On 27 Mar 2017, at 04:06, Christian D. Ott <cott@tapir.caltech.edu> wrote:

Hi All,

I have been experimenting with the GW150914 par file (Thanks for putting
it together!), which uses Llama multipatch (MP) with McLachlan (ML) and,
of course, Carpet AMR in the interior Cartesian patch, tracking the
punctures.

I'm noticing three things when looking at Psi4 l2,m2 waveforms (and this
is largely independent of extraction radius):

(1) The waveforms have high-frequency wiggles that similar pure-AMR
simulations do not show. I don't have a pure AMR simulation for
GW150914, but am comparing with an 8-orbit, equal mass, non-spinnning
case. I can run GW150914 with pure AMR if need be.

(2) The high-frequency wiggles get *worse* if I decrease the finite
differencing order from 8th to 4th order.

(3) This appears to be a wave amplitude-dependent 'feature', since the
wiggles are much less pronounced once the waves reach higher amplitudes.

I'm attaching two gnuplot screenshots: fig1.png shows the first ~800 M
of Psi4 l2,m2 real at r=136 M with the stock par file and with a
modified par file for 4th order. fig2.png is a zoom-in.

I'm also attaching the par file that I'm using for the 4th-order run.

Now my questions: Does anybody have an idea where the high-f noise is
coming from and why it's getting worth for lower FD order? Any
suggestions on how to mitigate it?

Hi,

Yes, I have observed this as well. I saw it originally with CTGamma when I first started using Llama, and now see it with McLachlan. I believe I have looked at 2D movies of Psi4r and seen the junk radiation reflecting off the interpatch boundary at r ~ 45 M, hitting the BHs, and causing them to emit high frequency noise in the waves.

Note that the boundary condition "generating" the reflections in this case would be the Cartesian boundary at x^i = 45 M, which takes its data from the angular grid. I'm not sure why this is worse than in a pure Cartesian run, but it might be because the high frequencies are dissipated away by being under-resolved in the wave zone before they get to the extraction spheres in the Cartesian case.

I think this can be improved by moving the spherical inner radius from 40 M to something larger, e.g. 80 M. I have also tried adjusting the angular resolution, but this doesn't seem to help very much. Another option is to switch to using constant Courant factor, which will give lower time resolution in the wave zone, and hence reduce the highest frequency oscillations.

There are two possible explanations for why the wiggles get worse once the waves reach higher amplitude. One is that the noise is sourced only once, initially, from the junk radiation, and the effects simply diminish with time, so by the time the wave amplitude is large, you cannot see it any more. However, I think I have observed that the noise is much worse in longer runs, indicating that instead, perhaps the reason is that the noise has the same amplitude a certain time after the start of the run, independent of the separation, but for longer runs, the real waves are weaker, so the noise is relatively stronger. The noise amplitude being related to the junk amplitude would fit with this.

I don't know why the noise would get worse with 4th order. A 4th order run is not only different by the finite differencing order. It also has fewer ghost (and hence buffer) zones, and is usually run with lower order dissipation. It may be interesting to run the 4th order case with everything else the same as in the 8th order case (i.e. with 5 ghost zones, and 9th order dissipation) to see if it is really the finite differencing order, or something else. By changing the number of buffer zones, the grid structure can change dramatically in some cases.

In your plot, I can't actually see any wiggles in the 8th order case.

It would be really good to find a solution to this.