Date: 2026-03-01T05:25:18+00:00

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;    /* g(x) Work vector holding YdotRHS during residual evaluation */
     16:   Vec          YdotI;      /* xdot-f(x) Work vector holding YdotI = F(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;

     37:   PetscFunctionBegin;
     38:   PetscCall(VecCopy(ext->T[Map(ext->row_ind, ext->col_ind, ns)], X));
     39:   PetscFunctionReturn(PETSC_SUCCESS);
     40: }

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

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

     59:   for (i = 0; i < ext->N[istage]; i++) {
     60:     ext->ctime = ts->ptime + h * i;
     61:     PetscCall(VecCopy(Y, Z)); /* Save the solution of the previous substep */
     62:     PetscCall(SNESSolve(snes, NULL, Y));
     63:     PetscCall(SNESGetIterationNumber(snes, &its));
     64:     PetscCall(SNESGetLinearSolveIterations(snes, &lits));
     65:     ts->snes_its += its;
     66:     ts->ksp_its += lits;
     67:     PetscCall(TSGetAdapt(ts, &adapt));
     68:     PetscCall(TSAdaptCheckStage(adapt, ts, ext->ctime, Y, &accept));
     69:   }
     70:   PetscFunctionReturn(PETSC_SUCCESS);
     71: }

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

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

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

     90:   /* Apply n_j steps of the base method to obtain solutions of T(j,1),1<=j<=s */
     91:   for (j = 0; j < ns; j++) {
     92:     PetscCall(TSStage_EIMEX(ts, j));
     93:     PetscCall(VecCopy(Y, T[j]));
     94:   }

     96:   for (i = 1; i < ns; i++) {
     97:     for (j = i; j < ns; j++) {
     98:       alpha = -(PetscReal)ext->N[j] / ext->N[j - i];
     99:       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] */
    100:       alpha = 1.0 / (1.0 + alpha);
    101:       PetscCall(VecScale(T[Map(j, i, ns)], alpha));
    102:     }
    103:   }

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

    107:   if (ext->ord_adapt && ext->nstages < ext->max_rows) {
    108:     accept = PETSC_FALSE;
    109:     while (!accept && ext->nstages < ext->max_rows) {
    110:       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));
    111:       accept = (local_error < 1.0) ? PETSC_TRUE : PETSC_FALSE;

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

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

    144:   if (ext->status != TS_STEP_COMPLETE && !ts->reason) ts->reason = TS_DIVERGED_STEP_REJECTED;
    145:   PetscFunctionReturn(PETSC_SUCCESS);
    146: }

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

    156:   PetscFunctionBegin;
    157:   t = (itime - ts->ptime + h) / h;
    158:   /* YdotI = -f(x)-g(x) */

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

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

    167:   PetscCall(TSComputeIFunction(ts, ts->ptime, Y1, Ydot, YdotI, PETSC_FALSE));
    168:   a = -2.0 * t * t * t + 3.0 * t * t;
    169:   b = -(t * t * t - t * t) * h;
    170:   PetscCall(VecAXPBYPCZ(X, a, b, 1.0, Y1, YdotI));
    171:   PetscFunctionReturn(PETSC_SUCCESS);
    172: }

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

    179:   PetscFunctionBegin;
    180:   ns = ext->nstages;
    181:   PetscCall(VecDestroyVecs((1 + ns) * ns / 2, &ext->T));
    182:   PetscCall(VecDestroy(&ext->Y));
    183:   PetscCall(VecDestroy(&ext->Z));
    184:   PetscCall(VecDestroy(&ext->YdotRHS));
    185:   PetscCall(VecDestroy(&ext->YdotI));
    186:   PetscCall(VecDestroy(&ext->Ydot));
    187:   PetscCall(VecDestroy(&ext->VecSolPrev));
    188:   PetscCall(PetscFree(ext->N));
    189:   PetscFunctionReturn(PETSC_SUCCESS);
    190: }

    192: static PetscErrorCode TSDestroy_EIMEX(TS ts)
    193: {
    194:   PetscFunctionBegin;
    195:   PetscCall(TSReset_EIMEX(ts));
    196:   PetscCall(PetscFree(ts->data));
    197:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSEIMEXSetMaxRows_C", NULL));
    198:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSEIMEXSetRowCol_C", NULL));
    199:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSEIMEXSetOrdAdapt_C", NULL));
    200:   PetscFunctionReturn(PETSC_SUCCESS);
    201: }

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

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

    227: static PetscErrorCode TSEIMEXRestoreVecs(TS ts, DM dm, Vec *Z, Vec *Ydot, Vec *YdotI, Vec *YdotRHS)
    228: {
    229:   PetscFunctionBegin;
    230:   if (Z) {
    231:     if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSEIMEX_Z", Z));
    232:   }
    233:   if (Ydot) {
    234:     if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSEIMEX_Ydot", Ydot));
    235:   }
    236:   if (YdotI) {
    237:     if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSEIMEX_YdotI", YdotI));
    238:   }
    239:   if (YdotRHS) {
    240:     if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSEIMEX_YdotRHS", YdotRHS));
    241:   }
    242:   PetscFunctionReturn(PETSC_SUCCESS);
    243: }

    245: /*
    246:   This defines the nonlinear equation that is to be solved with SNES
    247:   Fn[t0+Theta*dt, U, (U-U0)*shift] = 0
    248:   In the case of Backward Euler, Fn = (U-U0)/h-g(t1,U))
    249:   Since FormIFunction calculates G = ydot - g(t,y), ydot will be set to (U-U0)/h
    250: */
    251: static PetscErrorCode SNESTSFormFunction_EIMEX(SNES snes, Vec X, Vec G, TS ts)
    252: {
    253:   TS_EIMEX *ext = (TS_EIMEX *)ts->data;
    254:   Vec       Ydot, Z;
    255:   DM        dm, dmsave;

    257:   PetscFunctionBegin;
    258:   PetscCall(VecZeroEntries(G));

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

    273: /*
    274:  This defined the Jacobian matrix for SNES. Jn = (I/h-g'(t,y))
    275:  */
    276: static PetscErrorCode SNESTSFormJacobian_EIMEX(SNES snes, Vec X, Mat A, Mat B, TS ts)
    277: {
    278:   TS_EIMEX *ext = (TS_EIMEX *)ts->data;
    279:   Vec       Ydot;
    280:   DM        dm, dmsave;

    282:   PetscFunctionBegin;
    283:   PetscCall(SNESGetDM(snes, &dm));
    284:   PetscCall(TSEIMEXGetVecs(ts, dm, NULL, &Ydot, NULL, NULL));
    285:   /*  PetscCall(VecZeroEntries(Ydot)); */
    286:   /* ext->Ydot have already been computed in SNESTSFormFunction_EIMEX (SNES guarantees this) */
    287:   dmsave = ts->dm;
    288:   ts->dm = dm;
    289:   PetscCall(TSComputeIJacobian(ts, ts->ptime, X, Ydot, ext->shift, A, B, PETSC_TRUE));
    290:   ts->dm = dmsave;
    291:   PetscCall(TSEIMEXRestoreVecs(ts, dm, NULL, &Ydot, NULL, NULL));
    292:   PetscFunctionReturn(PETSC_SUCCESS);
    293: }

    295: static PetscErrorCode DMCoarsenHook_TSEIMEX(DM fine, DM coarse, void *ctx)
    296: {
    297:   PetscFunctionBegin;
    298:   PetscFunctionReturn(PETSC_SUCCESS);
    299: }

    301: static PetscErrorCode DMRestrictHook_TSEIMEX(DM fine, Mat restrct, Vec rscale, Mat inject, DM coarse, void *ctx)
    302: {
    303:   TS  ts = (TS)ctx;
    304:   Vec Z, Z_c;

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

    316: static PetscErrorCode TSSetUp_EIMEX(TS ts)
    317: {
    318:   TS_EIMEX *ext = (TS_EIMEX *)ts->data;
    319:   DM        dm;

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

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

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

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

    352: static PetscErrorCode TSSetFromOptions_EIMEX(TS ts, PetscOptionItems PetscOptionsObject)
    353: {
    354:   TS_EIMEX *ext = (TS_EIMEX *)ts->data;
    355:   PetscInt  tindex[2];
    356:   PetscInt  np = 2, nrows = TSEIMEXDefault;

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

    374: static PetscErrorCode TSView_EIMEX(TS ts, PetscViewer viewer)
    375: {
    376:   PetscFunctionBegin;
    377:   PetscFunctionReturn(PETSC_SUCCESS);
    378: }

    380: /*@
    381:   TSEIMEXSetMaxRows - Set the maximum number of rows for `TSEIMEX` schemes

    383:   Logically Collective

    385:   Input Parameters:
    386: + ts    - timestepping context
    387: - nrows - maximum number of rows

    389:   Level: intermediate

    391: .seealso: [](ch_ts), `TSEIMEXSetRowCol()`, `TSEIMEXSetOrdAdapt()`, `TSEIMEX`
    392: @*/
    393: PetscErrorCode TSEIMEXSetMaxRows(TS ts, PetscInt nrows)
    394: {
    395:   PetscFunctionBegin;
    397:   PetscTryMethod(ts, "TSEIMEXSetMaxRows_C", (TS, PetscInt), (ts, nrows));
    398:   PetscFunctionReturn(PETSC_SUCCESS);
    399: }

    401: /*@
    402:   TSEIMEXSetRowCol - Set the number of rows and the number of columns for the tableau that represents the T solution in the `TSEIMEX` scheme

    404:   Logically Collective

    406:   Input Parameters:
    407: + ts  - timestepping context
    408: . row - the row
    409: - col - the column

    411:   Level: intermediate

    413: .seealso: [](ch_ts), `TSEIMEXSetMaxRows()`, `TSEIMEXSetOrdAdapt()`, `TSEIMEX`
    414: @*/
    415: PetscErrorCode TSEIMEXSetRowCol(TS ts, PetscInt row, PetscInt col)
    416: {
    417:   PetscFunctionBegin;
    419:   PetscTryMethod(ts, "TSEIMEXSetRowCol_C", (TS, PetscInt, PetscInt), (ts, row, col));
    420:   PetscFunctionReturn(PETSC_SUCCESS);
    421: }

    423: /*@
    424:   TSEIMEXSetOrdAdapt - Set the order adaptativity for the `TSEIMEX` schemes

    426:   Logically Collective

    428:   Input Parameters:
    429: + ts  - timestepping context
    430: - flg - index in the T table

    432:   Level: intermediate

    434: .seealso: [](ch_ts), `TSEIMEXSetRowCol()`, `TSEIMEX`
    435: @*/
    436: PetscErrorCode TSEIMEXSetOrdAdapt(TS ts, PetscBool flg)
    437: {
    438:   PetscFunctionBegin;
    440:   PetscTryMethod(ts, "TSEIMEXSetOrdAdapt_C", (TS, PetscBool), (ts, flg));
    441:   PetscFunctionReturn(PETSC_SUCCESS);
    442: }

    444: static PetscErrorCode TSEIMEXSetMaxRows_EIMEX(TS ts, PetscInt nrows)
    445: {
    446:   TS_EIMEX *ext = (TS_EIMEX *)ts->data;
    447:   PetscInt  i;

    449:   PetscFunctionBegin;
    450:   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);
    451:   PetscCall(PetscFree(ext->N));
    452:   ext->max_rows = nrows;
    453:   PetscCall(PetscMalloc1(nrows, &ext->N));
    454:   for (i = 0; i < nrows; i++) ext->N[i] = i + 1;
    455:   PetscFunctionReturn(PETSC_SUCCESS);
    456: }

    458: static PetscErrorCode TSEIMEXSetRowCol_EIMEX(TS ts, PetscInt row, PetscInt col)
    459: {
    460:   TS_EIMEX *ext = (TS_EIMEX *)ts->data;

    462:   PetscFunctionBegin;
    463:   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);
    464:   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,
    465:              ext->max_rows);
    466:   PetscCheck(col <= row, ((PetscObject)ts)->comm, PETSC_ERR_ARG_OUTOFRANGE, "The column index (%" PetscInt_FMT ") exceeds the row index (%" PetscInt_FMT ")", col, row);

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

    473: static PetscErrorCode TSEIMEXSetOrdAdapt_EIMEX(TS ts, PetscBool flg)
    474: {
    475:   TS_EIMEX *ext = (TS_EIMEX *)ts->data;

    477:   PetscFunctionBegin;
    478:   ext->ord_adapt = flg;
    479:   PetscFunctionReturn(PETSC_SUCCESS);
    480: }

    482: /*MC
    483:    TSEIMEX - Time stepping with Extrapolated W-IMEX methods {cite}`constantinescu_a2010a`.

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

    489:       Level: beginner

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

    494:   This method currently only works with ODEs, for which the stiff part $ F(t,X,Xdot) $  has the form $ Xdot + Fhat(t,X)$.

    496:   The general system is written as

    498:   $$
    499:   F(t,X,Xdot) = G(t,X)
    500:   $$

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

    506:   Another common form for the system is

    508:   $$
    509:   y'=f(x)+g(x)
    510:   $$

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

    514:   $$
    515:   F = y'-f(x), G = g(x)
    516:   $$

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

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

    537:   ts->usessnes = PETSC_TRUE;

    539:   PetscCall(PetscNew(&ext));
    540:   ts->data = (void *)ext;

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

    548:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSEIMEXSetMaxRows_C", TSEIMEXSetMaxRows_EIMEX));
    549:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSEIMEXSetRowCol_C", TSEIMEXSetRowCol_EIMEX));
    550:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSEIMEXSetOrdAdapt_C", TSEIMEXSetOrdAdapt_EIMEX));
    551:   PetscFunctionReturn(PETSC_SUCCESS);
    552: }