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

Abstract

For given computational resources, one of the main limitations in the accuracy of plasma simulations using particles comes from the noise due to limited statistical sampling in the reconstruction of the particle distribution function. A method based on wavelet multiresolution 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 nite number of independent measurements. Its novel application to plasma simulations can be viewed as a natural extension of the nite 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 timestep of a FSP simulation. The method is compared with a recently proposed proper orthogonal decomposition based method, and it is tested with particle data corresponding to strongly collisional, weakly collisional, and collisionless plasmas simulations.