[Users] Poisson equation

[Taishi Ikeda]

Dear Roland
Thank you for your e-mail.
>  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. 

I notice that I may use Dirichlet boundary similar way.
I will try it.
Thank you for your suggestion.
Best.
Taishi.
************************************
Taishi Ikeda
Physics Department
Sapienza University of Rome (Italy)
taishi.ikeda at uniroma1.it
************************************

> On Oct 16, 2020, at 16:10, Roland Haas <rhaas at 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 <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 <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/007562.html>
>  http://lists.einsteintoolkit.org/pipermail/users/2020-August/007563.html <http://lists.einsteintoolkit.org/pipermail/users/2020-August/007563.html>
>  http://lists.einsteintoolkit.org/pipermail/users/2020-August/007575.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 at uniroma1.it <mailto: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 <http://pgp.mit.edu/> .


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