PPPS-2013: Topic 1.2: A domain decomposition method for pseudo-spectral electromagnetic simulations of plasmas

Abstract

Summary form only given. Particle-In-Cell (PIC) has been the method of choice for the last fifty years for modeling plasmas that include kinetic effects. The most popular electromagnetic formulation uses finite difference discretization of Maxwell's equations in both space and time (FDTD), which produces fast solvers that scale well in parallel, but suffers from various anomalous numerical effects resulting from discretization, field staggering, and numerical dispersion. Pseudo-spectral methods, which advance fields in Fourier space, offer a number of advantages over FDTD algorithms. In particular, Haber's Pseudo-Spectral Analytical Time-Domain (PSATD) algorithm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> has dispersion-free propagation and no Courant limit in vacuum. Yet, pseudo-spectral solvers have not been widely used, due in part to the difficulty for efficient parallelization owing to global communications associated with global FFTs. We present a novel method2 for the parallelization of electromagnetic pseudo-spectral solvers that requires only local FFTs and exchange of local guard cell data between neighboring regions, by taking advantage of the properties of DFTs, the linearity of Maxwell's equations and the finite speed of light. Although this requires a small approximation, test results show that no significant error is made on the test cases such as single electromagnetic pulse expansion, or Particle-In-Cell simulations of the wakefield formation in a laser plasma accelerator. Extension to other equations beyond electromagnetic PIC will be discussed.