topic Re: poisson solver varying dielectric in Intel® oneAPI Math Kernel Library

poisson solver varying dielectric

amariani — Fri, 30 Dec 2022 16:02:08 GMT

Hello everyone,

I recently started trying to get familiar with the fast Poisson solvers that are part of the package.

My question is: it seems to me that the routine only solves for the case where the dielectric constant is constant across the domain, is that so?

regards

Re:poisson solver varying dielectric

VidyalathaB_Intel — Tue, 03 Jan 2023 13:23:23 GMT

Hi Augusto,

Thanks for reaching out to us.

>>it seems to me that the routine only solves for the case where the dielectric constant is constant across the domain, is that so?

Could you please let us know the reference article/manual from which you are quoting the above statement?

Also, it would be great if you could describe the use case and elaborate a bit more on the issue.

Regards,

Vidya.

Re: Re:poisson solver varying dielectric

amariani — Tue, 03 Jan 2023 19:24:23 GMT

Hello Vidya, thanks for reaching out.

Referring to the first point, here it is the link to the page within the documentation:

https://www.intel.com/content/www/us/en/develop/documentation/onemkl-developer-reference-c/top/partial-differential-equations-support/fast-poisson-solver-routines/poisson-solver-implementation.html

in there, the form of the PDE to be solved implies that the dielectric is constant throughout the domain so that it could be incorporated as a multiplicative term on the left hand side of the equation in the doc. Otherwise the form would be different, since the relative dielectric constant could not be taken out of the divergence operator, thus not leading to the laplacian as-is.

As far as my usecase, I was thinking about using the fast Poisson solver for a domain that has a relative dielectric constant varying across the domain itself.

Let me know if that is enough information,

Regards.

Re:poisson solver varying dielectric

VidyalathaB_Intel — Tue, 10 Jan 2023 13:09:42 GMT

Hi Augusto,

Thanks for providing us with the details.

We are working on your issue. we will get back to you soon.

Regards,

Vidya.

Re:poisson solver varying dielectric

VidyalathaB_Intel — Thu, 12 Jan 2023 11:56:34 GMT

Hi Augusto,

You can keep the constant within the Laplacian operator and change the variable to solve for "u \epsilon", where the "\epsilon" is the dielectric constant, "u" is the unknown to be solved. The boundary conditions should be modified as well. Once "u \epsilon" is obtained, it is then straightforward to get "u".

Regards,

Vidya.

Re: poisson solver varying dielectric

akalinkin — Sat, 14 Jan 2023 04:00:59 GMT

Hi,

You are right, from my best in current release Poisson solver supports uniform media only. However, if you media is non-uniform you can always use poisson solver as precondition for iterative solver with non-uniform media

Thanks,

Alex

Re:poisson solver varying dielectric

VidyalathaB_Intel — Fri, 20 Jan 2023 04:26:51 GMT

Hi Augusto,

As we haven't heard back from you, could you please provide us with an update regarding the issue?

Regards,

Vidya.

Re: Re:poisson solver varying dielectric

amariani — Fri, 20 Jan 2023 15:15:13 GMT

Hello Vidya,

sorry for the delay. The fact is that under the condition I am depicting I think that you would just not arrive to have the laplacian operator, hence I think the solution you proposed is not viable. I also think, as @akalinkin was suggesting, that an iterative solution, probably through a non linear system solver is the best option.

Regards

Re:poisson solver varying dielectric

VidyalathaB_Intel — Tue, 24 Jan 2023 05:58:26 GMT

Hi Augusto,

>>I am depicting I think that you would just not arrive to have the laplacian operator...I also think, as @akalinkin was suggesting, that an iterative solution, probably through a non linear system solver is the best option.

>>my best in current release Poisson solver supports uniform media only.

ok, I see. You are trying to solve for \nabla\cdot (\epsilon\nabla u) = f, not \nabla\cdot\nabla (\epsilon u) = f. In this case, @akalinkin is correct. The current Poisson solver doesn't support it.

Please let us know if your issue is addressed so that we can close this thread.

Regards,

Vidya.

Re: poisson solver varying dielectric

VidyalathaB_Intel — Fri, 03 Feb 2023 16:11:19 GMT

Hi @amariani ,

As we haven't heard back from you, we are closing this thread. Please post a new question if you need any additional assistance from Intel as this thread will no longer be monitored.

Regards,

Vidya.