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) [1,2]. We provide one and two dimensional implementations of this algorithm with an asymptotic runtime of O(Np+NmDlogNmD) for each iteration, identical to the standard PIC algorithm (where Np is the number of particles, Nm 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.
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