# [Users] Poisson equation

Roland Haas rhaas at illinois.edu
Fri Oct 16 09:10:12 CDT 2020

```Hello Taishi,

the participants discussed your email at yesterday's public Einstein
Toolkit user call, see:
https://docs.einsteintoolkit.org/et-docs/Meeting_agenda

Unfortunately no experts in the CT_MultiLevel code were present.

I am certainly no expert myself but will try to offer some suggestions:

* CT_MultiLevel is indeed compatible (in fact uses and relies) on
Carpet and the grid setup requires that you cover your solution
domain with multiple refinement levels.
* The Poisson equation can be solved and you can see eg an example in
our gallery: http://einsteintoolkit.org/gallery/poisson/index.html
CT_MultiLevel:
http://lists.einsteintoolkit.org/pipermail/users/2020-August/007562.html
http://lists.einsteintoolkit.org/pipermail/users/2020-August/007563.html
http://lists.einsteintoolkit.org/pipermail/users/2020-August/007575.html
* Since CT_MultiLevel only supports Cartesian grids a boundary
condition like 1/r which typically ends up being implemented as a
robin type conditions a f(r) + b f'(r) = 0 is (to my understanding)
not well posed since the r-derivative is not a normal derivative (in
the normal direction of the boundary) on the x,y,z boundary faces. It
would require a boundary that is a sphere. The TwoPunctures
CT_MultiLevel test "cheats" by (also) solving the equation using
TwoPunctures and then using the known TwoPunctures solution as a
Dirichlet type boundary condition. You may be able to get away with a
Dirichlet type b/c using M/r as the value where "M" is the desired

Hopefully someone with more in-depth understanding of CT_MultiLevel
will be able to chip in.

Yours,
Roland

> Dear all
> Hello, I’m a user of EinsteinToolkit.
> Now, I’m trying to solve Poisson's equation using ctthorn as initial data before time evolution on EinsteinToolkit.
> The boundary condition is 1/r.
>
> I already implemented my thorns for the source term of the equation,
> and solved the equation using "CT_MutiLevel”.
> I checked if the final solution is real solution of the original equation, but
> it is not good solution.
> I changed the resolution, but it is not improved.
>
> So, I may misunderstand how to use CT_MutiLevel thorns, and I have questions relate to "CT_MutiLevel" :
> 1)
> In order to understand correct behavior,
> I want to try test simulation using poisson.par, which is one of the example parameter file.
>
> But, it does not work.
> The output told me the grid structure is inconsistent,
> and I also try another example, but it also has same error.
> Are there other available par file for CT_MutiLevel ?
>
> 2)
> To solve the elliptic equation with 1/r boundary condition, is CT_MutiLevel the best way ?
> If there are another thorn to solve elliptic equation in EinsteinToolkit, let me know.
> Since I want to use Carpet, the thorn should be compatible with Carpet.
>
> 3)
> After solving elliptic equation, I want to solve time evolution.
> Since CT_MutiLevel is a solver using MultiGrid method, we must prepare several Carpet grids on whole domain.
> But, is it consist with time evolution ?
> If there is an example par file, let me know.
>
> Best.
> Taishi.
>
> ************************************
> Taishi Ikeda
> Physics Department
> Sapienza University of Rome (Italy)
> taishi.ikeda at uniroma1.it
> ************************************
>
>

--
My email is as private as my paper mail. I therefore support encrypting
and signing email messages. Get my PGP key from http://pgp.mit.edu .
-------------- next part --------------
A non-text attachment was scrubbed...
Name: not available
Type: application/pgp-signature
Size: 833 bytes
Desc: OpenPGP digital signature
Url : http://lists.einsteintoolkit.org/pipermail/users/attachments/20201016/b1a67b50/attachment-0001.bin
```