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

[Lisandro Dalcin]

On 24 March 2015 at 01:34, Jed Brown <jed at jedbrown.org> wrote:
> Lisandro Dalcin <dalcinl at gmail.com> writes:
>
>> On 21 March 2015 at 17:32, Emil Constantinescu <emconsta at mcs.anl.gov> wrote:
>>> When -ts_theta_adapt is used, then it detects the instability as an error
>>> and reduces the step by a lot! wlte=1.24e+03 which means that the reduction
>>> should be severe but the controller tries 0.1*dt and that seems to pass but
>>> it "jig-saws" (take a look at the next attempted step), which means that it
>>> is likely unstable.
>>
>> I think -ts_theta_adapt is seriously broken, I cannot make sense of
>> the way the error estimator is computed.
>
> This was Shri's implementation.  TSEvaluateStep_Theta looks wrong to me,
> both using U as an input and assuming that Xdot is set.  I don't even
> know what the intended math is for a first-order embedded estimate in
> midpoint (theta=0.5).

Pease note that -ts_adapt_tetha errors for midpoint. You actually need
-ts_theta_endpoint to use adaptivity. But it is there, in the endpoint
version, that I cannot make sense of the implementation. The
trapezoidal rule is second-order, thus the LTE is O(dt^3). The
computed error estimator should be O(dt^2), but the current code seems
to compute an estimator O(dt), and that's the root of all evil.


-- 
Lisandro Dalcin
============
Research Scientist
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