We introduce a novel particle-in-Fourier (PIF) scheme that extends its applicability to non-periodic boundary conditions. Our method handles free space boundary conditions by replacing the Fourier Laplacian operator in PIF with a mollified Green's function as first introduced by Vico-Greengard-Ferrando. This modification yields highly accurate free space solutions to the Vlasov-Poisson system, while still maintaining energy conservation up to an error bounded by the time step size. We also explain how to extend our scheme to arbitrary Dirichlet boundary conditions via standard potential theory, which we illustrate in detail for Dirichlet boundary conditions on a circular boundary. We support our approach with proof-of-concept numerical results from two-dimensional plasma test cases to demonstrate the accuracy, efficiency, and conservation properties of the scheme.

翻译：我们提出了一种新颖的粒子-傅里叶（PIF）格式，将其适用范围扩展至非周期性边界条件。该方法通过采用Vico-Greengard-Ferrando首次提出的光滑格林函数替代PIF中的傅里叶拉普拉斯算子，从而处理自由空间边界条件。这一改进能够为Vlasov-Poisson系统提供高精度的自由空间解，同时将能量守恒误差控制在时间步长数量级内。我们还阐述了如何通过标准位势理论将该格式推广至任意狄利克雷边界条件，并以圆形边界上的狄利克雷边界条件为例进行了详细说明。基于二维等离子体测试算例的数值验证结果，我们论证了该格式在精度、效率及守恒特性方面的性能。