Projective multiscale time-integration for electrostatic particle-in-cell methods

TL;DR

This paper introduces a wavelet-based projective integration method for kinetic plasma simulations, enabling efficient long-term predictions by combining short PIC simulations with coarse-grained extrapolation, validated through 1D experiments.

Contribution

It presents a novel multiscale time-integration scheme that combines wavelet discretization with Equation-Free Projective Integration for kinetic plasma systems.

Findings

Good agreement with full PIC simulations

Speedup scales linearly with system size

Effective for large-scale, multiscale plasma problems

Abstract

The simulation of problems in kinetic plasma physics are often challenging due to strongly coupled phenomena across multiple scales. In this work, we propose a wavelet-based coarse-grained numerical scheme, based on the framework of Equation-Free Projective Integration, for a kinetic plasma system modeled by the Vlasov-Poisson equations. A kinetic particle-in-cell (PIC) code is used to simulate the meso scale dynamics for short time intervals. This allows the extrapolation over long time-steps of the behavior of a coarse wavelet-based discretization of the system. To validate the approach and the underlying concepts, we perform two 1D1V numerical experiments: nonlinear propagation and steepening of an ion wave, and the expansion of a plasma slab in vacuum. The direct comparisons to resolved PIC simulations show good agreement. We show that the speedup of the projective integration scheme over the full particle scheme scales linearly with the system size, demonstrating efficiency while taking into account fully kinetic, non-Maxwellian effects. This suggests that the approach is potentially interesting for kinetic plasma problems with a large separation of scales, especially in higher dimensions.