# Moment Preserving Constrained Resampling with Applications to Particle-in-Cell Methods

## TL;DR

This paper introduces MPCR, a particle resampling algorithm for PIC methods that conserves quantities with high accuracy, improving simulation stability and accuracy with negligible additional computational cost.

## Contribution

The paper presents MPCR, a novel, general algorithm for particle resampling in PIC simulations that conserves multiple quantities with machine precision.

## Key findings

- MPCR improves accuracy and stability in PIC simulations.
- The computational cost of MPCR is negligible.
- Numerical tests demonstrate enhanced simulation performance.

## Abstract

In simulations of partial differential equations using particle-in-cell (PIC) methods, it is often advantageous to resample the particle distribution function to increase simulation accuracy, reduce compute cost, and/or avoid numerical instabilities. We introduce an algorithm for particle resampling called Moment Preserving Contrained Resampling (MPCR). The general algorithm partitions the system space into smaller subsets and is designed to conserve any number of particle and grid quantities with a high degree of accuracy (i.e. machine accuracy). The resampling scheme can be integrated into any PIC code. The advantages of MPCR, including performance, accuracy, and stability, are presented by examining several numerical tests, including a use-case study in gyrokinetic fusion plasma simulations. The tests demonstrate that while the computational cost of MPCR is negligible compared to the nascent particle evolution in PIC methods, periodic particle resampling yields a significant improvement in the accuracy and stability of the results.