[Users] Can't evolve Minkowski with RK4 integrator?

[Erik Schnetter]

Guys

Thanks for all the pointers!

I'm not using the device branch (vanilla checkout of ET development
branch), and I'm not adding any noise. I really only evolve Minkowski,
all variables are initially zero except for lapse and metric
diagonals, which are one.

The RHS are not identically zero -- the RHS of the curvature and its
trace are about 10^-30. (Should it be exactly zero?)

In unigrid, I see a secular drift; e.g. the lapse grows by 10^-15
every few time steps. Otherwise, things remain fine. With mesh
refinement, the RHS soon becomes 10^-12 near refinement boundaries,
and this triggers real badness.

MoL's generic RK4 integrator works fine for me, only the
space-efficient RK4 integrator leads to problems.

-erik

On Wed, Feb 29, 2012 at 9:36 AM, Ian Hawke <I.Hawke at soton.ac.uk> wrote:
> It's true that it should reproduce it at the continuum, but the use of
> the sum_alpha term may leading to differences at floating point
> round-off (as alpha is, for most substeps, not perfectly representable
> by floating point [alpha=1/3 in many cases], and sum_alpha is used in
> the form ...(1 - sum_alpha)). The effect that Erik describes may be
> accumulated floating point error. I'd expect this to manifest itself as
> a bulk secular drift (in the unigrid case); with MR the boundaries get
> involved (as the drift occurs depends on timesteps taken on the current
> level).
>
> If the error is oscillatory in space even in unigrid then this can't be
> the problem, I don't think.
>
> Ian
>
> On 29/02/12 03:16, Yosef Zlochower wrote:
>> MoL RK4 should reproduce generic RK4. The only difference
>> should be that MoL RK4 is more efficient with memory.
>>
>> On 02/28/2012 08:48 PM, Erik Schnetter wrote:
>>> I've just encountered a strange problem: I can't evolve Minkowski with
>>> MoL's RK4 integrator. Small errors in K grow from floating-point
>>> round-off, and the simulation quickly goes bad. The error grows slowly
>>> (but measurably) in unigrid, but much faster with mesh refinement.
>>>
>>> For example, with unigrid the lapse grows by about 10^-15 every ten
>>> time steps or so; with mesh refinement, the simulation dies after a
>>> few ten time steps.
>>>
>>> However, things are fine with other time integrators, in particular
>>> with the generic RK1 and RK4 integrators.
>>>
>>> I've looked at other things as well, e.g. the CFL factor, the
>>> McLachlan implementation, the gauge parameters, dissipation, but could
>>> not find anything else that made a difference.
>>>
>>> Is there something bad about the RK4 integrator? Is it intrinsically
>>> unstable, more so than other RK schemes? Or did it break in some of
>>> the recent changes?
>>>
>>> -erik
>>>
>>
>
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-- 
Erik Schnetter <schnetter at cct.lsu.edu>
http://www.perimeterinstitute.ca/personal/eschnetter/