[Users] Loss of convergence with subcycling in time

[Erik Schnetter]

Miguel

If I recall correctly, Ian Hinder studied convergence of black hole simulations with subcycling in time in great detail. The Einstein Toolkit gallery example for GW150914 contains the respective distilled knowledge. https://einsteintoolkit.org/gallery/bbh/index.html

Some important details that I recall:
- You can regrid only when the fine and coarse grids are aligned
- You cannot use time interpolation at all. You need to use enough buffer zones for all the RK substeps for all the fine timesteps for each coarse time step. With 3 ghost zones and RK4 you need 21 buffer zones.

You likely do not need to evolve for a long time to see loss of convergence. It might suffice to run for just a few time steps (a few coarse grid steps) and study convergence of one of the evolved variables (e.g. the lapse) in great detail over a wide range of resolutions. For this you do not need a large domain, nor do you need many refinement levels, nor do you need many grid points. For example, studying convergence near the point (1,0,0) requires probably about 100^3 points for each resolution in a two-level setup.

-erik

> On Nov 19, 2025, at 06:17, Miguel Zilhão <mzilhao at ua.pt> wrote:
> 
> hi all,
> 
> we've recently added the option to compute the Gauss constraint in the ProcaEvolve thorn (https://bitbucket.org/canuda/proca/src/experimental_miguel/ProcaEvolve/) and we were surprised to see that, even for very small evolutions of a simple (unperturbed) charged black hole, this constraint violation does not converge. of course everything is converging just fine at t=0, but once the evolution starts, convergence is lost really quickly.
> 
> after experimenting with different things, i think i've narrowed the issue down to the subcycling in time. i've attached some plots as well as the corresponding parameter files. these plots are not convergence tests, it's just what i'm observing with and without subcycling in time (everything else is the same as you can see from the parfiles).
> 
> these are evolutions for a single charged BH, with Q=0.2.
> in one of the parfiles (LeanBSSN_RN_Q0.2_nosubcycl_hf40_202509.par) all timelevels update at the same rate with
> 
>  Carpet::time_refinement_factors         = "[1, 1, 1, 1, 1, 1, 1]"
> 
> for the other parfile (LeanBSSN_RN_Q0.2_hf40_202509.par), all timelevels update at the same rate *except* the two inner ones. for the "base" grid functions, i see no noticeable difference insofar as i've checked, but for the Gauss constraint violation the results are very different as you can see from the plots attached:
> 
> - in the gc_x_RN_nosubcycl.pdf plot, everything looks fine
> - in the gc_x_RN_subcycl.pdf case, notice how a lot of noise propagates from the two inner refinements levels -- the ones that updated more frequently than the rest.
> 
> the problem is that this noise is not contained in the buffer region (if it was, we'd be fine), but propagates out, contaminates the rest of the grid, and totally ruins any convergence study.
> 
> actually a similar thing also happens for the hamiltonian constraint -- plots also attached (hc_x_RN_nosubcycl.pdf, hc_x_RN_subcycl.pdf) -- but in this case the effect is smaller and it doesn't spoil convergence studies.
> 
> so i was wondering whether this is at all expected and/or if there are some parameters or setting that we may have overlooked?
> 
> thanks,
> Miguel
> <hc_x_RN_nosubcycl.pdf><hc_x_RN_subcycl.pdf><gc_x_RN_subcycl.pdf><gc_x_RN_nosubcycl.pdf><LeanBSSN_RN_Q0.2_hf40_202509.par><LeanBSSN_RN_Q0.2_nosubcycl_hf40_202509.par>_______________________________________________
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