Sparse Grid reconstructions for Particle-In-Cell methods

Abstract

In this article, we propose and analyse Particle-In-Cell (PIC) methods embedding sparse grid reconstruction as those introduced in [1, 2]. The sparse grid reconstructions offer a significant improvement on the sta- tistical error of PIC schemes as well as a reduction in the complexity of the problem providing the electric field. Main results on the convergence of the electric field interpolant and conservation properties are provided in this pa- per. Besides, tailored sparse grid reconstructions, in the frame of the offset combination technique, are proposed to introduce PIC methods with improved efficiency. The methods are assessed numerically and compared to existing PIC schemes thanks to classical benchmarks with remarkable prospects for three dimensional computations.