[petsc-users] TimeStepper norm problems. EMIL Please read this

[Lisandro Dalcin]

On 16 April 2015 at 16:44, Emil Constantinescu <emconsta at mcs.anl.gov> wrote:
> On 4/16/15 2:13 AM, Lisandro Dalcin wrote:
>>
>> On 16 April 2015 at 04:51, Emil Constantinescu <emconsta at mcs.anl.gov>
>> wrote:
>>>
>>>
>>> On 3/24/15 5:31 AM, Lisandro Dalcin wrote:
>>>>
>>>>
>>>> Emil, is there any chance you can try my code with your problem? I
>>>> really need some feedback to push this to PETSc, otherwise
>>>
>>>
>>>
>>> Hi Lisandro - we checked ts_alpha_adapt and we tested it on a small
>>> system
>>> (mildly stiff van der Pol ODE). I enclosed a Figure generated by Debo
>>> that
>>> compares the error at the final time against ATOL - there alpha is the
>>> original one (with original adaptor).
>>
>>
>> Original adaptor? Do you mean
>> TSAlphaSetAdapt(ts,TSAlphaAdaptDefault,NULL)?
>>
>> In such a case, no surprises, TSAlphaAdaptDefault() is quite naive, it
>> does not estimate the LTE, it is actually based in the change of the
>> solution.
>
>
> Yups, that's the one;

I was the author of TSAlphaAdaptDefault (the whole TSALPHA, in fact).
I coded that beast "out of desperation" long time ago. This thing is
not even implemented withing the current TSAdapt framework!. I think
at least we should re-implement this beast within TSAdapt (I mean,
similar as in -ts_theta_adapt).

> but that still needs to be available unless a better
> one-step one is implemented.

I think you have that feeling simply because TSAlphaAdaptDefault()
seems to work, but if you look carefully at the code, it does not make
sense from the point of view of a LTE-based theory.

 OK, Then let's define a poor's man one-step adapt that at least have
some sense. How would you implement adaptivity for backward Euler or
the midpoint rule? Something based exclusively in some l2/inf norm of
Xdot? IOW, we define LTE = X^{n+1} - X^n of O(\delta_t) and use the
usual formula with exponent order=1 ?

> Note however that even estimating exactly LTE
> is not a guarantee that the error will be within ATOL.
>

Well, ATOL is to keep the LTE under control, of course there are no
guarantees about the global error at the end step. That's what you
meant?


-- 
Lisandro Dalcin
============
Research Scientist
Computer, Electrical and Mathematical Sciences & Engineering (CEMSE)
Numerical Porous Media Center (NumPor)
King Abdullah University of Science and Technology (KAUST)
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