Efficient Fourier Basis Particle Simulation

TL;DR

This paper introduces an efficient gridless particle simulation method using USFFT that improves energy conservation and reduces noise compared to traditional PIC algorithms.

Contribution

The paper presents a novel Fourier basis particle simulation method that is computationally efficient and superior in energy conservation, bypassing grid heating issues.

Findings

Achieves asymptotic runtime comparable to standard PIC algorithms.

Demonstrates superior energy conservation and reduced noise.

Shows convergence of energy conservation at small time steps.

Abstract

The standard particle-in-cell algorithm suffers from grid heating. There exists a gridless alternative which bypasses the deposition step and calculates each Fourier mode of the charge density directly from the particle positions. We show that a gridless method can be computed efficiently through the use of an Unequally Spaced Fast Fourier Transform (USFFT) algorithm. After a spectral field solve, the forces on the particles are calculated via the inverse USFFT (a rapid solution of an approximate linear system). We provide one and two dimensional implementations of this algorithm with an asymptotic runtime of $O(N_p + N_m^D \log N_m^D)$ for each iteration, identical to the standard PIC algorithm (where $N_p$ is the number of particles and $N_m$ is the number of Fourier modes, and $D$ is the spatial dimensionality of the problem) We demonstrate superior energy conservation and reduced noise, as well as convergence of the energy conservation at small time steps.