Particle Simulation in Fourier Space
Matthew S. Mitchell, Matthew Miecnikowski, Scott Parker, Gregory Beylkin · 2018
The standard particle-in-cell algorithm suffers from finite grid effects which break energy conservation, cause numerical dispersion, and create numerical instabilities. We present a gridless alternative, bypassing the deposition step and calculating each Fourier mode of the charge density directly from the particle positions. This can be done efficiently through the use of an Unequally Spaced Fast Fourier Transform (USFFT) algorithm1 2. 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 a 1D implementation of this algorithm with an asymptotic runtime of O(Np + Nm log Nm) for each iteration, identical to the standard PIC algorithm (where Np is the number of particles and Nm is the number of Fourier modes). We demonstrate superior energy conservation and reduced noise, as well as convergence at small time steps.