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

[Ian Hinder]

On 29 Feb 2012, at 02:48, 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?


I don't think there is anything "bad" about RK4 itself.  What gauge condition are you using to evolve Minkowski?  If you are using lapse = 1 and shift = 0, I believe that the solution should be exact.  1 and 0 can both be represented exactly with floating point, all derivatives will be zero as the subtraction in the finite difference will be exact, and I think there are no other nonzero terms.

If RK4 is giving a different behaviour to generic RK4, I would look into where the differences are.  Are you using the "device" branch of MoL?  Have you tried the trunk?  It might be that the linear combination function is not implemented correctly in the device branch.

-- 
Ian Hinder
http://numrel.aei.mpg.de/people/hinder