On 4/16/15 9:25 AM, Lisandro Dalcin wrote:
On 16 April 2015 at 16:44, Emil Constantinescu <[email protected]> wrote:
On 4/16/15 2:13 AM, Lisandro Dalcin wrote:
On 16 April 2015 at 04:51, Emil Constantinescu <[email protected]>
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.
