explicit/rk/mrk.c

/*
  Code for time stepping with the multi-rate Runge-Kutta method

  Notes:
  1) The general system is written as
     Udot = F(t,U) for the nonsplit version of multi-rate RK,
     user should give the indexes for both slow and fast components;
  2) The general system is written as
     Usdot = Fs(t,Us,Uf)
     Ufdot = Ff(t,Us,Uf) for multi-rate RK with RHS splits,
     user should partition RHS by themselves and also provide the indexes for both slow and fast components.
*/

#include <petsc/private/tsimpl.h>
#include <petscdm.h>
#include <../src/ts/impls/explicit/rk/rk.h>
#include <../src/ts/impls/explicit/rk/mrk.h>

static PetscErrorCode TSReset_RK_MultirateNonsplit(TS ts)
{
  TS_RK    *rk  = (TS_RK *)ts->data;
  RKTableau tab = rk->tableau;

  PetscFunctionBegin;
  PetscCall(VecDestroy(&rk->X0));
  PetscCall(VecDestroyVecs(tab->s, &rk->YdotRHS_slow));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TSInterpolate_RK_MultirateNonsplit(TS ts, PetscReal itime, Vec X)
{
  TS_RK           *rk = (TS_RK *)ts->data;
  PetscInt         s = rk->tableau->s, p = rk->tableau->p, i, j;
  PetscReal        h = ts->time_step;
  PetscReal        tt, t;
  PetscScalar     *b;
  const PetscReal *B = rk->tableau->binterp;

  PetscFunctionBegin;
  PetscCheck(B, PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "TSRK %s does not have an interpolation formula", rk->tableau->name);
  t = (itime - rk->ptime) / h;
  PetscCall(PetscMalloc1(s, &b));
  for (i = 0; i < s; i++) b[i] = 0;
  for (j = 0, tt = t; j < p; j++, tt *= t) {
    for (i = 0; i < s; i++) b[i] += h * B[i * p + j] * tt;
  }
  PetscCall(VecCopy(rk->X0, X));
  PetscCall(VecMAXPY(X, s, b, rk->YdotRHS_slow));
  PetscCall(PetscFree(b));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TSStepRefine_RK_MultirateNonsplit(TS ts)
{
  TS               previousts, subts;
  TS_RK           *rk  = (TS_RK *)ts->data;
  RKTableau        tab = rk->tableau;
  Vec             *Y = rk->Y, *YdotRHS = rk->YdotRHS;
  Vec              vec_fast, subvec_fast;
  const PetscInt   s = tab->s;
  const PetscReal *A = tab->A, *c = tab->c;
  PetscScalar     *w = rk->work;
  PetscInt         i, j, k;
  PetscReal        t = ts->ptime, h = ts->time_step;

  PetscFunctionBegin;
  PetscCall(VecDuplicate(ts->vec_sol, &vec_fast));
  previousts = rk->subts_current;
  PetscCall(TSRHSSplitGetSubTS(rk->subts_current, "fast", &subts));
  PetscCall(TSRHSSplitGetSubTS(subts, "fast", &subts));
  for (k = 0; k < rk->dtratio; k++) {
    for (i = 0; i < s; i++) {
      PetscCall(TSInterpolate_RK_MultirateNonsplit(ts, t + k * h / rk->dtratio + h / rk->dtratio * c[i], Y[i]));
      for (j = 0; j < i; j++) w[j] = h / rk->dtratio * A[i * s + j];
      /* update the fast components in the stage value, the slow components will be ignored, so we do not care the slow part in vec_fast */
      PetscCall(VecCopy(ts->vec_sol, vec_fast));
      PetscCall(VecMAXPY(vec_fast, i, w, YdotRHS));
      /* update the fast components in the stage value */
      PetscCall(VecGetSubVector(vec_fast, rk->is_fast, &subvec_fast));
      PetscCall(VecISCopy(Y[i], rk->is_fast, SCATTER_FORWARD, subvec_fast));
      PetscCall(VecRestoreSubVector(vec_fast, rk->is_fast, &subvec_fast));
      /* compute the stage RHS */
      PetscCall(TSComputeRHSFunction(ts, t + k * h / rk->dtratio + h / rk->dtratio * c[i], Y[i], YdotRHS[i]));
    }
    PetscCall(VecCopy(ts->vec_sol, vec_fast));
    PetscCall(TSEvaluateStep(ts, tab->order, vec_fast, NULL));
    /* update the fast components in the solution */
    PetscCall(VecGetSubVector(vec_fast, rk->is_fast, &subvec_fast));
    PetscCall(VecISCopy(ts->vec_sol, rk->is_fast, SCATTER_FORWARD, subvec_fast));
    PetscCall(VecRestoreSubVector(vec_fast, rk->is_fast, &subvec_fast));

    if (subts) {
      Vec *YdotRHS_copy;
      PetscCall(VecDuplicateVecs(ts->vec_sol, s, &YdotRHS_copy));
      rk->subts_current = rk->subts_fast;
      ts->ptime         = t + k * h / rk->dtratio;
      ts->time_step     = h / rk->dtratio;
      PetscCall(TSRHSSplitGetIS(rk->subts_current, "fast", &rk->is_fast));
      for (i = 0; i < s; i++) {
        PetscCall(VecCopy(rk->YdotRHS_slow[i], YdotRHS_copy[i]));
        PetscCall(VecCopy(YdotRHS[i], rk->YdotRHS_slow[i]));
      }

      PetscCall(TSStepRefine_RK_MultirateNonsplit(ts));

      rk->subts_current = previousts;
      ts->ptime         = t;
      ts->time_step     = h;
      PetscCall(TSRHSSplitGetIS(previousts, "fast", &rk->is_fast));
      for (i = 0; i < s; i++) PetscCall(VecCopy(YdotRHS_copy[i], rk->YdotRHS_slow[i]));
      PetscCall(VecDestroyVecs(s, &YdotRHS_copy));
    }
  }
  PetscCall(VecDestroy(&vec_fast));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TSStep_RK_MultirateNonsplit(TS ts)
{
  TS_RK           *rk  = (TS_RK *)ts->data;
  RKTableau        tab = rk->tableau;
  Vec             *Y = rk->Y, *YdotRHS = rk->YdotRHS, *YdotRHS_slow = rk->YdotRHS_slow;
  Vec              stage_slow, sol_slow; /* vectors store the slow components */
  Vec              subvec_slow;          /* sub vector to store the slow components */
  IS               is_slow = rk->is_slow;
  const PetscInt   s       = tab->s;
  const PetscReal *A = tab->A, *c = tab->c;
  PetscScalar     *w = rk->work;
  PetscInt         i, j, dtratio = rk->dtratio;
  PetscReal        next_time_step = ts->time_step, t = ts->ptime, h = ts->time_step;

  PetscFunctionBegin;
  rk->status = TS_STEP_INCOMPLETE;
  PetscCall(VecDuplicate(ts->vec_sol, &stage_slow));
  PetscCall(VecDuplicate(ts->vec_sol, &sol_slow));
  PetscCall(VecCopy(ts->vec_sol, rk->X0));
  for (i = 0; i < s; i++) {
    rk->stage_time = t + h * c[i];
    PetscCall(TSPreStage(ts, rk->stage_time));
    PetscCall(VecCopy(ts->vec_sol, Y[i]));
    for (j = 0; j < i; j++) w[j] = h * A[i * s + j];
    PetscCall(VecMAXPY(Y[i], i, w, YdotRHS_slow));
    PetscCall(TSPostStage(ts, rk->stage_time, i, Y));
    /* compute the stage RHS */
    PetscCall(TSComputeRHSFunction(ts, t + h * c[i], Y[i], YdotRHS_slow[i]));
  }
  /* update the slow components in the solution */
  rk->YdotRHS = YdotRHS_slow;
  rk->dtratio = 1;
  PetscCall(TSEvaluateStep(ts, tab->order, sol_slow, NULL));
  rk->dtratio = dtratio;
  rk->YdotRHS = YdotRHS;
  /* update the slow components in the solution */
  PetscCall(VecGetSubVector(sol_slow, is_slow, &subvec_slow));
  PetscCall(VecISCopy(ts->vec_sol, is_slow, SCATTER_FORWARD, subvec_slow));
  PetscCall(VecRestoreSubVector(sol_slow, is_slow, &subvec_slow));

  rk->subts_current = ts;
  rk->ptime         = t;
  rk->time_step     = h;
  PetscCall(TSStepRefine_RK_MultirateNonsplit(ts));

  ts->ptime     = t + ts->time_step;
  ts->time_step = next_time_step;
  rk->status    = TS_STEP_COMPLETE;

  /* free memory of work vectors */
  PetscCall(VecDestroy(&stage_slow));
  PetscCall(VecDestroy(&sol_slow));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TSSetUp_RK_MultirateNonsplit(TS ts)
{
  TS_RK    *rk  = (TS_RK *)ts->data;
  RKTableau tab = rk->tableau;

  PetscFunctionBegin;
  PetscCall(TSRHSSplitGetIS(ts, "slow", &rk->is_slow));
  PetscCall(TSRHSSplitGetIS(ts, "fast", &rk->is_fast));
  PetscCheck(rk->is_slow && rk->is_fast, PetscObjectComm((PetscObject)ts), PETSC_ERR_USER, "Must set up RHSSplits with TSRHSSplitSetIS() using split names 'slow' and 'fast' respectively in order to use multirate RK");
  PetscCall(TSRHSSplitGetSubTS(ts, "slow", &rk->subts_slow));
  PetscCall(TSRHSSplitGetSubTS(ts, "fast", &rk->subts_fast));
  PetscCheck(rk->subts_slow && rk->subts_fast, PetscObjectComm((PetscObject)ts), PETSC_ERR_USER, "Must set up the RHSFunctions for 'slow' and 'fast' components using TSRHSSplitSetRHSFunction() or calling TSSetRHSFunction() for each sub-TS");
  PetscCall(VecDuplicate(ts->vec_sol, &rk->X0));
  PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &rk->YdotRHS_slow));
  rk->subts_current = rk->subts_fast;

  ts->ops->step        = TSStep_RK_MultirateNonsplit;
  ts->ops->interpolate = TSInterpolate_RK_MultirateNonsplit;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
  Copy DM from tssrc to tsdest, while keeping the original DMTS and DMSNES in tsdest.
*/
static PetscErrorCode TSCopyDM(TS tssrc, TS tsdest)
{
  DM newdm, dmsrc, dmdest;

  PetscFunctionBegin;
  PetscCall(TSGetDM(tssrc, &dmsrc));
  PetscCall(DMClone(dmsrc, &newdm));
  PetscCall(TSGetDM(tsdest, &dmdest));
  PetscCall(DMCopyDMTS(dmdest, newdm));
  PetscCall(DMCopyDMSNES(dmdest, newdm));
  PetscCall(TSSetDM(tsdest, newdm));
  PetscCall(DMDestroy(&newdm));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TSReset_RK_MultirateSplit(TS ts)
{
  TS_RK *rk = (TS_RK *)ts->data;

  PetscFunctionBegin;
  if (rk->subts_slow) {
    PetscCall(PetscFree(rk->subts_slow->data));
    rk->subts_slow = NULL;
  }
  if (rk->subts_fast) {
    PetscCall(PetscFree(rk->YdotRHS_fast));
    PetscCall(PetscFree(rk->YdotRHS_slow));
    PetscCall(VecDestroy(&rk->X0));
    PetscCall(TSReset_RK_MultirateSplit(rk->subts_fast));
    PetscCall(PetscFree(rk->subts_fast->data));
    rk->subts_fast = NULL;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TSInterpolate_RK_MultirateSplit(TS ts, PetscReal itime, Vec X)
{
  TS_RK           *rk = (TS_RK *)ts->data;
  Vec              Xslow;
  PetscInt         s = rk->tableau->s, p = rk->tableau->p, i, j;
  PetscReal        h;
  PetscReal        tt, t;
  PetscScalar     *b;
  const PetscReal *B = rk->tableau->binterp;

  PetscFunctionBegin;
  PetscCheck(B, PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "TSRK %s does not have an interpolation formula", rk->tableau->name);

  switch (rk->status) {
  case TS_STEP_INCOMPLETE:
  case TS_STEP_PENDING:
    h = ts->time_step;
    t = (itime - ts->ptime) / h;
    break;
  case TS_STEP_COMPLETE:
    h = ts->ptime - ts->ptime_prev;
    t = (itime - ts->ptime) / h + 1; /* In the interval [0,1] */
    break;
  default:
    SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_PLIB, "Invalid TSStepStatus");
  }
  PetscCall(PetscMalloc1(s, &b));
  for (i = 0; i < s; i++) b[i] = 0;
  for (j = 0, tt = t; j < p; j++, tt *= t) {
    for (i = 0; i < s; i++) b[i] += h * B[i * p + j] * tt;
  }
  for (i = 0; i < s; i++) PetscCall(VecGetSubVector(rk->YdotRHS[i], rk->is_slow, &rk->YdotRHS_slow[i]));
  PetscCall(VecGetSubVector(X, rk->is_slow, &Xslow));
  PetscCall(VecISCopy(rk->X0, rk->is_slow, SCATTER_REVERSE, Xslow));
  PetscCall(VecMAXPY(Xslow, s, b, rk->YdotRHS_slow));
  PetscCall(VecRestoreSubVector(X, rk->is_slow, &Xslow));
  for (i = 0; i < s; i++) PetscCall(VecRestoreSubVector(rk->YdotRHS[i], rk->is_slow, &rk->YdotRHS_slow[i]));
  PetscCall(PetscFree(b));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
 This is for partitioned RHS multirate RK method
 The step completion formula is

 x1 = x0 + h b^T YdotRHS

*/
static PetscErrorCode TSEvaluateStep_RK_MultirateSplit(TS ts, PetscInt order, Vec X, PetscBool *done)
{
  TS_RK       *rk  = (TS_RK *)ts->data;
  RKTableau    tab = rk->tableau;
  Vec          Xslow, Xfast; /* subvectors of X which store slow components and fast components respectively */
  PetscScalar *w = rk->work;
  PetscReal    h = ts->time_step;
  PetscInt     s = tab->s, j;

  PetscFunctionBegin;
  PetscCall(VecCopy(ts->vec_sol, X));
  if (rk->slow) {
    for (j = 0; j < s; j++) w[j] = h * tab->b[j];
    PetscCall(VecGetSubVector(ts->vec_sol, rk->is_slow, &Xslow));
    PetscCall(VecMAXPY(Xslow, s, w, rk->YdotRHS_slow));
    PetscCall(VecRestoreSubVector(ts->vec_sol, rk->is_slow, &Xslow));
  } else {
    for (j = 0; j < s; j++) w[j] = h / rk->dtratio * tab->b[j];
    PetscCall(VecGetSubVector(X, rk->is_fast, &Xfast));
    PetscCall(VecMAXPY(Xfast, s, w, rk->YdotRHS_fast));
    PetscCall(VecRestoreSubVector(X, rk->is_fast, &Xfast));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TSStepRefine_RK_MultirateSplit(TS ts)
{
  TS_RK           *rk         = (TS_RK *)ts->data;
  TS               subts_fast = rk->subts_fast, currentlevelts;
  TS_RK           *subrk_fast = (TS_RK *)subts_fast->data;
  RKTableau        tab        = rk->tableau;
  Vec             *Y          = rk->Y;
  Vec             *YdotRHS = rk->YdotRHS, *YdotRHS_fast = rk->YdotRHS_fast;
  Vec              Yfast, Xfast;
  const PetscInt   s = tab->s;
  const PetscReal *A = tab->A, *c = tab->c;
  PetscScalar     *w = rk->work;
  PetscInt         i, j, k;
  PetscReal        t = ts->ptime, h = ts->time_step;

  PetscFunctionBegin;
  for (k = 0; k < rk->dtratio; k++) {
    PetscCall(VecGetSubVector(ts->vec_sol, rk->is_fast, &Xfast));
    for (i = 0; i < s; i++) PetscCall(VecGetSubVector(YdotRHS[i], rk->is_fast, &YdotRHS_fast[i]));
    /* propagate fast component using small time steps */
    for (i = 0; i < s; i++) {
      /* stage value for slow components */
      PetscCall(TSInterpolate_RK_MultirateSplit(rk->ts_root, t + k * h / rk->dtratio + h / rk->dtratio * c[i], Y[i]));
      currentlevelts = rk->ts_root;
      while (currentlevelts != ts) { /* all the slow parts need to be interpolated separated */
        currentlevelts = ((TS_RK *)currentlevelts->data)->subts_fast;
        PetscCall(TSInterpolate_RK_MultirateSplit(currentlevelts, t + k * h / rk->dtratio + h / rk->dtratio * c[i], Y[i]));
      }
      for (j = 0; j < i; j++) w[j] = h / rk->dtratio * A[i * s + j];
      subrk_fast->stage_time = t + h / rk->dtratio * c[i];
      PetscCall(TSPreStage(subts_fast, subrk_fast->stage_time));
      /* stage value for fast components */
      PetscCall(VecGetSubVector(Y[i], rk->is_fast, &Yfast));
      PetscCall(VecCopy(Xfast, Yfast));
      PetscCall(VecMAXPY(Yfast, i, w, YdotRHS_fast));
      PetscCall(VecRestoreSubVector(Y[i], rk->is_fast, &Yfast));
      PetscCall(TSPostStage(subts_fast, subrk_fast->stage_time, i, Y));
      /* compute the stage RHS for fast components */
      PetscCall(TSComputeRHSFunction(subts_fast, t + k * h * rk->dtratio + h / rk->dtratio * c[i], Y[i], YdotRHS_fast[i]));
    }
    PetscCall(VecRestoreSubVector(ts->vec_sol, rk->is_fast, &Xfast));
    /* update the value of fast components using fast time step */
    rk->slow = PETSC_FALSE;
    PetscCall(TSEvaluateStep_RK_MultirateSplit(ts, tab->order, ts->vec_sol, NULL));
    for (i = 0; i < s; i++) PetscCall(VecRestoreSubVector(YdotRHS[i], rk->is_fast, &YdotRHS_fast[i]));

    if (subrk_fast->subts_fast) {
      subts_fast->ptime     = t + k * h / rk->dtratio;
      subts_fast->time_step = h / rk->dtratio;
      PetscCall(TSStepRefine_RK_MultirateSplit(subts_fast));
    }
    /* update the fast components of the solution */
    PetscCall(VecGetSubVector(ts->vec_sol, rk->is_fast, &Xfast));
    PetscCall(VecISCopy(rk->X0, rk->is_fast, SCATTER_FORWARD, Xfast));
    PetscCall(VecRestoreSubVector(ts->vec_sol, rk->is_fast, &Xfast));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TSStep_RK_MultirateSplit(TS ts)
{
  TS_RK           *rk  = (TS_RK *)ts->data;
  RKTableau        tab = rk->tableau;
  Vec             *Y = rk->Y, *YdotRHS = rk->YdotRHS;
  Vec             *YdotRHS_fast = rk->YdotRHS_fast, *YdotRHS_slow = rk->YdotRHS_slow;
  Vec              Yslow, Yfast; /* subvectors store the stges of slow components and fast components respectively                           */
  const PetscInt   s = tab->s;
  const PetscReal *A = tab->A, *c = tab->c;
  PetscScalar     *w = rk->work;
  PetscInt         i, j;
  PetscReal        next_time_step = ts->time_step, t = ts->ptime, h = ts->time_step;

  PetscFunctionBegin;
  rk->status = TS_STEP_INCOMPLETE;
  for (i = 0; i < s; i++) {
    PetscCall(VecGetSubVector(YdotRHS[i], rk->is_slow, &YdotRHS_slow[i]));
    PetscCall(VecGetSubVector(YdotRHS[i], rk->is_fast, &YdotRHS_fast[i]));
  }
  PetscCall(VecCopy(ts->vec_sol, rk->X0));
  /* propagate both slow and fast components using large time steps */
  for (i = 0; i < s; i++) {
    rk->stage_time = t + h * c[i];
    PetscCall(TSPreStage(ts, rk->stage_time));
    PetscCall(VecCopy(ts->vec_sol, Y[i]));
    PetscCall(VecGetSubVector(Y[i], rk->is_fast, &Yfast));
    PetscCall(VecGetSubVector(Y[i], rk->is_slow, &Yslow));
    for (j = 0; j < i; j++) w[j] = h * A[i * s + j];
    PetscCall(VecMAXPY(Yfast, i, w, YdotRHS_fast));
    PetscCall(VecMAXPY(Yslow, i, w, YdotRHS_slow));
    PetscCall(VecRestoreSubVector(Y[i], rk->is_fast, &Yfast));
    PetscCall(VecRestoreSubVector(Y[i], rk->is_slow, &Yslow));
    PetscCall(TSPostStage(ts, rk->stage_time, i, Y));
    PetscCall(TSComputeRHSFunction(rk->subts_slow, t + h * c[i], Y[i], YdotRHS_slow[i]));
    PetscCall(TSComputeRHSFunction(rk->subts_fast, t + h * c[i], Y[i], YdotRHS_fast[i]));
  }
  rk->slow = PETSC_TRUE;
  /* update the slow components of the solution using slow time step */
  PetscCall(TSEvaluateStep_RK_MultirateSplit(ts, tab->order, ts->vec_sol, NULL));
  /* YdotRHS will be used for interpolation during refinement */
  for (i = 0; i < s; i++) {
    PetscCall(VecRestoreSubVector(YdotRHS[i], rk->is_slow, &YdotRHS_slow[i]));
    PetscCall(VecRestoreSubVector(YdotRHS[i], rk->is_fast, &YdotRHS_fast[i]));
  }

  PetscCall(TSStepRefine_RK_MultirateSplit(ts));

  ts->ptime     = t + ts->time_step;
  ts->time_step = next_time_step;
  rk->status    = TS_STEP_COMPLETE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TSSetUp_RK_MultirateSplit(TS ts)
{
  TS_RK *rk = (TS_RK *)ts->data, *nextlevelrk, *currentlevelrk;
  TS     nextlevelts;
  Vec    X0;

  PetscFunctionBegin;
  PetscCall(TSRHSSplitGetIS(ts, "slow", &rk->is_slow));
  PetscCall(TSRHSSplitGetIS(ts, "fast", &rk->is_fast));
  PetscCheck(rk->is_slow && rk->is_fast, PetscObjectComm((PetscObject)ts), PETSC_ERR_USER, "Must set up RHSSplits with TSRHSSplitSetIS() using split names 'slow' and 'fast' respectively in order to use -ts_type bsi");
  PetscCall(TSRHSSplitGetSubTS(ts, "slow", &rk->subts_slow));
  PetscCall(TSRHSSplitGetSubTS(ts, "fast", &rk->subts_fast));
  PetscCheck(rk->subts_slow && rk->subts_fast, PetscObjectComm((PetscObject)ts), PETSC_ERR_USER, "Must set up the RHSFunctions for 'slow' and 'fast' components using TSRHSSplitSetRHSFunction() or calling TSSetRHSFunction() for each sub-TS");

  PetscCall(VecDuplicate(ts->vec_sol, &X0));
  /* The TS at each level share the same tableau, work array, solution vector, stage values and stage derivatives */
  currentlevelrk = rk;
  while (currentlevelrk->subts_fast) {
    PetscCall(PetscMalloc1(rk->tableau->s, &currentlevelrk->YdotRHS_fast));
    PetscCall(PetscMalloc1(rk->tableau->s, &currentlevelrk->YdotRHS_slow));
    PetscCall(PetscObjectReference((PetscObject)X0));
    currentlevelrk->X0      = X0;
    currentlevelrk->ts_root = ts;

    /* set up the ts for the slow part */
    nextlevelts = currentlevelrk->subts_slow;
    PetscCall(PetscNew(&nextlevelrk));
    nextlevelrk->tableau = rk->tableau;
    nextlevelrk->work    = rk->work;
    nextlevelrk->Y       = rk->Y;
    nextlevelrk->YdotRHS = rk->YdotRHS;
    nextlevelts->data    = (void *)nextlevelrk;
    PetscCall(TSCopyDM(ts, nextlevelts));
    PetscCall(TSSetSolution(nextlevelts, ts->vec_sol));

    /* set up the ts for the fast part */
    nextlevelts = currentlevelrk->subts_fast;
    PetscCall(PetscNew(&nextlevelrk));
    nextlevelrk->tableau = rk->tableau;
    nextlevelrk->work    = rk->work;
    nextlevelrk->Y       = rk->Y;
    nextlevelrk->YdotRHS = rk->YdotRHS;
    nextlevelrk->dtratio = rk->dtratio;
    PetscCall(TSRHSSplitGetIS(nextlevelts, "slow", &nextlevelrk->is_slow));
    PetscCall(TSRHSSplitGetSubTS(nextlevelts, "slow", &nextlevelrk->subts_slow));
    PetscCall(TSRHSSplitGetIS(nextlevelts, "fast", &nextlevelrk->is_fast));
    PetscCall(TSRHSSplitGetSubTS(nextlevelts, "fast", &nextlevelrk->subts_fast));
    nextlevelts->data = (void *)nextlevelrk;
    PetscCall(TSCopyDM(ts, nextlevelts));
    PetscCall(TSSetSolution(nextlevelts, ts->vec_sol));

    currentlevelrk = nextlevelrk;
  }
  PetscCall(VecDestroy(&X0));

  ts->ops->step         = TSStep_RK_MultirateSplit;
  ts->ops->evaluatestep = TSEvaluateStep_RK_MultirateSplit;
  ts->ops->interpolate  = TSInterpolate_RK_MultirateSplit;
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode TSRKSetMultirate_RK(TS ts, PetscBool use_multirate)
{
  TS_RK *rk = (TS_RK *)ts->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts, TS_CLASSID, 1);
  rk->use_multirate = use_multirate;
  if (use_multirate) {
    rk->dtratio = 2;
    PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSSetUp_RK_MultirateSplit_C", TSSetUp_RK_MultirateSplit));
    PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSReset_RK_MultirateSplit_C", TSReset_RK_MultirateSplit));
    PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSSetUp_RK_MultirateNonsplit_C", TSSetUp_RK_MultirateNonsplit));
    PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSReset_RK_MultirateNonsplit_C", TSReset_RK_MultirateNonsplit));
  } else {
    rk->dtratio = 0;
    PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSSetUp_RK_MultirateSplit_C", NULL));
    PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSReset_RK_MultirateSplit_C", NULL));
    PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSSetUp_RK_MultirateNonsplit_C", NULL));
    PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSReset_RK_MultirateNonsplit_C", NULL));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode TSRKGetMultirate_RK(TS ts, PetscBool *use_multirate)
{
  TS_RK *rk = (TS_RK *)ts->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts, TS_CLASSID, 1);
  *use_multirate = rk->use_multirate;
  PetscFunctionReturn(PETSC_SUCCESS);
}