MLPoisson with free-space boundary conditions

[BenWibking]

Is it possible to do a cell-centered Poisson solve with MLMG but with a FFT solve on level 0? This would be very useful for self-gravitating simulations with non-periodic boundary conditions using the zero-padding method or, e.g., this method.

The only other method I am aware of to do free-space boundary conditions for general mass distributions appears to be FMM-type methods, such as McCorquodale05, but this appears to be significantly more complicated but may require less communication.

[zingale]

Ben, you should look at the method on Castro which uses a multipole method to get Dirichlet BCs for the multigrid solve. It works well. See Katz et al. 2016 for details.

[BenWibking]

I'm currently pretty busy with things that have deadlines in the next few weeks, but I should have time to work on the implementation after that.

Just for reference, I found this tech report with more details on the McCorquodale+ method. They do in fact use 2D cartesian multipoles for the potential of the induced surface charge. However, everything in that work is node-centered. I'm not sure whether WarpX uses cell-centered or node-centered. For my code at least, I will need to work out the changes in stencil etc., for cell-centered potential/charge.

[WeiqunZhang]

Maybe I am missing something. I don't see the index type is an issue. WarpX's solver is node based. We can support both.

[BenWibking]

Yes, either case should work. I just meant that I think the calculation of the surface charge is slightly different between the two cases (although I haven't checked yet to be sure, it might actually be the same).

[WeiqunZhang]

@BenWibking Could you give this a try? #2912

[BenWibking]

This will be great to have. Unfortunately, I'm in the middle of moving back to the US from Australia at the moment, so I won't be able to try it out with Quokka for at least a few weeks.