An adaptive Particle-In-Cell method using multi-resolution analysis

Abstract

In this paper we introduce a new PIC method based on an adaptive multi-resolution scheme for solving the one dimensional Vlasov–Poisson equation. Our approach is based on a description of the solution by particles of unit weight and on a reconstruction of the density at each time step of the numerical scheme by an adaptive wavelet technique: the density is firstly estimated in a proper wavelet basis as a distribution function from the current empirical data and then “de-noised” by a thresholding procedure. The so-called Landau damping problem is considered for validating our method. The numerical results agree with those obtained by the classical PIC scheme, suggesting that this multi-resolution procedure could be extended with success to plasma dynamics in higher dimensions.