On Oct 16, 2020, at 16:10, Roland Haas <rhaas@illinois.edu> wrote:

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
* Please see the mailing list for previous questions about
 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
 ADM mass of the system. 

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@uniroma1.it
************************************

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