[petsc-dev] Strange behaviour from TSARKIMEX

[Emil Constantinescu]

Stefano,

Sorry, the equation type is needed for when the fully implicit option is 
used.

I assume you are in the b) case, that would correspond to "mass & 
stiff-nonstiff ODE" entry in Table 11 with f(t,y)=0. Have you tried the 
forms suggested there, they are slightly different from what you 
indicate in your original message for case b)? Also, please use 
-ts_monitor and comment out the equation type.

In your case, you would either use the setup corresponding to "stiff ODE 
w/ mass matrix" or "nonstiff  ODE  w/  mass  matrix".

It is difficult to create a decision tree for every way of writing the 
splittings. Do you find Table 11 not clear about what splitting to use? 
I would welcome any kind of feedback for improving it.

Thanks,
Emil

On 11/14/16 11:45 AM, Stefano Zampini wrote:
> Emil,
>
> thanks for the explanations. I’ve added
> TSSetEquationType(ts,TS_EQ_IMPLICIT) and things actually got worse with
> arkimex.
> Adding -ts_arkimex_fully_implicit still gives the same inconsistency.
>
> Running with -m_lhs -snes_monitor -ts_type arkimex -ts_arkimex_type 5,
> it reports for the first three TSSteps
>
> 0 TS dt 0.01 time 0.
>     0 SNES Function norm 2.881332954700e-01
>     1 SNES Function norm 5.764785317497e-16
>     0 SNES Function norm 2.656435502730e-01
>     1 SNES Function norm 1.351993391899e-15
>     0 SNES Function norm 2.748681648224e-01
>     1 SNES Function norm 9.153705366186e-16
>     0 SNES Function norm 2.654405587243e-01
>     1 SNES Function norm 2.165715847788e-15
>     0 SNES Function norm 1.327202793622e-01
>     1 SNES Function norm 1.851465123731e-15
>     0 SNES Function norm 3.703291910243e-02
>     1 SNES Function norm 1.946066132445e-15
>     0 SNES Function norm 2.917498324433e-01
>     1 SNES Function norm 1.680056316341e-15
>     0 SNES Function norm 1.972362337024e-01
>     1 SNES Function norm 1.055632173875e-15
>     0 SNES Function norm 4.087125686933e-02
>     1 SNES Function norm 2.555645968009e-15
>     0 SNES Function norm 3.547915829559e-01
>     1 SNES Function norm 2.103175616151e-15
> 2 TS dt 0.01 time 0.02
>     0 SNES Function norm 1.965807268111e-15
>     1 SNES Function norm 0.000000000000e+00
>     0 SNES Function norm 1.597532788386e-19
>     1 SNES Function norm 0.000000000000e+00
>     0 SNES Function norm 1.965807242146e-15
>     1 SNES Function norm 0.000000000000e+00
>     0 SNES Function norm 3.815060728816e-15
>     1 SNES Function norm 7.476292242926e-16
>     0 SNES Function norm 1.837692463276e-15
>     1 SNES Function norm 0.000000000000e+00
>     0 SNES Function norm 0.000000000000e+00
>     0 SNES Function norm 1.965807300567e-15
>     1 SNES Function norm 0.000000000000e+00
> 3 TS dt 0.01 time 0.03
>     0 SNES Function norm 0.000000000000e+00
>     0 SNES Function norm 0.000000000000e+00
>     0 SNES Function norm 0.000000000000e+00
>     0 SNES Function norm 0.000000000000e+00
>     0 SNES Function norm 0.000000000000e+00
>     0 SNES Function norm 0.000000000000e+00
>     0 SNES Function norm 0.000000000000e+00
>
> Then, all the other SNES function norms are zero.
>
>
>
> On Nov 14, 2016, at 6:23 PM, Emil Constantinescu <emconsta at mcs.anl.gov
> <mailto: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.
>>
>> 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
>> <1_Warning.txt>
>