Actual source code: eimex.c

  1: #include <petsc/private/tsimpl.h>
  2: #include <petscdm.h>

  4: static const PetscInt TSEIMEXDefault = 3;

  6: typedef struct {
  7:   PetscInt     row_ind;    /* Return the term T[row_ind][col_ind] */
  8:   PetscInt     col_ind;    /* Return the term T[row_ind][col_ind] */
  9:   PetscInt     nstages;    /* Numbers of stages in current scheme */
 10:   PetscInt     max_rows;   /* Maximum number of rows */
 11:   PetscInt    *N;          /* Harmonic sequence N[max_rows] */
 12:   Vec          Y;          /* States computed during the step, used to complete the step */
 13:   Vec          Z;          /* For shift*(Y-Z) */
 14:   Vec         *T;          /* Working table, size determined by nstages */
 15:   Vec          YdotRHS;    /* f(x) Work vector holding YdotRHS during residual evaluation */
 16:   Vec          YdotI;      /* xdot-g(x) Work vector holding YdotI = G(t,x,xdot) when xdot =0 */
 17:   Vec          Ydot;       /* f(x)+g(x) Work vector */
 18:   Vec          VecSolPrev; /* Work vector holding the solution from the previous step (used for interpolation) */
 19:   PetscReal    shift;
 20:   PetscReal    ctime;
 21:   PetscBool    recompute_jacobian; /* Recompute the Jacobian at each stage, default is to freeze the Jacobian at the start of each step */
 22:   PetscBool    ord_adapt;          /* order adapativity */
 23:   TSStepStatus status;
 24: } TS_EIMEX;

 26: /* This function is pure */
 27: static PetscInt Map(PetscInt i, PetscInt j, PetscInt s)
 28: {
 29:   return ((2 * s - j + 1) * j / 2 + i - j);
 30: }

 32: static PetscErrorCode TSEvaluateStep_EIMEX(TS ts, PetscInt order, Vec X, PetscBool *done)
 33: {
 34:   TS_EIMEX      *ext = (TS_EIMEX *)ts->data;
 35:   const PetscInt ns  = ext->nstages;
 36:   PetscFunctionBegin;
 37:   PetscCall(VecCopy(ext->T[Map(ext->row_ind, ext->col_ind, ns)], X));
 38:   PetscFunctionReturn(PETSC_SUCCESS);
 39: }

 41: static PetscErrorCode TSStage_EIMEX(TS ts, PetscInt istage)
 42: {
 43:   TS_EIMEX *ext = (TS_EIMEX *)ts->data;
 44:   PetscReal h;
 45:   Vec       Y = ext->Y, Z = ext->Z;
 46:   SNES      snes;
 47:   TSAdapt   adapt;
 48:   PetscInt  i, its, lits;
 49:   PetscBool accept;

 51:   PetscFunctionBegin;
 52:   PetscCall(TSGetSNES(ts, &snes));
 53:   h          = ts->time_step / ext->N[istage]; /* step size for the istage-th stage */
 54:   ext->shift = 1. / h;
 55:   PetscCall(SNESSetLagJacobian(snes, -2)); /* Recompute the Jacobian on this solve, but not again */
 56:   PetscCall(VecCopy(ext->VecSolPrev, Y));  /* Take the previous solution as initial step */

 58:   for (i = 0; i < ext->N[istage]; i++) {
 59:     ext->ctime = ts->ptime + h * i;
 60:     PetscCall(VecCopy(Y, Z)); /* Save the solution of the previous substep */
 61:     PetscCall(SNESSolve(snes, NULL, Y));
 62:     PetscCall(SNESGetIterationNumber(snes, &its));
 63:     PetscCall(SNESGetLinearSolveIterations(snes, &lits));
 64:     ts->snes_its += its;
 65:     ts->ksp_its += lits;
 66:     PetscCall(TSGetAdapt(ts, &adapt));
 67:     PetscCall(TSAdaptCheckStage(adapt, ts, ext->ctime, Y, &accept));
 68:   }
 69:   PetscFunctionReturn(PETSC_SUCCESS);
 70: }

 72: static PetscErrorCode TSStep_EIMEX(TS ts)
 73: {
 74:   TS_EIMEX      *ext = (TS_EIMEX *)ts->data;
 75:   const PetscInt ns  = ext->nstages;
 76:   Vec           *T = ext->T, Y = ext->Y;
 77:   SNES           snes;
 78:   PetscInt       i, j;
 79:   PetscBool      accept = PETSC_FALSE;
 80:   PetscReal      alpha, local_error, local_error_a, local_error_r;

 82:   PetscFunctionBegin;
 83:   PetscCall(TSGetSNES(ts, &snes));
 84:   PetscCall(SNESSetType(snes, "ksponly"));
 85:   ext->status = TS_STEP_INCOMPLETE;

 87:   PetscCall(VecCopy(ts->vec_sol, ext->VecSolPrev));

 89:   /* Apply n_j steps of the base method to obtain solutions of T(j,1),1<=j<=s */
 90:   for (j = 0; j < ns; j++) {
 91:     PetscCall(TSStage_EIMEX(ts, j));
 92:     PetscCall(VecCopy(Y, T[j]));
 93:   }

 95:   for (i = 1; i < ns; i++) {
 96:     for (j = i; j < ns; j++) {
 97:       alpha = -(PetscReal)ext->N[j] / ext->N[j - i];
 98:       PetscCall(VecAXPBYPCZ(T[Map(j, i, ns)], alpha, 1.0, 0, T[Map(j, i - 1, ns)], T[Map(j - 1, i - 1, ns)])); /* T[j][i]=alpha*T[j][i-1]+T[j-1][i-1] */
 99:       alpha = 1.0 / (1.0 + alpha);
100:       PetscCall(VecScale(T[Map(j, i, ns)], alpha));
101:     }
102:   }

104:   PetscCall(TSEvaluateStep(ts, ns, ts->vec_sol, NULL)); /*update ts solution */

106:   if (ext->ord_adapt && ext->nstages < ext->max_rows) {
107:     accept = PETSC_FALSE;
108:     while (!accept && ext->nstages < ext->max_rows) {
109:       PetscCall(TSErrorWeightedNorm(ts, ts->vec_sol, T[Map(ext->nstages - 1, ext->nstages - 2, ext->nstages)], ts->adapt->wnormtype, &local_error, &local_error_a, &local_error_r));
110:       accept = (local_error < 1.0) ? PETSC_TRUE : PETSC_FALSE;

112:       if (!accept) { /* add one more stage*/
113:         PetscCall(TSStage_EIMEX(ts, ext->nstages));
114:         ext->nstages++;
115:         ext->row_ind++;
116:         ext->col_ind++;
117:         /*T table need to be recycled*/
118:         PetscCall(VecDuplicateVecs(ts->vec_sol, (1 + ext->nstages) * ext->nstages / 2, &ext->T));
119:         for (i = 0; i < ext->nstages - 1; i++) {
120:           for (j = 0; j <= i; j++) PetscCall(VecCopy(T[Map(i, j, ext->nstages - 1)], ext->T[Map(i, j, ext->nstages)]));
121:         }
122:         PetscCall(VecDestroyVecs(ext->nstages * (ext->nstages - 1) / 2, &T));
123:         T = ext->T; /*reset the pointer*/
124:         /*recycling finished, store the new solution*/
125:         PetscCall(VecCopy(Y, T[ext->nstages - 1]));
126:         /*extrapolation for the newly added stage*/
127:         for (i = 1; i < ext->nstages; i++) {
128:           alpha = -(PetscReal)ext->N[ext->nstages - 1] / ext->N[ext->nstages - 1 - i];
129:           PetscCall(VecAXPBYPCZ(T[Map(ext->nstages - 1, i, ext->nstages)], alpha, 1.0, 0, T[Map(ext->nstages - 1, i - 1, ext->nstages)], T[Map(ext->nstages - 1 - 1, i - 1, ext->nstages)])); /*T[ext->nstages-1][i]=alpha*T[ext->nstages-1][i-1]+T[ext->nstages-1-1][i-1]*/
130:           alpha = 1.0 / (1.0 + alpha);
131:           PetscCall(VecScale(T[Map(ext->nstages - 1, i, ext->nstages)], alpha));
132:         }
133:         /*update ts solution */
134:         PetscCall(TSEvaluateStep(ts, ext->nstages, ts->vec_sol, NULL));
135:       } /*end if !accept*/
136:     }   /*end while*/

138:     if (ext->nstages == ext->max_rows) PetscCall(PetscInfo(ts, "Max number of rows has been used\n"));
139:   } /*end if ext->ord_adapt*/
140:   ts->ptime += ts->time_step;
141:   ext->status = TS_STEP_COMPLETE;

143:   if (ext->status != TS_STEP_COMPLETE && !ts->reason) ts->reason = TS_DIVERGED_STEP_REJECTED;
144:   PetscFunctionReturn(PETSC_SUCCESS);
145: }

147: /* cubic Hermit spline */
148: static PetscErrorCode TSInterpolate_EIMEX(TS ts, PetscReal itime, Vec X)
149: {
150:   TS_EIMEX       *ext = (TS_EIMEX *)ts->data;
151:   PetscReal       t, a, b;
152:   Vec             Y0 = ext->VecSolPrev, Y1 = ext->Y, Ydot = ext->Ydot, YdotI = ext->YdotI;
153:   const PetscReal h = ts->ptime - ts->ptime_prev;
154:   PetscFunctionBegin;
155:   t = (itime - ts->ptime + h) / h;
156:   /* YdotI = -f(x)-g(x) */

158:   PetscCall(VecZeroEntries(Ydot));
159:   PetscCall(TSComputeIFunction(ts, ts->ptime - h, Y0, Ydot, YdotI, PETSC_FALSE));

161:   a = 2.0 * t * t * t - 3.0 * t * t + 1.0;
162:   b = -(t * t * t - 2.0 * t * t + t) * h;
163:   PetscCall(VecAXPBYPCZ(X, a, b, 0.0, Y0, YdotI));

165:   PetscCall(TSComputeIFunction(ts, ts->ptime, Y1, Ydot, YdotI, PETSC_FALSE));
166:   a = -2.0 * t * t * t + 3.0 * t * t;
167:   b = -(t * t * t - t * t) * h;
168:   PetscCall(VecAXPBYPCZ(X, a, b, 1.0, Y1, YdotI));

170:   PetscFunctionReturn(PETSC_SUCCESS);
171: }

173: static PetscErrorCode TSReset_EIMEX(TS ts)
174: {
175:   TS_EIMEX *ext = (TS_EIMEX *)ts->data;
176:   PetscInt  ns;

178:   PetscFunctionBegin;
179:   ns = ext->nstages;
180:   PetscCall(VecDestroyVecs((1 + ns) * ns / 2, &ext->T));
181:   PetscCall(VecDestroy(&ext->Y));
182:   PetscCall(VecDestroy(&ext->Z));
183:   PetscCall(VecDestroy(&ext->YdotRHS));
184:   PetscCall(VecDestroy(&ext->YdotI));
185:   PetscCall(VecDestroy(&ext->Ydot));
186:   PetscCall(VecDestroy(&ext->VecSolPrev));
187:   PetscCall(PetscFree(ext->N));
188:   PetscFunctionReturn(PETSC_SUCCESS);
189: }

191: static PetscErrorCode TSDestroy_EIMEX(TS ts)
192: {
193:   PetscFunctionBegin;
194:   PetscCall(TSReset_EIMEX(ts));
195:   PetscCall(PetscFree(ts->data));
196:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSEIMEXSetMaxRows_C", NULL));
197:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSEIMEXSetRowCol_C", NULL));
198:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSEIMEXSetOrdAdapt_C", NULL));
199:   PetscFunctionReturn(PETSC_SUCCESS);
200: }

202: static PetscErrorCode TSEIMEXGetVecs(TS ts, DM dm, Vec *Z, Vec *Ydot, Vec *YdotI, Vec *YdotRHS)
203: {
204:   TS_EIMEX *ext = (TS_EIMEX *)ts->data;

206:   PetscFunctionBegin;
207:   if (Z) {
208:     if (dm && dm != ts->dm) {
209:       PetscCall(DMGetNamedGlobalVector(dm, "TSEIMEX_Z", Z));
210:     } else *Z = ext->Z;
211:   }
212:   if (Ydot) {
213:     if (dm && dm != ts->dm) {
214:       PetscCall(DMGetNamedGlobalVector(dm, "TSEIMEX_Ydot", Ydot));
215:     } else *Ydot = ext->Ydot;
216:   }
217:   if (YdotI) {
218:     if (dm && dm != ts->dm) {
219:       PetscCall(DMGetNamedGlobalVector(dm, "TSEIMEX_YdotI", YdotI));
220:     } else *YdotI = ext->YdotI;
221:   }
222:   if (YdotRHS) {
223:     if (dm && dm != ts->dm) {
224:       PetscCall(DMGetNamedGlobalVector(dm, "TSEIMEX_YdotRHS", YdotRHS));
225:     } else *YdotRHS = ext->YdotRHS;
226:   }
227:   PetscFunctionReturn(PETSC_SUCCESS);
228: }

230: static PetscErrorCode TSEIMEXRestoreVecs(TS ts, DM dm, Vec *Z, Vec *Ydot, Vec *YdotI, Vec *YdotRHS)
231: {
232:   PetscFunctionBegin;
233:   if (Z) {
234:     if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSEIMEX_Z", Z));
235:   }
236:   if (Ydot) {
237:     if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSEIMEX_Ydot", Ydot));
238:   }
239:   if (YdotI) {
240:     if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSEIMEX_YdotI", YdotI));
241:   }
242:   if (YdotRHS) {
243:     if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSEIMEX_YdotRHS", YdotRHS));
244:   }
245:   PetscFunctionReturn(PETSC_SUCCESS);
246: }

248: /*
249:   This defines the nonlinear equation that is to be solved with SNES
250:   Fn[t0+Theta*dt, U, (U-U0)*shift] = 0
251:   In the case of Backward Euler, Fn = (U-U0)/h-g(t1,U))
252:   Since FormIFunction calculates G = ydot - g(t,y), ydot will be set to (U-U0)/h
253: */
254: static PetscErrorCode SNESTSFormFunction_EIMEX(SNES snes, Vec X, Vec G, TS ts)
255: {
256:   TS_EIMEX *ext = (TS_EIMEX *)ts->data;
257:   Vec       Ydot, Z;
258:   DM        dm, dmsave;

260:   PetscFunctionBegin;
261:   PetscCall(VecZeroEntries(G));

263:   PetscCall(SNESGetDM(snes, &dm));
264:   PetscCall(TSEIMEXGetVecs(ts, dm, &Z, &Ydot, NULL, NULL));
265:   PetscCall(VecZeroEntries(Ydot));
266:   dmsave = ts->dm;
267:   ts->dm = dm;
268:   PetscCall(TSComputeIFunction(ts, ext->ctime, X, Ydot, G, PETSC_FALSE));
269:   /* PETSC_FALSE indicates non-imex, adding explicit RHS to the implicit I function.  */
270:   PetscCall(VecCopy(G, Ydot));
271:   ts->dm = dmsave;
272:   PetscCall(TSEIMEXRestoreVecs(ts, dm, &Z, &Ydot, NULL, NULL));

274:   PetscFunctionReturn(PETSC_SUCCESS);
275: }

277: /*
278:  This defined the Jacobian matrix for SNES. Jn = (I/h-g'(t,y))
279:  */
280: static PetscErrorCode SNESTSFormJacobian_EIMEX(SNES snes, Vec X, Mat A, Mat B, TS ts)
281: {
282:   TS_EIMEX *ext = (TS_EIMEX *)ts->data;
283:   Vec       Ydot;
284:   DM        dm, dmsave;
285:   PetscFunctionBegin;
286:   PetscCall(SNESGetDM(snes, &dm));
287:   PetscCall(TSEIMEXGetVecs(ts, dm, NULL, &Ydot, NULL, NULL));
288:   /*  PetscCall(VecZeroEntries(Ydot)); */
289:   /* ext->Ydot have already been computed in SNESTSFormFunction_EIMEX (SNES guarantees this) */
290:   dmsave = ts->dm;
291:   ts->dm = dm;
292:   PetscCall(TSComputeIJacobian(ts, ts->ptime, X, Ydot, ext->shift, A, B, PETSC_TRUE));
293:   ts->dm = dmsave;
294:   PetscCall(TSEIMEXRestoreVecs(ts, dm, NULL, &Ydot, NULL, NULL));
295:   PetscFunctionReturn(PETSC_SUCCESS);
296: }

298: static PetscErrorCode DMCoarsenHook_TSEIMEX(DM fine, DM coarse, void *ctx)
299: {
300:   PetscFunctionBegin;
301:   PetscFunctionReturn(PETSC_SUCCESS);
302: }

304: static PetscErrorCode DMRestrictHook_TSEIMEX(DM fine, Mat restrct, Vec rscale, Mat inject, DM coarse, void *ctx)
305: {
306:   TS  ts = (TS)ctx;
307:   Vec Z, Z_c;

309:   PetscFunctionBegin;
310:   PetscCall(TSEIMEXGetVecs(ts, fine, &Z, NULL, NULL, NULL));
311:   PetscCall(TSEIMEXGetVecs(ts, coarse, &Z_c, NULL, NULL, NULL));
312:   PetscCall(MatRestrict(restrct, Z, Z_c));
313:   PetscCall(VecPointwiseMult(Z_c, rscale, Z_c));
314:   PetscCall(TSEIMEXRestoreVecs(ts, fine, &Z, NULL, NULL, NULL));
315:   PetscCall(TSEIMEXRestoreVecs(ts, coarse, &Z_c, NULL, NULL, NULL));
316:   PetscFunctionReturn(PETSC_SUCCESS);
317: }

319: static PetscErrorCode TSSetUp_EIMEX(TS ts)
320: {
321:   TS_EIMEX *ext = (TS_EIMEX *)ts->data;
322:   DM        dm;

324:   PetscFunctionBegin;
325:   if (!ext->N) { /* ext->max_rows not set */
326:     PetscCall(TSEIMEXSetMaxRows(ts, TSEIMEXDefault));
327:   }
328:   if (-1 == ext->row_ind && -1 == ext->col_ind) {
329:     PetscCall(TSEIMEXSetRowCol(ts, ext->max_rows, ext->max_rows));
330:   } else { /* ext->row_ind and col_ind already set */
331:     if (ext->ord_adapt) PetscCall(PetscInfo(ts, "Order adaptivity is enabled and TSEIMEXSetRowCol or -ts_eimex_row_col option will take no effect\n"));
332:   }

334:   if (ext->ord_adapt) {
335:     ext->nstages = 2; /* Start with the 2-stage scheme */
336:     PetscCall(TSEIMEXSetRowCol(ts, ext->nstages, ext->nstages));
337:   } else {
338:     ext->nstages = ext->max_rows; /* by default nstages is the same as max_rows, this can be changed by setting order adaptivity */
339:   }

341:   PetscCall(TSGetAdapt(ts, &ts->adapt));

343:   PetscCall(VecDuplicateVecs(ts->vec_sol, (1 + ext->nstages) * ext->nstages / 2, &ext->T)); /* full T table */
344:   PetscCall(VecDuplicate(ts->vec_sol, &ext->YdotI));
345:   PetscCall(VecDuplicate(ts->vec_sol, &ext->YdotRHS));
346:   PetscCall(VecDuplicate(ts->vec_sol, &ext->Ydot));
347:   PetscCall(VecDuplicate(ts->vec_sol, &ext->VecSolPrev));
348:   PetscCall(VecDuplicate(ts->vec_sol, &ext->Y));
349:   PetscCall(VecDuplicate(ts->vec_sol, &ext->Z));
350:   PetscCall(TSGetDM(ts, &dm));
351:   if (dm) PetscCall(DMCoarsenHookAdd(dm, DMCoarsenHook_TSEIMEX, DMRestrictHook_TSEIMEX, ts));
352:   PetscFunctionReturn(PETSC_SUCCESS);
353: }

355: static PetscErrorCode TSSetFromOptions_EIMEX(TS ts, PetscOptionItems *PetscOptionsObject)
356: {
357:   TS_EIMEX *ext = (TS_EIMEX *)ts->data;
358:   PetscInt  tindex[2];
359:   PetscInt  np = 2, nrows = TSEIMEXDefault;

361:   PetscFunctionBegin;
362:   tindex[0] = TSEIMEXDefault;
363:   tindex[1] = TSEIMEXDefault;
364:   PetscOptionsHeadBegin(PetscOptionsObject, "EIMEX ODE solver options");
365:   {
366:     PetscBool flg;
367:     PetscCall(PetscOptionsInt("-ts_eimex_max_rows", "Define the maximum number of rows used", "TSEIMEXSetMaxRows", nrows, &nrows, &flg)); /* default value 3 */
368:     if (flg) PetscCall(TSEIMEXSetMaxRows(ts, nrows));
369:     PetscCall(PetscOptionsIntArray("-ts_eimex_row_col", "Return the specific term in the T table", "TSEIMEXSetRowCol", tindex, &np, &flg));
370:     if (flg) PetscCall(TSEIMEXSetRowCol(ts, tindex[0], tindex[1]));
371:     PetscCall(PetscOptionsBool("-ts_eimex_order_adapt", "Solve the problem with adaptive order", "TSEIMEXSetOrdAdapt", ext->ord_adapt, &ext->ord_adapt, NULL));
372:   }
373:   PetscOptionsHeadEnd();
374:   PetscFunctionReturn(PETSC_SUCCESS);
375: }

377: static PetscErrorCode TSView_EIMEX(TS ts, PetscViewer viewer)
378: {
379:   PetscFunctionBegin;
380:   PetscFunctionReturn(PETSC_SUCCESS);
381: }

383: /*@C
384:   TSEIMEXSetMaxRows - Set the maximum number of rows for `TSEIMEX` schemes

386:   Logically Collective

388:   Input Parameters:
389: + ts    - timestepping context
390: - nrows - maximum number of rows

392:   Level: intermediate

394: .seealso: [](ch_ts), `TSEIMEXSetRowCol()`, `TSEIMEXSetOrdAdapt()`, `TSEIMEX`
395: @*/
396: PetscErrorCode TSEIMEXSetMaxRows(TS ts, PetscInt nrows)
397: {
398:   PetscFunctionBegin;
400:   PetscTryMethod(ts, "TSEIMEXSetMaxRows_C", (TS, PetscInt), (ts, nrows));
401:   PetscFunctionReturn(PETSC_SUCCESS);
402: }

404: /*@C
405:   TSEIMEXSetRowCol - Set the number of rows and the number of columns for the tableau that represents the T solution in the `TSEIMEX` scheme

407:   Logically Collective

409:   Input Parameters:
410: + ts  - timestepping context
411: . row - the row
412: - col - the column

414:   Level: intermediate

416: .seealso: [](ch_ts), `TSEIMEXSetMaxRows()`, `TSEIMEXSetOrdAdapt()`, `TSEIMEX`
417: @*/
418: PetscErrorCode TSEIMEXSetRowCol(TS ts, PetscInt row, PetscInt col)
419: {
420:   PetscFunctionBegin;
422:   PetscTryMethod(ts, "TSEIMEXSetRowCol_C", (TS, PetscInt, PetscInt), (ts, row, col));
423:   PetscFunctionReturn(PETSC_SUCCESS);
424: }

426: /*@C
427:   TSEIMEXSetOrdAdapt - Set the order adaptativity for the `TSEIMEX` schemes

429:   Logically Collective

431:   Input Parameters:
432: + ts  - timestepping context
433: - flg - index in the T table

435:   Level: intermediate

437: .seealso: [](ch_ts), `TSEIMEXSetRowCol()`, `TSEIMEX`
438: @*/
439: PetscErrorCode TSEIMEXSetOrdAdapt(TS ts, PetscBool flg)
440: {
441:   PetscFunctionBegin;
443:   PetscTryMethod(ts, "TSEIMEXSetOrdAdapt_C", (TS, PetscBool), (ts, flg));
444:   PetscFunctionReturn(PETSC_SUCCESS);
445: }

447: static PetscErrorCode TSEIMEXSetMaxRows_EIMEX(TS ts, PetscInt nrows)
448: {
449:   TS_EIMEX *ext = (TS_EIMEX *)ts->data;
450:   PetscInt  i;

452:   PetscFunctionBegin;
453:   PetscCheck(nrows >= 0 && nrows <= 100, ((PetscObject)ts)->comm, PETSC_ERR_ARG_OUTOFRANGE, "Max number of rows (current value %" PetscInt_FMT ") should be an integer number between 1 and 100", nrows);
454:   PetscCall(PetscFree(ext->N));
455:   ext->max_rows = nrows;
456:   PetscCall(PetscMalloc1(nrows, &ext->N));
457:   for (i = 0; i < nrows; i++) ext->N[i] = i + 1;
458:   PetscFunctionReturn(PETSC_SUCCESS);
459: }

461: static PetscErrorCode TSEIMEXSetRowCol_EIMEX(TS ts, PetscInt row, PetscInt col)
462: {
463:   TS_EIMEX *ext = (TS_EIMEX *)ts->data;

465:   PetscFunctionBegin;
466:   PetscCheck(row >= 1 && col >= 1, ((PetscObject)ts)->comm, PETSC_ERR_ARG_OUTOFRANGE, "The row or column index (current value %" PetscInt_FMT ",%" PetscInt_FMT ") should not be less than 1 ", row, col);
467:   PetscCheck(row <= ext->max_rows && col <= ext->max_rows, ((PetscObject)ts)->comm, PETSC_ERR_ARG_OUTOFRANGE, "The row or column index (current value %" PetscInt_FMT ",%" PetscInt_FMT ") exceeds the maximum number of rows %" PetscInt_FMT, row, col,
468:              ext->max_rows);
469:   PetscCheck(col <= row, ((PetscObject)ts)->comm, PETSC_ERR_ARG_OUTOFRANGE, "The column index (%" PetscInt_FMT ") exceeds the row index (%" PetscInt_FMT ")", col, row);

471:   ext->row_ind = row - 1;
472:   ext->col_ind = col - 1; /* Array index in C starts from 0 */
473:   PetscFunctionReturn(PETSC_SUCCESS);
474: }

476: static PetscErrorCode TSEIMEXSetOrdAdapt_EIMEX(TS ts, PetscBool flg)
477: {
478:   TS_EIMEX *ext = (TS_EIMEX *)ts->data;
479:   PetscFunctionBegin;
480:   ext->ord_adapt = flg;
481:   PetscFunctionReturn(PETSC_SUCCESS);
482: }

484: /*MC
485:    TSEIMEX - Time stepping with Extrapolated IMEX methods {cite}`constantinescu_a2010a`.

487:    These methods are intended for problems with well-separated time scales, especially when a slow scale is strongly nonlinear such that it
488:    is expensive to solve with a fully implicit method. The user should provide the stiff part of the equation using `TSSetIFunction()` and the
489:    non-stiff part with `TSSetRHSFunction()`.

491:       Level: beginner

493:   Notes:
494:   The default is a 3-stage scheme, it can be changed with `TSEIMEXSetMaxRows()` or -ts_eimex_max_rows

496:   This method currently only works with ODE, for which the stiff part $ G(t,X,Xdot) $  has the form $ Xdot + Ghat(t,X)$.

498:   The general system is written as

500:   $$
501:   G(t,X,Xdot) = F(t,X)
502:   $$

504:   where G represents the stiff part and F represents the non-stiff part. The user should provide the stiff part
505:   of the equation using TSSetIFunction() and the non-stiff part with `TSSetRHSFunction()`.
506:   This method is designed to be linearly implicit on G and can use an approximate and lagged Jacobian.

508:   Another common form for the system is

510:   $$
511:   y'=f(x)+g(x)
512:   $$

514:   The relationship between F,G and f,g is

516:   $$
517:   G = y'-g(x), F = f(x)
518:   $$

520: .seealso: [](ch_ts), `TSCreate()`, `TS`, `TSSetType()`, `TSEIMEXSetMaxRows()`, `TSEIMEXSetRowCol()`, `TSEIMEXSetOrdAdapt()`, `TSType`
521:  M*/
522: PETSC_EXTERN PetscErrorCode TSCreate_EIMEX(TS ts)
523: {
524:   TS_EIMEX *ext;

526:   PetscFunctionBegin;

528:   ts->ops->reset          = TSReset_EIMEX;
529:   ts->ops->destroy        = TSDestroy_EIMEX;
530:   ts->ops->view           = TSView_EIMEX;
531:   ts->ops->setup          = TSSetUp_EIMEX;
532:   ts->ops->step           = TSStep_EIMEX;
533:   ts->ops->interpolate    = TSInterpolate_EIMEX;
534:   ts->ops->evaluatestep   = TSEvaluateStep_EIMEX;
535:   ts->ops->setfromoptions = TSSetFromOptions_EIMEX;
536:   ts->ops->snesfunction   = SNESTSFormFunction_EIMEX;
537:   ts->ops->snesjacobian   = SNESTSFormJacobian_EIMEX;
538:   ts->default_adapt_type  = TSADAPTNONE;

540:   ts->usessnes = PETSC_TRUE;

542:   PetscCall(PetscNew(&ext));
543:   ts->data = (void *)ext;

545:   ext->ord_adapt = PETSC_FALSE; /* By default, no order adapativity */
546:   ext->row_ind   = -1;
547:   ext->col_ind   = -1;
548:   ext->max_rows  = TSEIMEXDefault;
549:   ext->nstages   = TSEIMEXDefault;

551:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSEIMEXSetMaxRows_C", TSEIMEXSetMaxRows_EIMEX));
552:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSEIMEXSetRowCol_C", TSEIMEXSetRowCol_EIMEX));
553:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSEIMEXSetOrdAdapt_C", TSEIMEXSetOrdAdapt_EIMEX));
554:   PetscFunctionReturn(PETSC_SUCCESS);
555: }