[Users] Loss of convergence with subcycling in time

[Steven Brandt]

On 11/19/2025 8:24 AM, Erik Schnetter wrote:
> 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.

Does no time interpolation mean no dense output? That didn't exist when 
Ian did these tests, right?

--Steve

>
> 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>_______________________________________________
>> Users mailing list
>> Users at einsteintoolkit.org
>> http://lists.einsteintoolkit.org/mailman/listinfo/users
>
>
> _______________________________________________
> Users mailing list
> Users at einsteintoolkit.org
> http://lists.einsteintoolkit.org/mailman/listinfo/users
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.einsteintoolkit.org/pipermail/users/attachments/20251119/3d1c67a8/attachment.htm>