Wavelet-based density estimation for noise reduction in plasma simulations using particles

TL;DR

This paper introduces a wavelet-based density estimation method to reduce noise in particle-based plasma simulations, improving accuracy without significant computational overhead and adapting locally to density features.

Contribution

The novel application of wavelet-based density estimation to plasma simulations enhances noise reduction and accuracy, especially for localized sharp features, with minimal computational cost.

Findings

Effective noise reduction in plasma simulations.

Preserves moments of particle distribution accurately.

Comparable computational cost to a single simulation time step.

Abstract

For given computational resources, the accuracy of plasma simulations using particles is mainly held back by the noise due to limited statistical sampling in the reconstruction of the particle distribution function. A method based on wavelet analysis is proposed and tested to reduce this noise. The method, known as wavelet based density estimation (WBDE), was previously introduced in the statistical literature to estimate probability densities given a finite number of independent measurements. Its novel application to plasma simulations can be viewed as a natural extension of the finite size particles (FSP) approach, with the advantage of estimating more accurately distribution functions that have localized sharp features. The proposed method preserves the moments of the particle distribution function to a good level of accuracy, has no constraints on the dimensionality of the system, does not require an a priori selection of a global smoothing scale, and its able to adapt locally to the smoothness of the density based on the given discrete particle data. Most importantly, the computational cost of the denoising stage is of the same order as one time step of a FSP simulation. The method is compared with a recently proposed proper orthogonal decomposition based method, and it is tested with three particle data sets that involve different levels of collisionality and interaction with external and self-consistent fields.