[Users] questions about working elliptic solver thorns

[Erik Schnetter]

On Wed, May 27, 2015 at 2:50 PM, Comer Duncan <comer.duncan at gmail.com>
wrote:

> Hi Erik,
>
> Frank suggested you might be an appropriate person to ask about elliptic
> solver thorns that work in the current release of ET. I have, as you know,
> built Hilbert and have built the development version.
>
> I am wanting to write a thorn which prepares a geon, approximated by
> initial data which has toroidal symmetry and is bounded. The desired
> distribution would be placed on the r axis in cylindrical coordinates and
> have a gaussian distribution. In the actual application, of course the
> initial data would be interpolated onto a Cartesian coordinate mesh or
> meshes.  I just want to solve the Hamiltonian constraint and have the
> initial data be time-symmetric. This sounds like a pretty simple thing to
> do. I think I could start with Brill and put q to my purposes and pretty
> much get out what I want.  However, the IDBrill does not seem to work.
> Also, I am wondering what kinds of elliptic solvers you know of that are
> fully supported in ET?  Frank mentioned a petsc thorn. It does not get
> downloaded and built by default and looking at the einsteintoolkit.th
> file it is mentioned in:
>
> # CactusElliptic thorns
> !TARGET   = $ARR
> !TYPE     = git
> !URL      = https://bitbucket.org/cactuscode/cactuselliptic.git
> !REPO_PATH= $2
> !CHECKOUT = CactusElliptic/EllPETSc CactusElliptic/TATPETSc
> CactusElliptic/EllBase
> #DISABLED CactusElliptic/EllPETSc
> CactusElliptic/EllSOR
> CactusElliptic/TATelliptic
> #DISABLED CactusElliptic/TATPETSc
>
> However, what's with the DISABLED reference to EllPETSc is a bit
> concerning. So before I go though the exercise to look more into the
> EllPETSc, I thought  I'd ask whether the EllPETSc thorn is fully compatible
> with Hilbert?
>
> Can you thus please bring me up to the current moment on just what
> elliptic solvers are in use for initial data construction in Hilbert?  I
> know many people have been focussing on the multiple BH problem, so there's
> not much traffic anymore about Brill.  I do want to run Brill though and
> also do the "geon" problem.
>
> Thanks for your advice and any pointers you can give.
>

Comer

The #DISABLED just means that it has been disabled, not that the thorn is
bad. We only disable it because PETSc is a large package and may be
difficult to install, and only very few people use PETSc with Cactus. I am
regularly building with PETSc, and have also run the ET tests with PETSc
enable on some of our machines.

I don't recommend using SOR. If you use mesh refinement, or if you use a
machine more powerful than a laptop, then you can afford domains that are
so large that SOR converges too slowly to be useful.

BAM_Elliptic is not freely available. It also has not been used in more
than a decade, and I doubt it would be useful to resurrect it.

PETSc is a modern, full-featured elliptic solver. Unfortunately, there is
no integration with Cactus's grid functions if you want to use mesh
refinement. If you can live with a unigrid simulation, then EllPETSc allows
you to solve linear elliptic equations. The thorns EllBase or EllPETSc
should have some documentation on this; if not, maybe we can discuss next
Monday during the ET telecon.

There is also a thorn TATPETSc that can solve non-linear elliptic equations
(also unigrid only).

I haven't used these thorns in production in quite some time. Our initial
conditions typically come from third-party solvers, e.g. Lorene or
TwoPunctures.

The most modern solution is probably the multigrid solver that Eloisa wrote
and that Ian described.


The situation of elliptic solvers in Cactus is not as good as I would like
it to be. To help you out, it is probably best to talk in person, so that
we see what you need. Do you have time next Monday to call in to our ET
telecon?

-erik

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