xref: /petsc/src/ts/impls/implicit/discgrad/tsdiscgrad.c (revision dadcf80911fb48939c55327431ae8d7e47dbe367)

/*
  Code for timestepping with discrete gradient integrators
*/
#include <petsc/private/tsimpl.h>                /*I   "petscts.h"   I*/
#include <petscdm.h>

PetscBool DGCite = PETSC_FALSE;
const char DGCitation[] = "@article{Gonzalez1996,\n"
                          "  title   = {Time integration and discrete Hamiltonian systems},\n"
                          "  author  = {Oscar Gonzalez},\n"
                          "  journal = {Journal of Nonlinear Science},\n"
                          "  volume  = {6},\n"
                          "  pages   = {449--467},\n"
                          "  doi     = {10.1007/978-1-4612-1246-1_10},\n"
                          "  year    = {1996}\n}\n";

typedef struct {
  PetscReal    stage_time;
  Vec          X0, X, Xdot;
  void        *funcCtx;
  PetscBool    gonzalez;
  PetscErrorCode (*Sfunc)(TS, PetscReal, Vec, Mat, void *);
  PetscErrorCode (*Ffunc)(TS, PetscReal, Vec, PetscScalar *, void *);
  PetscErrorCode (*Gfunc)(TS, PetscReal, Vec, Vec, void *);
} TS_DiscGrad;

static PetscErrorCode TSDiscGradGetX0AndXdot(TS ts, DM dm, Vec *X0, Vec *Xdot)
{
  TS_DiscGrad   *dg = (TS_DiscGrad *) ts->data;

  PetscFunctionBegin;
  if (X0) {
    if (dm && dm != ts->dm) CHKERRQ(DMGetNamedGlobalVector(dm, "TSDiscGrad_X0", X0));
    else                    {*X0  = ts->vec_sol;}
  }
  if (Xdot) {
    if (dm && dm != ts->dm) CHKERRQ(DMGetNamedGlobalVector(dm, "TSDiscGrad_Xdot", Xdot));
    else                    {*Xdot = dg->Xdot;}
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode TSDiscGradRestoreX0AndXdot(TS ts, DM dm, Vec *X0, Vec *Xdot)
{
  PetscFunctionBegin;
  if (X0) {
    if (dm && dm != ts->dm) CHKERRQ(DMRestoreNamedGlobalVector(dm, "TSDiscGrad_X0", X0));
  }
  if (Xdot) {
    if (dm && dm != ts->dm) CHKERRQ(DMRestoreNamedGlobalVector(dm, "TSDiscGrad_Xdot", Xdot));
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode DMCoarsenHook_TSDiscGrad(DM fine, DM coarse, void *ctx)
{
  PetscFunctionBegin;
  PetscFunctionReturn(0);
}

static PetscErrorCode DMRestrictHook_TSDiscGrad(DM fine, Mat restrct, Vec rscale, Mat inject, DM coarse, void *ctx)
{
  TS             ts = (TS) ctx;
  Vec            X0, Xdot, X0_c, Xdot_c;

  PetscFunctionBegin;
  CHKERRQ(TSDiscGradGetX0AndXdot(ts, fine, &X0, &Xdot));
  CHKERRQ(TSDiscGradGetX0AndXdot(ts, coarse, &X0_c, &Xdot_c));
  CHKERRQ(MatRestrict(restrct, X0, X0_c));
  CHKERRQ(MatRestrict(restrct, Xdot, Xdot_c));
  CHKERRQ(VecPointwiseMult(X0_c, rscale, X0_c));
  CHKERRQ(VecPointwiseMult(Xdot_c, rscale, Xdot_c));
  CHKERRQ(TSDiscGradRestoreX0AndXdot(ts, fine, &X0, &Xdot));
  CHKERRQ(TSDiscGradRestoreX0AndXdot(ts, coarse, &X0_c, &Xdot_c));
  PetscFunctionReturn(0);
}

static PetscErrorCode DMSubDomainHook_TSDiscGrad(DM dm, DM subdm, void *ctx)
{
  PetscFunctionBegin;
  PetscFunctionReturn(0);
}

static PetscErrorCode DMSubDomainRestrictHook_TSDiscGrad(DM dm, VecScatter gscat, VecScatter lscat, DM subdm, void *ctx)
{
  TS             ts = (TS) ctx;
  Vec            X0, Xdot, X0_sub, Xdot_sub;

  PetscFunctionBegin;
  CHKERRQ(TSDiscGradGetX0AndXdot(ts, dm, &X0, &Xdot));
  CHKERRQ(TSDiscGradGetX0AndXdot(ts, subdm, &X0_sub, &Xdot_sub));

  CHKERRQ(VecScatterBegin(gscat, X0, X0_sub, INSERT_VALUES, SCATTER_FORWARD));
  CHKERRQ(VecScatterEnd(gscat, X0, X0_sub, INSERT_VALUES, SCATTER_FORWARD));

  CHKERRQ(VecScatterBegin(gscat, Xdot, Xdot_sub, INSERT_VALUES, SCATTER_FORWARD));
  CHKERRQ(VecScatterEnd(gscat, Xdot, Xdot_sub, INSERT_VALUES, SCATTER_FORWARD));

  CHKERRQ(TSDiscGradRestoreX0AndXdot(ts, dm, &X0, &Xdot));
  CHKERRQ(TSDiscGradRestoreX0AndXdot(ts, subdm, &X0_sub, &Xdot_sub));
  PetscFunctionReturn(0);
}

static PetscErrorCode TSSetUp_DiscGrad(TS ts)
{
  TS_DiscGrad   *dg = (TS_DiscGrad *) ts->data;
  DM             dm;

  PetscFunctionBegin;
  if (!dg->X)    CHKERRQ(VecDuplicate(ts->vec_sol, &dg->X));
  if (!dg->X0)   CHKERRQ(VecDuplicate(ts->vec_sol, &dg->X0));
  if (!dg->Xdot) CHKERRQ(VecDuplicate(ts->vec_sol, &dg->Xdot));

  CHKERRQ(TSGetDM(ts, &dm));
  CHKERRQ(DMCoarsenHookAdd(dm, DMCoarsenHook_TSDiscGrad, DMRestrictHook_TSDiscGrad, ts));
  CHKERRQ(DMSubDomainHookAdd(dm, DMSubDomainHook_TSDiscGrad, DMSubDomainRestrictHook_TSDiscGrad, ts));
  PetscFunctionReturn(0);
}

static PetscErrorCode TSSetFromOptions_DiscGrad(PetscOptionItems *PetscOptionsObject, TS ts)
{
  TS_DiscGrad   *dg = (TS_DiscGrad *) ts->data;

  PetscFunctionBegin;
  CHKERRQ(PetscOptionsHead(PetscOptionsObject, "Discrete Gradients ODE solver options"));
  {
    CHKERRQ(PetscOptionsBool("-ts_discgrad_gonzalez","Use Gonzalez term in discrete gradients formulation","TSDiscGradUseGonzalez",dg->gonzalez,&dg->gonzalez,NULL));
  }
  CHKERRQ(PetscOptionsTail());
  PetscFunctionReturn(0);
}

static PetscErrorCode TSView_DiscGrad(TS ts,PetscViewer viewer)
{
  PetscBool      iascii;

  PetscFunctionBegin;
  CHKERRQ(PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii));
  if (iascii) {
    CHKERRQ(PetscViewerASCIIPrintf(viewer,"  Discrete Gradients\n"));
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode TSDiscGradIsGonzalez_DiscGrad(TS ts,PetscBool *gonzalez)
{
  TS_DiscGrad *dg = (TS_DiscGrad*)ts->data;

  PetscFunctionBegin;
  *gonzalez = dg->gonzalez;
  PetscFunctionReturn(0);
}

static PetscErrorCode TSDiscGradUseGonzalez_DiscGrad(TS ts,PetscBool flg)
{
  TS_DiscGrad *dg = (TS_DiscGrad*)ts->data;

  PetscFunctionBegin;
  dg->gonzalez = flg;
  PetscFunctionReturn(0);
}

static PetscErrorCode TSReset_DiscGrad(TS ts)
{
  TS_DiscGrad   *dg = (TS_DiscGrad *) ts->data;

  PetscFunctionBegin;
  CHKERRQ(VecDestroy(&dg->X));
  CHKERRQ(VecDestroy(&dg->X0));
  CHKERRQ(VecDestroy(&dg->Xdot));
  PetscFunctionReturn(0);
}

static PetscErrorCode TSDestroy_DiscGrad(TS ts)
{
  DM             dm;

  PetscFunctionBegin;
  CHKERRQ(TSReset_DiscGrad(ts));
  CHKERRQ(TSGetDM(ts, &dm));
  if (dm) {
    CHKERRQ(DMCoarsenHookRemove(dm, DMCoarsenHook_TSDiscGrad, DMRestrictHook_TSDiscGrad, ts));
    CHKERRQ(DMSubDomainHookRemove(dm, DMSubDomainHook_TSDiscGrad, DMSubDomainRestrictHook_TSDiscGrad, ts));
  }
  CHKERRQ(PetscFree(ts->data));
  CHKERRQ(PetscObjectComposeFunction((PetscObject)ts,"TSDiscGradGetFormulation_C",NULL));
  CHKERRQ(PetscObjectComposeFunction((PetscObject)ts,"TSDiscGradSetFormulation_C",NULL));
  PetscFunctionReturn(0);
}

static PetscErrorCode TSInterpolate_DiscGrad(TS ts, PetscReal t, Vec X)
{
  TS_DiscGrad   *dg = (TS_DiscGrad*)ts->data;
  PetscReal      dt = t - ts->ptime;

  PetscFunctionBegin;
  CHKERRQ(VecCopy(ts->vec_sol, dg->X));
  CHKERRQ(VecWAXPY(X, dt, dg->Xdot, dg->X));
  PetscFunctionReturn(0);
}

static PetscErrorCode TSDiscGrad_SNESSolve(TS ts, Vec b, Vec x)
{
  SNES           snes;
  PetscInt       nits, lits;

  PetscFunctionBegin;
  CHKERRQ(TSGetSNES(ts, &snes));
  CHKERRQ(SNESSolve(snes, b, x));
  CHKERRQ(SNESGetIterationNumber(snes, &nits));
  CHKERRQ(SNESGetLinearSolveIterations(snes, &lits));
  ts->snes_its += nits;
  ts->ksp_its  += lits;
  PetscFunctionReturn(0);
}

static PetscErrorCode TSStep_DiscGrad(TS ts)
{
  TS_DiscGrad   *dg = (TS_DiscGrad *) ts->data;
  TSAdapt        adapt;
  TSStepStatus   status          = TS_STEP_INCOMPLETE;
  PetscInt       rejections      = 0;
  PetscBool      stageok, accept = PETSC_TRUE;
  PetscReal      next_time_step  = ts->time_step;

  PetscFunctionBegin;
  CHKERRQ(TSGetAdapt(ts, &adapt));
  if (!ts->steprollback) CHKERRQ(VecCopy(ts->vec_sol, dg->X0));

  while (!ts->reason && status != TS_STEP_COMPLETE) {
    PetscReal shift = 1/(0.5*ts->time_step);

    dg->stage_time = ts->ptime + 0.5*ts->time_step;

    CHKERRQ(VecCopy(dg->X0, dg->X));
    CHKERRQ(TSPreStage(ts, dg->stage_time));
    CHKERRQ(TSDiscGrad_SNESSolve(ts, NULL, dg->X));
    CHKERRQ(TSPostStage(ts, dg->stage_time, 0, &dg->X));
    CHKERRQ(TSAdaptCheckStage(adapt, ts, dg->stage_time, dg->X, &stageok));
    if (!stageok) goto reject_step;

    status = TS_STEP_PENDING;
    CHKERRQ(VecAXPBYPCZ(dg->Xdot, -shift, shift, 0, dg->X0, dg->X));
    CHKERRQ(VecAXPY(ts->vec_sol, ts->time_step, dg->Xdot));
    CHKERRQ(TSAdaptChoose(adapt, ts, ts->time_step, NULL, &next_time_step, &accept));
    status = accept ? TS_STEP_COMPLETE : TS_STEP_INCOMPLETE;
    if (!accept) {
      CHKERRQ(VecCopy(dg->X0, ts->vec_sol));
      ts->time_step = next_time_step;
      goto reject_step;
    }
    ts->ptime    += ts->time_step;
    ts->time_step = next_time_step;
    break;

  reject_step:
    ts->reject++; accept = PETSC_FALSE;
    if (!ts->reason && ts->max_reject >= 0 && ++rejections > ts->max_reject) {
      ts->reason = TS_DIVERGED_STEP_REJECTED;
      CHKERRQ(PetscInfo(ts, "Step=%D, step rejections %D greater than current TS allowed, stopping solve\n", ts->steps, rejections));
    }
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode TSGetStages_DiscGrad(TS ts, PetscInt *ns, Vec **Y)
{
  TS_DiscGrad *dg = (TS_DiscGrad *) ts->data;

  PetscFunctionBegin;
  if (ns) *ns = 1;
  if (Y)  *Y  = &(dg->X);
  PetscFunctionReturn(0);
}

/*
  This defines the nonlinear equation that is to be solved with SNES
    G(U) = F[t0 + 0.5*dt, U, (U-U0)/dt] = 0
*/

/* x = (x+x')/2 */
/* NEED TO CALCULATE x_{n+1} from x and x_{n}*/
static PetscErrorCode SNESTSFormFunction_DiscGrad(SNES snes, Vec x, Vec y, TS ts)
{

  TS_DiscGrad   *dg    = (TS_DiscGrad *) ts->data;
  PetscReal      norm, shift = 1/(0.5*ts->time_step);
  PetscInt       n;
  Vec            X0, Xdot, Xp, Xdiff;
  Mat            S;
  PetscScalar    F=0, F0=0, Gp;
  Vec            G, SgF;
  DM             dm, dmsave;

  PetscFunctionBegin;
  CHKERRQ(SNESGetDM(snes, &dm));

  CHKERRQ(VecDuplicate(y, &Xp));
  CHKERRQ(VecDuplicate(y, &Xdiff));
  CHKERRQ(VecDuplicate(y, &SgF));
  CHKERRQ(VecDuplicate(y, &G));

  CHKERRQ(VecGetLocalSize(y, &n));
  CHKERRQ(MatCreate(PETSC_COMM_WORLD, &S));
  CHKERRQ(MatSetSizes(S, PETSC_DECIDE, PETSC_DECIDE, n, n));
  CHKERRQ(MatSetFromOptions(S));
  CHKERRQ(MatSetUp(S));
  CHKERRQ(MatAssemblyBegin(S,MAT_FINAL_ASSEMBLY));
  CHKERRQ(MatAssemblyEnd(S,MAT_FINAL_ASSEMBLY));

  CHKERRQ(TSDiscGradGetX0AndXdot(ts, dm, &X0, &Xdot));
  CHKERRQ(VecAXPBYPCZ(Xdot, -shift, shift, 0, X0, x)); /* Xdot = shift (x - X0) */

  CHKERRQ(VecAXPBYPCZ(Xp, -1, 2, 0, X0, x)); /* Xp = 2*x - X0 + (0)*Xmid */
  CHKERRQ(VecAXPBYPCZ(Xdiff, -1, 1, 0, X0, Xp)); /* Xdiff = xp - X0 + (0)*Xdiff */

  if (dg->gonzalez) {
    CHKERRQ((*dg->Sfunc)(ts, dg->stage_time, x ,   S,  dg->funcCtx));
    CHKERRQ((*dg->Ffunc)(ts, dg->stage_time, Xp,  &F,  dg->funcCtx));
    CHKERRQ((*dg->Ffunc)(ts, dg->stage_time, X0,  &F0, dg->funcCtx));
    CHKERRQ((*dg->Gfunc)(ts, dg->stage_time, x ,   G,  dg->funcCtx));

    /* Adding Extra Gonzalez Term */
    CHKERRQ(VecDot(Xdiff, G, &Gp));
    CHKERRQ(VecNorm(Xdiff, NORM_2, &norm));
    if (norm < PETSC_SQRT_MACHINE_EPSILON) {
      Gp = 0;
    } else {
      /* Gp = (1/|xn+1 - xn|^2) * (F(xn+1) - F(xn) - Gp) */
      Gp = (F - F0 - Gp)/PetscSqr(norm);
    }
    CHKERRQ(VecAXPY(G, Gp, Xdiff));
    CHKERRQ(MatMult(S, G , SgF)); /* S*gradF */

  } else {
    CHKERRQ((*dg->Sfunc)(ts, dg->stage_time, x, S,  dg->funcCtx));
    CHKERRQ((*dg->Gfunc)(ts, dg->stage_time, x, G,  dg->funcCtx));

    CHKERRQ(MatMult(S, G , SgF)); /* Xdot = S*gradF */
  }
  /* DM monkey-business allows user code to call TSGetDM() inside of functions evaluated on levels of FAS */
  dmsave = ts->dm;
  ts->dm = dm;
  CHKERRQ(VecAXPBYPCZ(y, 1, -1, 0, Xdot, SgF));
  ts->dm = dmsave;
  CHKERRQ(TSDiscGradRestoreX0AndXdot(ts, dm, &X0, &Xdot));

  CHKERRQ(VecDestroy(&Xp));
  CHKERRQ(VecDestroy(&Xdiff));
  CHKERRQ(VecDestroy(&SgF));
  CHKERRQ(VecDestroy(&G));
  CHKERRQ(MatDestroy(&S));

  PetscFunctionReturn(0);
}

static PetscErrorCode SNESTSFormJacobian_DiscGrad(SNES snes, Vec x, Mat A, Mat B, TS ts)
{
  TS_DiscGrad   *dg    = (TS_DiscGrad *) ts->data;
  PetscReal      shift = 1/(0.5*ts->time_step);
  Vec            Xdot;
  DM             dm,dmsave;

  PetscFunctionBegin;
  CHKERRQ(SNESGetDM(snes, &dm));
  /* Xdot has already been computed in SNESTSFormFunction_DiscGrad (SNES guarantees this) */
  CHKERRQ(TSDiscGradGetX0AndXdot(ts, dm, NULL, &Xdot));

  dmsave = ts->dm;
  ts->dm = dm;
  CHKERRQ(TSComputeIJacobian(ts, dg->stage_time, x, Xdot, shift, A, B, PETSC_FALSE));
  ts->dm = dmsave;
  CHKERRQ(TSDiscGradRestoreX0AndXdot(ts, dm, NULL, &Xdot));
  PetscFunctionReturn(0);
}

static PetscErrorCode TSDiscGradGetFormulation_DiscGrad(TS ts, PetscErrorCode (**Sfunc)(TS, PetscReal, Vec, Mat, void *), PetscErrorCode (**Ffunc)(TS, PetscReal, Vec, PetscScalar *, void *), PetscErrorCode (**Gfunc)(TS, PetscReal, Vec, Vec, void *), void *ctx)
{
  TS_DiscGrad *dg = (TS_DiscGrad *) ts->data;

  PetscFunctionBegin;
  *Sfunc = dg->Sfunc;
  *Ffunc = dg->Ffunc;
  *Gfunc = dg->Gfunc;
  PetscFunctionReturn(0);
}

static PetscErrorCode TSDiscGradSetFormulation_DiscGrad(TS ts, PetscErrorCode (*Sfunc)(TS, PetscReal, Vec, Mat, void *), PetscErrorCode (*Ffunc)(TS, PetscReal, Vec, PetscScalar *, void *), PetscErrorCode (*Gfunc)(TS, PetscReal, Vec, Vec, void *), void *ctx)
{
  TS_DiscGrad *dg = (TS_DiscGrad *) ts->data;

  PetscFunctionBegin;
  dg->Sfunc = Sfunc;
  dg->Ffunc = Ffunc;
  dg->Gfunc = Gfunc;
  dg->funcCtx = ctx;
  PetscFunctionReturn(0);
}

/*MC
  TSDISCGRAD - ODE solver using the discrete gradients version of the implicit midpoint method

  Notes:
  This is the implicit midpoint rule, with an optional term that guarantees the discrete gradient property. This
  timestepper applies to systems of the form
$ u_t = S(u) grad F(u)
  where S(u) is a linear operator, and F is a functional of u.

  Level: intermediate

.seealso: TSCreate(), TSSetType(), TS, TSDISCGRAD, TSDiscGradSetFormulation()
M*/
PETSC_EXTERN PetscErrorCode TSCreate_DiscGrad(TS ts)
{
  TS_DiscGrad       *th;

  PetscFunctionBegin;
  CHKERRQ(PetscCitationsRegister(DGCitation, &DGCite));
  ts->ops->reset           = TSReset_DiscGrad;
  ts->ops->destroy         = TSDestroy_DiscGrad;
  ts->ops->view            = TSView_DiscGrad;
  ts->ops->setfromoptions  = TSSetFromOptions_DiscGrad;
  ts->ops->setup           = TSSetUp_DiscGrad;
  ts->ops->step            = TSStep_DiscGrad;
  ts->ops->interpolate     = TSInterpolate_DiscGrad;
  ts->ops->getstages       = TSGetStages_DiscGrad;
  ts->ops->snesfunction    = SNESTSFormFunction_DiscGrad;
  ts->ops->snesjacobian    = SNESTSFormJacobian_DiscGrad;
  ts->default_adapt_type   = TSADAPTNONE;

  ts->usessnes = PETSC_TRUE;

  CHKERRQ(PetscNewLog(ts,&th));
  ts->data = (void*)th;

  th->gonzalez = PETSC_FALSE;

  CHKERRQ(PetscObjectComposeFunction((PetscObject)ts,"TSDiscGradGetFormulation_C",TSDiscGradGetFormulation_DiscGrad));
  CHKERRQ(PetscObjectComposeFunction((PetscObject)ts,"TSDiscGradSetFormulation_C",TSDiscGradSetFormulation_DiscGrad));
  CHKERRQ(PetscObjectComposeFunction((PetscObject)ts,"TSDiscGradIsGonzalez_C",TSDiscGradIsGonzalez_DiscGrad));
  CHKERRQ(PetscObjectComposeFunction((PetscObject)ts,"TSDiscGradUseGonzalez_C",TSDiscGradUseGonzalez_DiscGrad));
  PetscFunctionReturn(0);
}

/*@C
  TSDiscGradGetFormulation - Get the construction method for S, F, and grad F from the formulation u_t = S grad F

  Not Collective

  Input Parameter:
. ts - timestepping context

  Output Parameters:
+ Sfunc - constructor for the S matrix from the formulation
. Ffunc - functional F from the formulation
. Gfunc - constructor for the gradient of F from the formulation
- ctx   - the user context

  Calling sequence of Sfunc:
$ PetscErrorCode func(TS ts, PetscReal time, Vec u, Mat S, void *)

  Calling sequence of Ffunc:
$ PetscErrorCode func(TS ts, PetscReal time, Vec u, PetscScalar *F, void *)

  Calling sequence of Gfunc:
$ PetscErrorCode func(TS ts, PetscReal time, Vec u, Vec G, void *)

  Level: intermediate

.seealso: TSDiscGradSetFormulation()
@*/
PetscErrorCode TSDiscGradGetFormulation(TS ts, PetscErrorCode (**Sfunc)(TS, PetscReal, Vec, Mat, void *), PetscErrorCode (**Ffunc)(TS, PetscReal, Vec, PetscScalar *, void *), PetscErrorCode (**Gfunc)(TS, PetscReal, Vec, Vec, void *), void *ctx)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts, TS_CLASSID, 1);
  PetscValidPointer(Sfunc, 2);
  PetscValidPointer(Ffunc, 3);
  PetscValidPointer(Gfunc, 4);
  CHKERRQ(PetscUseMethod(ts,"TSDiscGradGetFormulation_C",(TS,PetscErrorCode(**Sfunc)(TS,PetscReal,Vec,Mat,void*),PetscErrorCode(**Ffunc)(TS,PetscReal,Vec,PetscScalar*,void*),PetscErrorCode(**Gfunc)(TS,PetscReal,Vec,Vec,void*), void*),(ts,Sfunc,Ffunc,Gfunc,ctx)));
  PetscFunctionReturn(0);
}

/*@C
  TSDiscGradSetFormulation - Set the construction method for S, F, and grad F from the formulation u_t = S(u) grad F(u)

  Not Collective

  Input Parameters:
+ ts    - timestepping context
. Sfunc - constructor for the S matrix from the formulation
. Ffunc - functional F from the formulation
- Gfunc - constructor for the gradient of F from the formulation
  Calling sequence of Sfunc:
$ PetscErrorCode func(TS ts, PetscReal time, Vec u, Mat S, void *)

  Calling sequence of Ffunc:
$ PetscErrorCode func(TS ts, PetscReal time, Vec u, PetscScalar *F, void *)

  Calling sequence of Gfunc:
$ PetscErrorCode func(TS ts, PetscReal time, Vec u, Vec G, void *)

  Level: Intermediate

.seealso: TSDiscGradGetFormulation()
@*/
PetscErrorCode TSDiscGradSetFormulation(TS ts, PetscErrorCode (*Sfunc)(TS, PetscReal, Vec, Mat, void *), PetscErrorCode (*Ffunc)(TS, PetscReal, Vec , PetscScalar *, void *), PetscErrorCode (*Gfunc)(TS, PetscReal, Vec, Vec, void *), void *ctx)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts, TS_CLASSID, 1);
  PetscValidFunction(Sfunc, 2);
  PetscValidFunction(Ffunc, 3);
  PetscValidFunction(Gfunc, 4);
  CHKERRQ(PetscTryMethod(ts,"TSDiscGradSetFormulation_C",(TS,PetscErrorCode(*Sfunc)(TS,PetscReal,Vec,Mat,void*),PetscErrorCode(*Ffunc)(TS,PetscReal,Vec,PetscScalar*,void*),PetscErrorCode(*Gfunc)(TS,PetscReal,Vec,Vec,void*), void*),(ts,Sfunc,Ffunc,Gfunc,ctx)));
  PetscFunctionReturn(0);
}

/*@
  TSDiscGradIsGonzalez - Checks flag for whether to use additional conservative terms in discrete gradient formulation.

  Not Collective

  Input Parameter:
.  ts - timestepping context

  Output Parameter:
.  gonzalez - PETSC_TRUE when using the Gonzalez term

  Level: Advanced

.seealso: TSDiscGradUseGonzalez(), TSDISCGRAD
@*/
PetscErrorCode TSDiscGradIsGonzalez(TS ts,PetscBool *gonzalez)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidBoolPointer(gonzalez,2);
  CHKERRQ(PetscUseMethod(ts,"TSDiscGradIsGonzalez_C",(TS,PetscBool*),(ts,gonzalez)));
  PetscFunctionReturn(0);
}

/*@
  TSDiscGradUseGonzalez - Sets discrete gradient formulation with or without additional conservative terms.  Without flag, the discrete gradients timestepper is just backwards euler

  Not Collective

  Input Parameters:
+ ts - timestepping context
- flg - PETSC_TRUE to use the Gonzalez term

  Options Database:
. -ts_discgrad_gonzalez <flg> - use the Gonzalez term for the discrete gradient formulation

  Level: Intermediate

.seealso: TSDISCGRAD
@*/
PetscErrorCode TSDiscGradUseGonzalez(TS ts,PetscBool flg)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  CHKERRQ(PetscTryMethod(ts,"TSDiscGradUseGonzalez_C",(TS,PetscBool),(ts,flg)));
  PetscFunctionReturn(0);
}