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

[Ian Hawke]

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
>>
>