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

Wed Feb 15 11:11:04 CST 2017

> On Feb 14, 2017, at 11:59 PM, Emil Constantinescu <emconsta at mcs.anl.gov> wrote:
> 
> We seem to be needing more than two components and ways to pack them. Allowing them to be dynamically assigned at run time would be really cool.
> 
> We seem to like an API that allows us to specify M and u_t; but would also like to keep support for f(t,u,u_t)=0.

   Absolutely! No one is saying that IFunction should be removed!

> 
> How about a costly experiment: build an API as discussed below (support the above) that would map everything to the current one 1xRHS and 1xIFunction to see how it would work? In other words, is there a scenario in which we could introduce the new but also keep the old and be reasonable about it? Of concern is whether the new one can be made friendly enough.
> 
> Emil
> 
> On 2/14/17 11:44 PM, Ed Bueler wrote:
>>>  Jed suggested having any number of "RHS" functions. I don't think we
>> need more than 2, 1 for left hand side
>>> and 1 for right. If that ends up being not enough we can change to
>> have any number of them. Just to be clear.
>>> I suggest three functions
>>>  IFunction which defaults to u_t  plus TSSetMassMatrix() which
>> changes the default IFunction to M u_t
>>>  LHS function which defaults to 0, if provided defaults to being
>> treated implicitly by IMEX
>>>  RHS function which defaults to 0, if provided defaults to being
>> treated explicitly by IMEX
>>> Then a TSSetStiffMatrix(ts,Mat L) (horrible name) that provides u_t
>> -Lu = g() + Lu
>> 
>> At my current level of understanding I get this trifecta (quad-fecta?).
>> 
>> In my ice sheet case  u_t = f(t,u) + g(t,u),  I would not set IFunction
>> at all, or I would use a constant.  The divergence of flux  f(t,u) =
>> div(q)  would go into the LHSFunction and the elevation-dependent mass
>> balance  g(t,u)  would go into the RHSFunction.  I would not use
>> TSSetStiffMatrix() at all.
>> 
>> Barry's suggestion makes sense for this and the few other usage cases I
>> have already experienced ... kind of a lame endorsement, but, on such a
>> weak basis one casts a vote ...
>> 
>> Ed
>> 
>> 
>> PS  I would not use TSSetStiffMatrix() because none of the
>> linearizations/simplfications known at the completion of a TS step could
>> "capture" the stiff part without being derived a la the Jacobian
>> anyway.  To see what I mean, note that VINEWTONRSLS has a different
>> *dimension* at each Newton iteration.  I don't know the
>> (in-active-constraint) dimension of the solution I'll get at each time
>> step, much less how to scale the various stiff-equation-parts for those
>> in-active dimensions.  In these problems there is a lot going on in the
>> implicit solve, besides just handling stiffness.
>> 
>> 
>> On Tue, Feb 14, 2017 at 6:20 PM, Barry Smith <bsmith at mcs.anl.gov
>> <mailto:bsmith at mcs.anl.gov>> wrote:
>> 
>> 
>>    > On Feb 14, 2017, at 8:56 PM, Emil Constantinescu <emconsta at mcs.anl.gov <mailto:emconsta at mcs.anl.gov>> wrote:
>>    >
>>    > On 2/14/17 4:10 PM, Barry Smith wrote:
>>    >>   Ok, you don't recompile but forcing that into user code is still disgusting. With my api the user code is
>>    >>
>>    >>>>> TSSetRHSFunction(ts,NULL,RHSFunction,&ptype[0]);
>>    >>>>> TSSetLHSFunction(ts,NULL,LHSFunction,&ptype[0]);
>>    >>>>>   TSSetRHSJacobian(ts,Jac,Jac,RHSJacobian,&ptype[0]);
>>    >>>>>  TSSetLHSJacobian(ts,Jac,Jac,LHSJacobian,&ptype[0]);
>>    >> and -ts_type xxx works correctly for ALL methods, implicit, explicit and imex without requiring any special command line options for different methods.
>>    >
>>    > Is this a viable solution? Growing the API to fix this situation will just put a burden with each new TS method after we refactor it in the current landscape.
>> 
>>       No just the opposite, the TS implementations will talk to
>>    functions who will put things together for it. So All implicit
>>    methods will call something like TSBuildImplicitFunction(), all
>>    explicit methods will call something like TSBuildExplicitFunction()
>>    and then IMEX methods will call both of these. In fact likely we can
>>    refactor to make things a little better than today.  Depending on
>>    options and flagsTSBuildExplicitFunction() would build out of all
>>    the user provided functions what it needs etc.
>> 
>>    One problem with the current code is the TS methods call things with
>>    the same names as the user API. So implicit methods call
>>    TSComputeIFunction() while explicit methods call
>>    TSComputeRHSFunction(). This is wrong because implicit methods
>>    actually also use the rhs function provided by the user.
>> 
>>    The function below absolutely should not be called
>>    TSComputeIFunction()! It does not just compute IFunction()
>>    PetscErrorCode TSComputeIFunction(TS ts,PetscReal t,Vec U,Vec
>>    Udot,Vec Y,PetscBool imex)
>>    {
>>      PetscErrorCode ierr;
>>      TSIFunction    ifunction;
>>      TSRHSFunction  rhsfunction;
>>      void           *ctx;
>>      DM             dm;
>> 
>>      PetscFunctionBegin;
>>      PetscValidHeaderSpecific(ts,TS_CLASSID,1);
>>      PetscValidHeaderSpecific(U,VEC_CLASSID,3);
>>      PetscValidHeaderSpecific(Udot,VEC_CLASSID,4);
>>      PetscValidHeaderSpecific(Y,VEC_CLASSID,5);
>> 
>>      ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
>>      ierr = DMTSGetIFunction(dm,&ifunction,&ctx);CHKERRQ(ierr);
>>      ierr = DMTSGetRHSFunction(dm,&rhsfunction,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,Udot,Y);CHKERRQ(ierr);
>>      if (ifunction) {
>>        PetscStackPush("TS user implicit function");
>>        ierr = (*ifunction)(ts,t,U,Udot,Y,ctx);CHKERRQ(ierr);
>>        PetscStackPop;
>>      }
>>      if (imex) {
>>        if (!ifunction) {
>>          ierr = VecCopy(Udot,Y);CHKERRQ(ierr);
>>        }
>>      } else if (rhsfunction) {
>>        if (ifunction) {
>>          Vec Frhs;
>>          ierr = TSGetRHSVec_Private(ts,&Frhs);CHKERRQ(ierr);
>>          ierr = TSComputeRHSFunction(ts,t,U,Frhs);CHKERRQ(ierr);
>>          ierr = VecAXPY(Y,-1,Frhs);CHKERRQ(ierr);
>>        } else {
>>          ierr = TSComputeRHSFunction(ts,t,U,Y);CHKERRQ(ierr);
>>          ierr = VecAYPX(Y,-1,Udot);CHKERRQ(ierr);
>>        }
>>      }
>>      ierr = PetscLogEventEnd(TS_FunctionEval,ts,U,Udot,Y);CHKERRQ(ierr);
>>      PetscFunctionReturn(0);
>>    }
>> 
>>    The current code entangles too much of the user API to the methods,
>>    this can be fixed.
>> 
>>    > If the user experiments with different ways of splitting the solution they would have to define RHS and IF or RHS and LHS in different ways (according to the splittings they experiment with). It may look disgusting, but I don't see another way around it unless you allow for a list of operators to be defined and then the user to assign them to LHS or RHS.
>> 
>>       Jed suggested having any number of "RHS" functions. I don't think
>>    we need more than 2, 1 for left hand side and 1 for right. If that
>>    ends up being not enough we can change to have any number of them.
>>    Just to be clear. I suggest three functions
>> 
>>       IFunction which defaults to u_t  plus TSSetMassMatrix() which
>>    changes the default IFunction to M u_t
>>       LHS function which defaults to 0, if provided defaults to being
>>    treated implicitly by IMEX
>>       RHS function which defaults to 0, if provided defaults to being
>>    treated explicitly by IMEX
>> 
>>       Then a TSSetStiffMatrix(ts,Mat L) (horrible name) that provides
>>    u_t -Lu = g() + Lu
>> 
>>       None of the TS implementations will every directly know about
>>    what the user has provided. They will call the wrapper functions I
>>    mention above.
>> 
>>       I think Jed and Emil may be too enamored with the reductionist
>>    model of only IFunction() and RHSFunction() to see that though it
>>    encompasses everything it may not be the best user API.
>> 
>> 
>> 
>>    >
>>    >>
>>    >>> Adding all that logic to keep track of left sides and right
>>    sides for academic examples is likely not the best development.
>>    >>  I don't think it is "just academic examples", it is all examples
>>    without a mass matrix.
>>    >>
>>    >>   Once the user has decided with ts_type to use for production if
>>    it is fully implicit or explicit then they can depending on the type
>>    selected, write just a left hand side, just a right hand side for
>>    higher efficiency (less update of ghost points, fewer iterations
>>    over loops etc).
>>    >>
>>    >>   With a constant mass matrix we can have TSSetMassMatrix() and
>>    then TSSetIFunction() is reserved for when it is absolutely needed.
>>    >
>>    > As much as I would disagree with growing the API at the level of
>>    defining the problem, I think TSSetMassMatrix() would let us do more
>>    things in the solvers. Also it would be useful to know if the mass
>>    matrix is singular or not for efficiency reasons.
>>    >
>>    > Emil
>>    >
>>    >>  Barry
>>    >>
>> 
>> 
>> 
>> 
>> --
>> 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)