  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.
