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

[Erik Schnetter]

Hee Il

Your setup for the generic RK4 integrator seems correct.

-erik

On Tue, Apr 3, 2012 at 6:04 AM, Heeil Kim <heeilkim at gmail.com> wrote:
> Hi,
>
> The problems in my binary NS merge simulations seem to be related to
> this (fast) RK4 integration. I didn't make runs for sufficiently long
> time but the run with RK3 didn't crash yet.
>
> But the generic RK4 doesn't seem to fix my problems. For this, I took
> the following parameter setup.
>
> ####### MoL  #####################
>
> mol::ode_method                 =   "generic"
> mol::generic_type               =   "rk"
> mol::mol_intermediate_steps             =   4
> methodoflines::mol_num_scratch_levels   =  3
>
>
> Did I make right setup, or do I need more elaborations?
>
> Cheers,
>
> Hee Il
>
>
>
> 2012/3/1 Erik Schnetter <schnetter at cct.lsu.edu>:
>> 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/
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-- 
Erik Schnetter <schnetter at cct.lsu.edu>
http://www.perimeterinstitute.ca/personal/eschnetter/