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" :
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 ?
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.
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