Optimized 1d-1v Vlasov-Poisson simulations using a filtered Fourier-Hermite spectral discretization

Summary form only given, as follows. The Vlasov-Poisson simulations to be presented evolve a spatially periodic phase-space distribution f(x,v,t) represented by a Fourier basis in space and an asymmetrically normalized Hermite representation in velocity. A filtered Vlasov equation is integrated through time with an O(/spl Delta/t/sup 2/)-accurate splitting method, using a O(/spl Delta/t/sup 4/) Runge-Kutta time advancement scheme on the v/spl delta//sub x/f,f and E/spl delta//sub v/f,f terms separately, between which the self-consistent electric field is calculated. This method improves upon that of previous works by the combined use of two optimization techniques: exact Gaussian filtering and variable velocity scale Hermite basis functions. The filter width, v/sub o/, reduces the error introduced by the finite computational system, yet does not alter the low-order velocity modes; therefore, the E-field information is not affected by the filtering. In addition, a variable velocity scale length U is introduced into the Hermite basis functions to provide improved spectral accuracy, yielding orders of magnitude reduction in the L/sub 2/-norm error. This algorithm conserves particles and momentum exactly, and total energy in the limit of continuous time. Relative errors with respect to linear plasma theory have been shown to be an order of magnitude lower than those found in comparable Fourier-Fourier schemes.