Agnostic conservative down-sampling for optimizing statistical representations and PIC simulations

TL;DR

This paper introduces an agnostic conservative down-sampling algorithm for particle-in-cell simulations that reduces macro-particle count while preserving distribution functions and conservation laws, enhancing accuracy and physical fidelity.

Contribution

The paper presents a novel probabilistic down-sampling method that maintains all distribution functions and conservation laws on average, improving upon existing resampling techniques.

Findings

Preserves distribution functions on average.

Maintains conservation laws during down-sampling.

Reduces macro-particle count without loss of physical accuracy.

Abstract

In particle-in-cell simulations and some other statistical computations, the representation of modelled distributions with tracked macro-particles can become locally excessive. Merging or resampling dense clusters or highly-populated phase space volumes may, however, remove or affect small-scale peculiarities in the modelled distribution or cause local changes of conserved quantities, such as energy and momenta. This may lead to additional noise, reduced accuracy or even unphysical effects. Here we describe a probabilistic algorithm for reducing the number of macro-particles in such clusters or volumes so that all the distribution functions are not affected on average and an arbitrary number of conservation laws, distribution central moments and contributions to the grid quantities (such as charge and current density) are preserved.