Kroneckerised Particle Mesh Ewald

TL;DR

This paper introduces a novel Kronecker-based variant of Particle Mesh Ewald that reduces FFT dependence, enhancing parallel scalability for large-scale N-body simulations.

Contribution

It proposes a new reciprocal space method using Sum of Kronecker Products, offering improved parallel performance over classical FFT-based PME.

Findings

The Kronecker-based method demonstrates comparable accuracy to classical PME.

The new scheme shows better scalability on distributed-memory architectures.

Numerical results confirm the method's effectiveness for large N-body problems.

Abstract

Particle Mesh Ewald (PME) methods accelerated through Fast Fourier Transforms (FFTs) for their reciprocal part are widely used to solve N -body problems over periodic structures with Laplace-like kernels. The FFT dependence of classical PME may mitigate its performance on parallel distributed-memory architectures. We here introduce a new variant of the reciprocal part based on Sum of Kronecker Products (SKP) instead of FFT. Moreover, our implementation of this new method is not linearithmic (as opposed to classical PME) but has an important parallel potential. We present the different approximation levels exploited in our new scheme and demonstrate to what extent it could be used on parallel distributed-memory architectures. Numerical examples supplement presented assertions.