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

[Emil Constantinescu]

On 4/16/15 9:25 AM, Lisandro Dalcin wrote:
> 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).

I agree. The adaptor is not using TSAdapt and at some point it should be 
refactored to be consistent. I could not find a good reference detailing 
the generalized alpha method ... it's always described in cryptic way or 
in embedded in a given context. But I know it's second order, so we 
should be able to construct a first order embedded approximation (there 
appear to be significant degrees of freedom).

>> 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 ?

I agree, we cannot do anything that's one step and computationally 
effective for BE of implicit midpoint; but I believe we can do something 
relevant for alpha.

>> 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?

Yes, I'm saying to emphasize that we cannot expect perfect results in 
that figure.

>