[Users] Boundary conditions in diagnostics with compute_every

[Gabriele Bozzola]

Hi Erik,

thanks for your response: it is very useful.

> > Also, is it a problem if I don't worry about the boundaries If I
> > want to interpolate the constraints onto a sphere?
>
> Yes it is. Interpolation requires a stencil, which requires boundaries.

I suspected so. Then, going back to the question in the first email, you
said that I am essentially forced to compute the diagnostic at
each timestep. The diagnostic I want to compute is very expensive,
and it would slow down dramatically the evolution, so I really want to
compute it only when I am going to output it. What I had in mind was
to copy grid function to the previous timelevels by setting _p and _p_p.
If I copy the same values as the one at the current time, this would
essentially disable time interpolation. But, if I output only when all
the refinement levels at the same time, this should not be a problem,
because there shouldn't be a need for time prolongation, right?

Thanks again for your help,
Gabriele

On Sat, Mar 6, 2021 at 7:45 AM Erik Schnetter <schnetter at cct.lsu.edu> wrote:

> On Fri, Mar 5, 2021 at 8:01 PM Gabriele Bozzola
> <bozzola.gabriele at gmail.com> wrote:
> >
> > Hi Erik,
> >
> > thank you very much for your answer.
> >
> > Just a clarification: what is 'boundary' exactly in this context?
>
> "Boundary" in the context are all grid points where the constraints
> cannot be calculated directly, i.e. by evaluating finite differences.
>
> > Also, is it a problem if I don't worry about the boundaries If I
> > want to interpolate the constraints onto a sphere?
>
> Yes it is. Interpolation requires a stencil, which requires boundaries.
>
> Cactus interpolation supports taking derivatives during interpolation.
> You can thus interpolate the ADM variables and their derivatives onto
> a sphere, and calculate the constraints there. You won't need to take
> derivatives on the sphere since you interpolated all derivatives, so
> evaluating the constraints on points on a sphere is then a point-wise
> operation. The horizon finder does this (calculating the expansion,
> not the constraints, but both have equivalent requirements).
>
> -erik
>
> > Thanks,
> > Gabriele
> >
> > Erik Schnetter <schnetter at cct.lsu.edu> writes:
> >
> > > Gabriele
> > >
> > > If you do not use the constraints, then you do not need to set
> > > the
> > > boundaries. That would simplify many things; for example, you
> > > can
> > > calculate them at any time, and you do not need to worry about
> > > time
> > > levels. However, you then need to be careful about visualization
> > > and
> > > reductions: You need to ensure that you don't accidentally
> > > visualize
> > > the boundaries, and you cannot perform vertex-centred reductions
> > > in
> > > Carpet because they need some boundary values.
> > >
> > > If you do need boundaries, then you need three time levels to
> > > allow
> > > prolongation on boundaries, and you are essentially forced to
> > > evaluate
> > > the constraints at every iteration. I recommend the schedule bin
> > > "MoL_PseudoEvolution" for this, which runs once per time step,
> > > after
> > > MoL's loop, at the right time (i.e. before restriction).
> > >
> > > -erik
> > >
> > > On Fri, Mar 5, 2021 at 11:01 AM Gabriele Bozzola
> > > <bozzola.gabriele at gmail.com> wrote:
> > >>
> > >> Hello,
> > >>
> > >> suppose (for clarity) that I want to write a thorn that
> > >> computes the constraint violations
> > >> as grid functions. Since this is a diagnostic, I don't need to
> > >> compute it at every iteration,
> > >> so I will add a parameter "compute every" and I will schedule
> > >> the computations in
> > >> CCTK_ANALYSIS. Then, I will be careful and make sure that
> > >> compute_every is a
> > >> multiple of when all the refinement levels are synced up.
> > >>
> > >> How are boundary conditions handled in this case?
> > >>
> > >> I can call Boundary_SelectGroupForBC every "compute_every" and
> > >> schedule the
> > >> corresponding functions in the scheduler. But, do I need to (1)
> > >> allocate multiple timelevels
> > >> for my grid functions, (2) do anything about filling previous
> > >> timelevels?
> > >>
> > >> I am looking at WeylScal4 as an example. The thorn has
> > >> parameters "compute_every",
> > >> the grid functions have 3 time levels, and
> > >> Boundary_SelectGroupForBC is called
> > >> every "compute_every", but nothing is done to fill the previous
> > >> timelevels. How does this
> > >> work?
> > >>
> > >> Assuming that the boundary conditions are 'flat', is there any
> > >> way to just work with one
> > >> timelevel?
> > >>
> > >> Thanks,
> > >> Gabriele
> > >>
> > >>
> > >> _______________________________________________
> > >> Users mailing list
> > >> Users at einsteintoolkit.org
> > >> http://lists.einsteintoolkit.org/mailman/listinfo/users
>
>
>
> --
> Erik Schnetter <schnetter at cct.lsu.edu>
> http://www.perimeterinstitute.ca/personal/eschnetter/
>
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