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

[Lisandro Dalcin]

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.

Can you send/point me your code to take a look?

> For this problem your adaptor works
> better [ error should be close to ATOL].

> So from my perspective, your
> adaptor works well. However, we need to keep the old too so that we have a
> one step adaptor available ... since alpha is a one step method.
>

Sorry, I'm not following you. Generalized alpha is not truly a
one-step method, because it retains Xdot from the previous time step.
In the initial step, other codes out there assume that Xdot_prev=0.

My "alpha1" implementation has a trick for the initial time step
(using the same ideas, i.e. a BD formula) to both estimate Xdot_prev
and the error. However, this is at the cost of performing two
nonlinear solves in the initial step (IOW, two internal timesteps with
backward Euler and dt/2). Please note this trick should be valid for
any second-order method, at least to estimate the initial LTE in the
first step.

BTW, Have you compared my "-ts_type tsalpha1 -ts_alpha_adapt" with
PETSc's "-ts_type cn -ts_theta adapt"?

-- 
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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