[petsc-dev] Strange behaviour from TSARKIMEX

Mon Nov 14 13:17:50 CST 2016

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

the output with -m_lhs -ts_type arkimex -ts_arkimex_type 5 -ts_arkimex_fully_implicit (case a) ) is different from -m_lhs 0 -ts_type arkimex -ts_arkimex_type 5 -ts_arkimex_fully_implicit (case b) )

> I assume you are in the b) case,

No,  case a) mass matrix on the left-hand side

> 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.
> 

I do have pasted the output for ts_monitor for the first three steps.

The entry you are referring to in Table 11 actually breaks the TS assumption that the ODE can be written F(u,udot,t) = G(u,t) (I was thinking it was a typo)

Indeed, using what is listed in Table 11 for the case  "mass & stiff-nonstiff ODE", we have
ODE: M * ydot = g(t,y) + f(t,y), F = M * ydot - f(t,u), G = M^-1 * g(t,y)
Putting F and G in the form F(u,udot,t) = G(u,t), we will have the ODE M * ydot  =  f(t,u) + M^-1 * g(t,y)

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

I’m not interested in solving this specific advection problem with arkimex. I came across this problem when writing a general interface to TS from a FEM library.

> 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.
> 

If the entry in Table 11 is correct, please add a comment on the manual stating that ARKIMEX does not fully support the F(u,udot,t) = G(u,t) interface.

> 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>

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