[petsc-dev] Strange behaviour from TSARKIMEX

[Matthew Knepley]

On Mon, Nov 14, 2016 at 9:23 AM, Emil Constantinescu <emconsta at mcs.anl.gov>
wrote:

> Stefano, thanks for your note. The consistent splittings currently
> supported under ts_type arkimex are give in Table 11 in the manual:
> http://www.mcs.anl.gov/petsc/petsc-current/docs/manual.pdf
>
> Your case a) is not treated as you wrote it down. The reasoning behind the
> use cases is that M will have to be inverted directly or indirectly if you
> put it in F(...) because it's in implicit ODE. In your case b) you handle
> that directly; however, in case a) the M in F(...) is ignored in some steps
> leading to inconsistent formulations. That being said, there are ways of
> solving it as in case a) if M is full rank: some hints are in the caption
> in Table 11, but I can expand.
>
> Also in Table 11, there is a note about instructing TS that the user is
> specifying an implicit ODE (M*ydot....): " set TSSetEquationType() to
> TS_EQ_IMPLICIT or higher". That sould solve the -ts_arkimex_fully_implicit
> inconsistency issue.


I did not know any of this. It also has to go in the manual pages.

   Matt


>
> Emil
>
>
>
> On 11/14/16 4:09 AM, Stefano Zampini wrote:
>
>> I came across this thing recently, and I couldn't figure out where the
>> issue could be.
>>
>> The problem I'm solving is a simple DG advection, the ode is M*udot =
>> K*u+b, M is diagonal.
>>
>> Attached is a MWE that reproduces the problem.
>>
>> The problem is formed in two different cases depending on the command
>> line option -m_lhs
>>
>> a) -m_lhs 1 : F(u,udot,t) = M*udot, G(u,t) = K*u+b
>> b) -m_lhs 0 : F(u,udot,t) = udot, G(u,t) = M^-1(K*u+b)
>>
>> Using option b) and RK4, the solution is ok.
>> If run with any implicit TS method except arkimex, no matter if I'm
>> choosing option a) or b), the solution is always very close (say, final
>> error < 0.05) to the expected one (computed with BDF).
>>
>> When using ARKIMEX, case b) gives a good solution, but not case a). In
>> fact, the solution does not seem to be advected at all in this case.
>>
>> I was wondering if I'm doing something wrong or there's a bug in the
>> ARKIMEX implementation.
>>
>> I also noticed that, using  -ts_arkimex_fully_implicit does not produce
>> the same output for case a) and b). Shouldn't they produce the same
>> method with this option?
>>
>> Thanks,
>> --
>> Stefano
>>
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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