[petsc-users] TS question 1: how to stop explicit methods because they do not use SNES(VI)?

[Barry Smith]

> On Feb 13, 2017, at 3:08 PM, Ed Bueler <elbueler at alaska.edu> wrote:
> 
> Barry --
> 
> >   Sounds like a bug to me. The methods should be checking if an
> > IFunction is being provided and error out in that case.
> 
> I don't think it is that simple.  I.e. having an IFunction and an explicit scheme is not, by itself, a bug.  I think.
> 
> If the user has provided IFunction
>    F(t,u,u_t) = u_t - f(t,u)
> which is the convenient form for e.g. TSARKIMEX,
> and RHSFunction
>   G(t,u)
> then I guess I assumed that explicit methods like TSRK should,for unconstrained cases, get their RHS by callback like this:
>   g(t,u) = - F(t,u,0) + G(t,u)
> so that the ODE is in form
>   u_t = g(t,u) = f(t,u) + g(t,u)

I guess in theory TSRK could do this but looking at the code

static PetscErrorCode TSStep_RK(TS ts)
{
  TS_RK           *rk   = (TS_RK*)ts->data;
  RKTableau        tab  = rk->tableau;
  const PetscInt   s = tab->s;
  const PetscReal *A = tab->A,*c = tab->c;
  PetscScalar     *w = rk->work;
  Vec             *Y = rk->Y,*YdotRHS = rk->YdotRHS;
  TSAdapt          adapt;
  PetscInt         i,j;
  PetscInt         rejections = 0;
  PetscBool        stageok,accept = PETSC_TRUE;
  PetscReal        next_time_step = ts->time_step;
  PetscErrorCode   ierr;

  PetscFunctionBegin;

  rk->status = TS_STEP_INCOMPLETE;
  while (!ts->reason && rk->status != TS_STEP_COMPLETE) {
    PetscReal t = ts->ptime;
    PetscReal h = ts->time_step;
    for (i=0; i<s; i++) {
      rk->stage_time = t + h*c[i];
      ierr = TSPreStage(ts,rk->stage_time); CHKERRQ(ierr);
      ierr = VecCopy(ts->vec_sol,Y[i]);CHKERRQ(ierr);
      for (j=0; j<i; j++) w[j] = h*A[i*s+j];
      ierr = VecMAXPY(Y[i],i,w,YdotRHS);CHKERRQ(ierr);
      ierr = TSPostStage(ts,rk->stage_time,i,Y); CHKERRQ(ierr);
      ierr = TSGetAdapt(ts,&adapt);CHKERRQ(ierr);
      ierr = TSAdaptCheckStage(adapt,ts,rk->stage_time,Y[i],&stageok);CHKERRQ(ierr);
      if (!stageok) goto reject_step;
      ierr = TSComputeRHSFunction(ts,t+h*c[i],Y[i],YdotRHS[i]);CHKERRQ(ierr);

etscErrorCode TSComputeRHSFunction(TS ts,PetscReal t,Vec U,Vec y)
{
  PetscErrorCode ierr;
  TSRHSFunction  rhsfunction;
  TSIFunction    ifunction;
  void           *ctx;
  DM             dm;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(ts,TS_CLASSID,1);
  PetscValidHeaderSpecific(U,VEC_CLASSID,3);
  PetscValidHeaderSpecific(y,VEC_CLASSID,4);
  ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
  ierr = DMTSGetRHSFunction(dm,&rhsfunction,&ctx);CHKERRQ(ierr);
  ierr = DMTSGetIFunction(dm,&ifunction,NULL);CHKERRQ(ierr);

  if (!rhsfunction && !ifunction) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_USER,"Must call TSSetRHSFunction() and / or TSSetIFunction()");

  ierr = PetscLogEventBegin(TS_FunctionEval,ts,U,y,0);CHKERRQ(ierr);
  if (rhsfunction) {
    PetscStackPush("TS user right-hand-side function");
    ierr = (*rhsfunction)(ts,t,U,y,ctx);CHKERRQ(ierr);
    PetscStackPop;
  } else {
    ierr = VecZeroEntries(y);CHKERRQ(ierr);
  }

  ierr = PetscLogEventEnd(TS_FunctionEval,ts,U,y,0);CHKERRQ(ie


  it doesn't do that. It simply ignores the ifunction the user provided. We should not do that since it will produce the wrong answer.

  Regarding the "poor man's way" of handling the constraint with projection methods. Our intention is that you would use TSSetPostStep() to provide a function that takes the computed solution by TSRK and "projects" it as you wish. You can try this now but note you will need to pack your ifunction() (with the u_t) and your rhsfunction() into a single right hand side function*.

  Barry

*Yes, eventually we should support the user not having to provide the function in a different form but we don't have anybody working on "useful and needed improvements to TS" we only have people working on "publishable and fundable cool new stuff" with TS.

> 
> I think that is the behavior I am seeing (i.e. on my problem, using PETSc master).
> 
> The "nonsense" I am referring to is only from the non-enforcement of the constraint; it would be o.k. for a pure ODE.
> 
> I would love to have some projection mechanism to try, for comparing explicit methods with projection to the SNESVI way (i.e. the right way), but that is asking for a lot of PETSc refactoring, I think.  For now I just want to error-out if the method is not going to call the SNES at each time step.
> 
> Ed
> 
> 
> 
> On Mon, Feb 13, 2017 at 11:26 AM, Barry Smith <bsmith at mcs.anl.gov> wrote:
> 
> > On Feb 13, 2017, at 1:53 PM, Ed Bueler <elbueler at alaska.edu> wrote:
> >
> > Dear Petsc --
> >
> > This is the first of two short TS usage questions.
> >
> > My problem is both stiff (diffusive PDE) and constrained, so I require
> >
> >    -snes_type vinewton{rs|ss}ls
> >
> > *and* I split my ODE system into IFunction and RHSFunction
> >
> >    F(t,u,u_t) = G(t,u)
> >
> > where F(t,u,u_t) = u_t + f(t,u) in my case (i.e. no mass matrix needed), and the stiff part goes in f(t,u).
> >
> > With this arrangement TS types beuler, theta, bdf, arkimex all work quite well.  However, the program runs and produces nonsense with type rk and ssp, that is, explicit methods.
> 
>    Sounds like a bug to me. The methods should be checking if an IFunction is being provided and error out in that case.
> 
>   Barry
> 
> >
> > So my question is, how do I ask the TS (at run time) whether the chosen TS type will or will not call its SNES at each step?  If SNES is not going to be used then I want to SETERRQ and stop.  That is, I want to error-out if the *method* is fully explicit.
> >
> > Note the constraints are enforced by the SNESVI, as they should be, not ad hoc projection.  Also, as a technical matter, I cannot require my iterates to be feasible inside my IFunction evaluation because that would break VINEWTONSSLS.
> >
> > Neither TSProblemType (mine is NONLINEAR) nor TSEquationType (mine is IMPLICIT I guess) seem to address this?  My problem is indeed nonlinear and has stiff parts, but it is not a DAE and it *is* constrained.
> >
> > Thanks!
> >
> > Ed
> >
> > PS  I'd prefer not to enumerate the existing TS types and error on the bad ones.  It is not nicely-maintainable.
> >
> >
> >
> > --
> > Ed Bueler
> > Dept of Math and Stat and Geophysical Institute
> > University of Alaska Fairbanks
> > Fairbanks, AK 99775-6660
> > 301C Chapman and 410D Elvey
> > 907 474-7693 and 907 474-7199  (fax 907 474-5394)
> 
> 
> 
> 
> -- 
> Ed Bueler
> Dept of Math and Stat and Geophysical Institute
> University of Alaska Fairbanks
> Fairbanks, AK 99775-6660
> 301C Chapman and 410D Elvey
> 907 474-7693 and 907 474-7199  (fax 907 474-5394)