_j
1221: .ve
1222: is interpreted as a formula for Y'_i in terms of Y_i and known values (Y'_j, j<i)
1224: .seealso: [](ch_ts), `TSCreate()`, `TS`, `TSSetType()`, `TSCN`, `TSBEULER`, `TSThetaSetTheta()`, `TSThetaSetEndpoint()`
1225: M*/
1226: PETSC_EXTERN PetscErrorCode TSCreate_Theta(TS ts)
1227: {
1228: TS_Theta *th;
1230: PetscFunctionBegin;
1231: ts->ops->reset = TSReset_Theta;
1232: ts->ops->adjointreset = TSAdjointReset_Theta;
1233: ts->ops->destroy = TSDestroy_Theta;
1234: ts->ops->view = TSView_Theta;
1235: ts->ops->setup = TSSetUp_Theta;
1236: ts->ops->adjointsetup = TSAdjointSetUp_Theta;
1237: ts->ops->adjointreset = TSAdjointReset_Theta;
1238: ts->ops->step = TSStep_Theta;
1239: ts->ops->interpolate = TSInterpolate_Theta;
1240: ts->ops->evaluatewlte = TSEvaluateWLTE_Theta;
1241: ts->ops->rollback = TSRollBack_Theta;
1242: ts->ops->resizeregister = TSResizeRegister_Theta;
1243: ts->ops->setfromoptions = TSSetFromOptions_Theta;
1244: ts->ops->snesfunction = SNESTSFormFunction_Theta;
1245: ts->ops->snesjacobian = SNESTSFormJacobian_Theta;
1246: #if defined(PETSC_HAVE_COMPLEX)
1247: ts->ops->linearstability = TSComputeLinearStability_Theta;
1248: #endif
1249: ts->ops->getstages = TSGetStages_Theta;
1250: ts->ops->adjointstep = TSAdjointStep_Theta;
1251: ts->ops->adjointintegral = TSAdjointCostIntegral_Theta;
1252: ts->ops->forwardintegral = TSForwardCostIntegral_Theta;
1253: ts->default_adapt_type = TSADAPTNONE;
1255: ts->ops->forwardsetup = TSForwardSetUp_Theta;
1256: ts->ops->forwardreset = TSForwardReset_Theta;
1257: ts->ops->forwardstep = TSForwardStep_Theta;
1258: ts->ops->forwardgetstages = TSForwardGetStages_Theta;
1260: ts->usessnes = PETSC_TRUE;
1262: PetscCall(PetscNew(&th));
1263: ts->data = (void *)th;
1265: th->VecsDeltaLam = NULL;
1266: th->VecsDeltaMu = NULL;
1267: th->VecsSensiTemp = NULL;
1268: th->VecsSensi2Temp = NULL;
1270: th->extrapolate = PETSC_FALSE;
1271: th->Theta = 0.5;
1272: th->order = 2;
1273: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSThetaGetTheta_C", TSThetaGetTheta_Theta));
1274: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSThetaSetTheta_C", TSThetaSetTheta_Theta));
1275: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSThetaGetEndpoint_C", TSThetaGetEndpoint_Theta));
1276: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSThetaSetEndpoint_C", TSThetaSetEndpoint_Theta));
1277: PetscFunctionReturn(PETSC_SUCCESS);
1278: }
1280: /*@
1281: TSThetaGetTheta - Get the abscissa of the stage in (0,1] for `TSTHETA`
1283: Not Collective
1285: Input Parameter:
1286: . ts - timestepping context
1288: Output Parameter:
1289: . theta - stage abscissa
1291: Level: advanced
1293: Note:
1294: Use of this function is normally only required to hack `TSTHETA` to use a modified integration scheme.
1296: .seealso: [](ch_ts), `TSThetaSetTheta()`, `TSTHETA`
1297: @*/
1298: PetscErrorCode TSThetaGetTheta(TS ts, PetscReal *theta)
1299: {
1300: PetscFunctionBegin;
1302: PetscAssertPointer(theta, 2);
1303: PetscUseMethod(ts, "TSThetaGetTheta_C", (TS, PetscReal *), (ts, theta));
1304: PetscFunctionReturn(PETSC_SUCCESS);
1305: }
1307: /*@
1308: TSThetaSetTheta - Set the abscissa of the stage in (0,1] for `TSTHETA`
1310: Not Collective
1312: Input Parameters:
1313: + ts - timestepping context
1314: - theta - stage abscissa
1316: Options Database Key:
1317: . -ts_theta_theta theta - set theta
1319: Level: intermediate
1321: .seealso: [](ch_ts), `TSThetaGetTheta()`, `TSTHETA`, `TSCN`
1322: @*/
1323: PetscErrorCode TSThetaSetTheta(TS ts, PetscReal theta)
1324: {
1325: PetscFunctionBegin;
1327: PetscTryMethod(ts, "TSThetaSetTheta_C", (TS, PetscReal), (ts, theta));
1328: PetscFunctionReturn(PETSC_SUCCESS);
1329: }
1331: /*@
1332: TSThetaGetEndpoint - Gets whether to use the endpoint variant of the method (e.g. trapezoid/Crank-Nicolson instead of midpoint rule) for `TSTHETA`
1334: Not Collective
1336: Input Parameter:
1337: . ts - timestepping context
1339: Output Parameter:
1340: . endpoint - `PETSC_TRUE` when using the endpoint variant
1342: Level: advanced
1344: .seealso: [](ch_ts), `TSThetaSetEndpoint()`, `TSTHETA`, `TSCN`
1345: @*/
1346: PetscErrorCode TSThetaGetEndpoint(TS ts, PetscBool *endpoint)
1347: {
1348: PetscFunctionBegin;
1350: PetscAssertPointer(endpoint, 2);
1351: PetscUseMethod(ts, "TSThetaGetEndpoint_C", (TS, PetscBool *), (ts, endpoint));
1352: PetscFunctionReturn(PETSC_SUCCESS);
1353: }
1355: /*@
1356: TSThetaSetEndpoint - Sets whether to use the endpoint variant of the method (e.g. trapezoid/Crank-Nicolson instead of midpoint rule) for `TSTHETA`
1358: Not Collective
1360: Input Parameters:
1361: + ts - timestepping context
1362: - flg - `PETSC_TRUE` to use the endpoint variant
1364: Options Database Key:
1365: . -ts_theta_endpoint flg - use the endpoint variant
1367: Level: intermediate
1369: .seealso: [](ch_ts), `TSTHETA`, `TSCN`
1370: @*/
1371: PetscErrorCode TSThetaSetEndpoint(TS ts, PetscBool flg)
1372: {
1373: PetscFunctionBegin;
1375: PetscTryMethod(ts, "TSThetaSetEndpoint_C", (TS, PetscBool), (ts, flg));
1376: PetscFunctionReturn(PETSC_SUCCESS);
1377: }
1379: /*
1380: * TSBEULER and TSCN are straightforward specializations of TSTHETA.
1381: * The creation functions for these specializations are below.
1382: */
1384: static PetscErrorCode TSSetUp_BEuler(TS ts)
1385: {
1386: TS_Theta *th = (TS_Theta *)ts->data;
1388: PetscFunctionBegin;
1389: 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");
1390: 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");
1391: PetscCall(TSSetUp_Theta(ts));
1392: PetscFunctionReturn(PETSC_SUCCESS);
1393: }
1395: static PetscErrorCode TSView_BEuler(TS ts, PetscViewer viewer)
1396: {
1397: PetscFunctionBegin;
1398: PetscFunctionReturn(PETSC_SUCCESS);
1399: }
1401: /*MC
1402: TSBEULER - ODE solver using the implicit backward Euler method
1404: Level: beginner
1406: Note:
1407: `TSBEULER` is equivalent to `TSTHETA` with Theta=1.0 or `-ts_type theta -ts_theta_theta 1.0`
1409: .seealso: [](ch_ts), `TSCreate()`, `TS`, `TSSetType()`, `TSEULER`, `TSCN`, `TSTHETA`
1410: M*/
1411: PETSC_EXTERN PetscErrorCode TSCreate_BEuler(TS ts)
1412: {
1413: PetscFunctionBegin;
1414: PetscCall(TSCreate_Theta(ts));
1415: PetscCall(TSThetaSetTheta(ts, 1.0));
1416: PetscCall(TSThetaSetEndpoint(ts, PETSC_FALSE));
1417: ts->ops->setup = TSSetUp_BEuler;
1418: ts->ops->view = TSView_BEuler;
1419: PetscFunctionReturn(PETSC_SUCCESS);
1420: }
1422: static PetscErrorCode TSSetUp_CN(TS ts)
1423: {
1424: TS_Theta *th = (TS_Theta *)ts->data;
1426: PetscFunctionBegin;
1427: 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");
1428: 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");
1429: PetscCall(TSSetUp_Theta(ts));
1430: PetscFunctionReturn(PETSC_SUCCESS);
1431: }
1433: static PetscErrorCode TSView_CN(TS ts, PetscViewer viewer)
1434: {
1435: PetscFunctionBegin;
1436: PetscFunctionReturn(PETSC_SUCCESS);
1437: }
1439: /*MC
1440: TSCN - ODE solver using the implicit Crank-Nicolson method.
1442: Level: beginner
1444: Notes:
1445: `TSCN` is equivalent to `TSTHETA` with Theta=0.5 and the "endpoint" option set. I.e.
1446: .vb
1447: -ts_type theta
1448: -ts_theta_theta 0.5
1449: -ts_theta_endpoint
1450: .ve
1452: .seealso: [](ch_ts), `TSCreate()`, `TS`, `TSSetType()`, `TSBEULER`, `TSTHETA`, `TSType`
1453: M*/
1454: PETSC_EXTERN PetscErrorCode TSCreate_CN(TS ts)
1455: {
1456: PetscFunctionBegin;
1457: PetscCall(TSCreate_Theta(ts));
1458: PetscCall(TSThetaSetTheta(ts, 0.5));
1459: PetscCall(TSThetaSetEndpoint(ts, PETSC_TRUE));
1460: ts->ops->setup = TSSetUp_CN;
1461: ts->ops->view = TSView_CN;
1462: PetscFunctionReturn(PETSC_SUCCESS);
1463: }