[petsc-dev] perhaps where the custom adapativity perversity began

[Jed Brown]

Lisandro Dalcin <dalcinl at gmail.com> writes:

> On 30 April 2017 at 23:34, Jed Brown <jed at jedbrown.org> wrote:
>>
>> One reliable, if somewhat expensive, option would be to use
>> extrapolation similar to TSARKIMEX1BEE.
>
> Somewhat expensive :-) ?

Naively, it's a 50% cost increase, but you have a good initial guess
from the two steps.  If you really benefit from adaptivity, this is
worthwhile.

>>  If this feels like reinventing
>> a wheel using stone tools, it is; we could just add a TSARKIMEX tableau
>> for Theta with extrapolation.
>>
>
> Oh, I'm not going to touch TSARKIMEX until the TSClone() business gets
> refactored/cleaned up.
>
> But in general, I'm not opposed to your suggestion.
>
>> Since Theta is supposed to be an implementation that newcomers use as an
>> example to learn how TS works, we should try to keep it as clean/simple
>> as possible.
>
> Too late, my friend:
>
> * THETA is backing the other two methods BEULER and CN.
> * We have the DM subdomain/restrict hooks stuff.
> * We have the adjoint stuff.
> * And finally, I already added time adaptivity in last release to
> contribute some extra entropy.
>
> so I think THETA abandoned simplicity in favor of features long time ago.

My point is that a few years ago, we had a discussion about why to keep
Theta, versus replacing it with equivalent ARKIMEX tableaus and having
no code to maintain.  The rationale at that time was that Theta would be
easier for people to look at to learn how to implement their own
methods.  Nobody argued that Theta should exist as an independent
implementation for capability reasons.  The BEuler and CN cases were
thought to be not sufficiently different to justify maintaining
independently (Theta was created by unifying those).

>>  I think it would also be okay to have no error estimator
>
> Why? Having support for some sort of adaptivity, that is not default,
> and based on a cheap estimator seems like a win-win for me... IMHO,
> practicality beats purity in this case.

It's a teaching method in the first place.

>> -- it seems likely that user implementations may not have an error
>> estimator (though maybe they should think about it up-front).
>
> What did you mean? I'm not following you in these lasts comments...

If someone is writing a new TS implementation, they might not have an
error estimator.  Theta exists as a demonstration of how to write a TS
implementation.
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