Re: [Users] Schedule options and uninitialized refinement levels

Hi Roland,

Thank you very much once again for the detailed answer!

In the meantime, I had a look at CarpetReduce's reduce.cc. Without going into full details, I could understand that reductions would indeed go through the various levels, with the correct multiplicative factor, as I first thought. But your explanation adds another layer of understanding.

While I'm at it, I would like to ask another question that came up during this experimentation process, regarding ghost points.

I could notice that at the first iteration which completes a time step for a given level - for instance, level N at iteration 1, level N-1 at iteration 2, level N-2 at iteration 4... - some points of density_rho at the edge of the refinement level were still uninitialized. I can see that this doesn't happen for evolved variables, or when UAv_Analysis_group is scheduled in EVOL (drawing inspiration from mclachlan's ML_ADMConstraints, I put it in MoL_PseudoEvolution after MoL_PostStep for experimentation).

While I assumed that there would be ghost_size such points, some quick experiments rather seemed to indicate ~3*ghost_size points. I could notice that the last points with actual values, correspond to points with coordinates \pm CarpetRegrid2::radius_1[i], where the proper end of the grid corresponds to the grid structure given in the standard output (and recovered with Kuibit, VisIt).

For example, with

CoordBase::dx = 1.0

driver::ghost_size = 3

CarpetRegrid2::radius_1[1] = 24.0

then level 1 extends up to 28.5, which is 9 points away from x=24.

Now, since UAv_Analysis variables focus on output at least every_coarse iterations, I was not too worried by this specifically. However, I have also noticed this pattern when looking at LeanBSSNMoL::ham for instance. I can see constraint violations related to level boundaries, which I expected. But they match with CarpetRegrid::radius_1[i], and not with the grid structure, a feature which I found puzzling. I can see that at iteration 0 already.

Would you have some more explanation about this please?

Best,

Jordan

________________________________ From: Roland Haas rhaas@illinois.edu Sent: Friday, September 27, 2024 21:53 To: Jordan Nicoules Cc: users@einsteintoolkit.org Subject: Re: [Users] Schedule options and uninitialized refinement levels

Hello Jordan,

By looking at the data on the grid, you mean like using a print in the code? Or is there another way through the parameter file? Indeed, what I was referring to was 'out_var = "density_rho"' in the parameter file.

Yes, if you were to add a printf (or so) statement then you would see the data on the grid eg during the next iteration (or in another `global loop-local` routine in ANALYS, but not in a `local` routine in ANALYSIS which would have the same issue as output).

To clarify: The density_rho and density_p grid functions are computed for output purposes. The variables dE_gf_volume, ... are auxiliary grid functions which are used to compute total_energy, ... through a sum reduction. So those only really make sense every coarse time step, thus do_analysis_every should indeed be a multiple of every_coarse. I used a smaller one only for debugging and understanding purposes. By the way, is "every_coarse" an actual parameter that I could call, for instance in a ParamCheck function, to ensure that do_analysis_every is well-chosen indeed?

No, there is not predefined such variable. It is just a "speaking" variable name.

Or is that ultimately up to the user to properly design the parameter file?

It is up to the user. You can define some helper variables if you like in parameter files eg like so:

$every_coarse = 2**(Carpet::max_num_levels - 1)

assuming all your time_refinement_factors are 2. It is up to the user to ensure that this is correct though.

All operations are indeed pointwise, there are no derivatives involved. Even though the GF variables are defined with 3 time levels, it feels to me that only one is necessary indeed (unless I'm missing something, but these are not evolved variables).

The 3 time levels would be used for interpolation in time if you ask for reduction output at timesteps that are not coarse time steps.

Do I understand correctly then, that in that case I will not get incorrect results in the regions of the coarse grid that are overlaid by the fine grid? In particular, as I compute the sum reduction of dE_gf_volume to get the integral total_energy, the result I get is very sensible. I was wondering if the reduction operation was somehow "magically" navigating the finer levels behind the scenes, but from what you say, it really does only the reduction on the coarser level, doesn't it?

It does navigate the finer levels. The "sum" reduction computes a Riemann sum taking the (relative) volume of grid cells on the refinement levels into account. It also takes care of removing double-counting due to the overlapping fine / coarse grids.

In your case, purely pointwise calculation, all will be fine and the answer will be correct.

For non-pointwise operations there is one point where you fill get very slightly different answer than what would be most correct: at the last fine grid point, where the grid transitions to the coarse grid the data will be slightly wrong since for that one location both the coarse and the fine grid contribute half a grid cell each but the coarse grid data has not been updated via restriction from the fine, so will result in slightly different answers than expected.

Basically if I try and draw this and give the weight that is used for each grid cell then this is what things look like:

transition v

fine level : x x x x x weight: 1/2 1 1 1 1/2 cell boundary: ^ ^ ^ ^ ^ ^ integration: |***************|

coarse level: x x x x x weight 1 1/2 0 1/2 1 cell boundary: ^ ^ ^ ^ ^ integration: **************| |******************

So you can see that for the cell that I have marked with "transition" when it comes to the Riemann sum, half the contribution should come from the fine grid (the right hand half of the fine cell centered at that location) and half from the coarse grid (the left hand half of the coarse cell centered at that same location).

Without the restriction the answer computed on the coarse grid for the grid point marked by the "transition" marker, will be slightly different (since the grid spacing is larger, the neighbouring values are different) than on the fine grid. For a purely pointwise calculation the same number will be computed on the fine and one the coarse grid.

I'm also not sure about the SYNC then. In the routine UAv_Analysis_gfs, the loop actually excludes ghost zones, in the fashion of do k = 1+cctk_nghostzones(3), cctk_lsh(3)-cctk_nghostzones(3) so it may seem pointless, except for visualization purposes, right? (for instance, in VisIt)

A SYNC will fill in values for the ghost zones and mesh refinement boundaries. Those are indeed used by visualization. They are skipped by reductions.

Note that by using

k = 1+cctk_nghostzones(3),cctk_lsh(3)-cctk_nghostzones(3)

you are also skipping a layer of ghost points at the outer (physical) boundaries, and those *will* be used by the reduction (or at least the innermost boundary point will be used, with a weight of 1/2).

Given the properties and goals of the quantities I'm using, and what you said, it sounds like I could leave that in ANALYSIS.

For just output you are fine. You cannot use anything computed in ANALYSIS in EVOL though (or at least it may not be what you expect it to be).

But you seemed to favor EVOL.

EVOL is safer since it can be used both in EVOL and in ANALYSIS / POSTSTEP, and is the only option for anything involving derivatives. So if you ask which option to choose and I do not want / cannot safely give you the detailed reasoning above / actually verify that things work as I think they should, I'll err on the side of caution. Note that CCTK_POSTSTEP and MoL_PostStep are very different.

What would now be your advice, with the additional information? I still need to get the mask from AHFinderDirect, and from my understanding of the param.ccl of this thorn, it's at best run at POSTSTEP, isn't it?

AHFinderDirect sets the mask in either ANALSYIS or POSTSTEP (depending on parameters). For modern codes ANALYSIS and POSTSTEP are identical (scheduled routines in ANALYSIS could use a TRIGGER but that one runs into the same problems I warned you about so it is not used nowadays anymore).

AHFidnerDirect reads variables that were set in EVOL (ADMBase variables) and then can set variables (ahmask, the spherical surfaces) that are usable in ANALYSIS / POSTSTEP (the mask). Using the mask (or spherical surface for that matter) in EVOL can be tricky, it will only kind of work if there is only one time level in which case the previous value of the mask will be used in EVOL.

Yours, Roland

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