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[lammps-users] Fast Multipole Method (FMM) - does it exist and if not, why not
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[lammps-users] Fast Multipole Method (FMM) - does it exist and if not, why not

From: Peter Spalthoff <peter.spalthoff@...24...>
Date: Tue, 5 Sep 2017 12:21:03 +0900

Dear all,

I have used LAMMPS in the past for MD simulations and became interested in long range solving methods. 
I will (hopefully) join a lab working on fast multipole methods and in that context was wondering if they are employed in LAMMPS.
I scoured the archives and to my surprise found nothing on the subject but a single vague claim that LAMMPS does not contain FMM code.

My questions are thus:
Does LAMMPS contain FMM code?
If not, why is that the case? 

If someone could point me to some literature on the subject, that would also be of great help. 

The following is just some (hopefully correct) information I have gathered in the research process:
The LAMMPS documentation on long range solvers mainly talks about Ewald and related pppm methods. Depending on the implementation, these methods are O(N Log N) (Wikipedia on Ewald summation) or even O(N) (a paper I found), but FMM codes can achieve the same asymptotic characteristics. I don't know anything about the hidden constants and am not sure how the code in LAMMPS scales (I sadly cannot try myself at the moment), but it would seem that FMMs might be competitive.
I have found papers describing the use of FMM with periodic boundary conditions. 

I am happy to provide some sources when I am back on my computer.

So long and all the best from Japan,

Peter Spalthoff