[Users] Boundary conditions in diagnostics with compute_every

[Erik Schnetter]

Gabriele

No, I think prolongation="copy" would choose the spatial prolongation
operator. InterpNumTimelevels = 1 might be the right choice. If you
declare and allocate only a single time level, then the code will
automatically fail if it tries to use older time levels.

-erik

On Mon, Mar 8, 2021 at 10:32 AM Gabriele Bozzola
<bozzola.gabriele at gmail.com> wrote:
>
> Hi Erik,
>
>> In this case, you can declare the grid function to use 0-th order time
>> interpolation, and allocate only a single time level. This would do
>> the same thing. I think the respective time prolongtation operator is
>> called "copy".
>
>
> Do I achieve this by setting the tags prolongation="copy" and InterpNumTimelevels = 1
> in the declaration of the grid function in the interface.ccl?
>
> Thanks again,
> Gabriele
>
> On Sun, Mar 7, 2021 at 10:05 AM Erik Schnetter <schnetter at cct.lsu.edu> wrote:
>>
>> On Sat, Mar 6, 2021 at 1:58 PM Gabriele Bozzola
>> <bozzola.gabriele at gmail.com> wrote:
>> >
>> > 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?
>>
>> In this case, you can declare the grid function to use 0-th order time
>> interpolation, and allocate only a single time level. This would do
>> the same thing. I think the respective time prolongtation operator is
>> called "copy".
>>
>> -erik
>>
>> > 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
>> >> > >>
>> >> > >>
>> >> > >> _______________________________________________
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>> >> > >> Users at einsteintoolkit.org
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>> >>
>> >>
>> >>
>> >> --
>> >> Erik Schnetter <schnetter at cct.lsu.edu>
>> >> http://www.perimeterinstitute.ca/personal/eschnetter/
>>
>>
>>
>> --
>> Erik Schnetter <schnetter at cct.lsu.edu>
>> http://www.perimeterinstitute.ca/personal/eschnetter/



-- 
Erik Schnetter <schnetter at cct.lsu.edu>
http://www.perimeterinstitute.ca/personal/eschnetter/