poisson solver varying dielectric

[amariani]

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

[VidyalathaB_Intel]

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.

[amariani]

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.

[VidyalathaB_Intel]

Hi Augusto,

Thanks for providing us with the details.

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

Regards,

Vidya.

[VidyalathaB_Intel]

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.

[akalinkin]

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

[VidyalathaB_Intel]

Hi Augusto,

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

Regards,

Vidya.

[amariani]

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

[VidyalathaB_Intel]

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.

[VidyalathaB_Intel]

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.