Moment preserving constrained resampling with applications to particle-in-cell methods

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.

An unsupervised machine-learning checkpoint-restart algorithm using Gaussian mixtures for particle-in-cell simulations

“…The implication in the context of GM is that the estimated continuum PDF may be able distinguishing between noise and signal, and, if so, provide a measure of noise reduction (i.e., variance control), such that the GM PDF, once resampled, may lead to an improved PIC solution vs. the unrestarted one. The subject of noise control in PIC algorithms has received significant attention recently [37,38,39], but it has mostly been circumscribed to the remapping of the particle PDF via interpolation to a (semi-)structured phase-space mesh (i.e., bins), and subsequent resampling within bins. Some of these approaches [39] explicitly embed arbitrary moment conservation in their formulation, which is a desirable property.…”

“…The subject of noise control in PIC algorithms has received significant attention recently [37,38,39], but it has mostly been circumscribed to the remapping of the particle PDF via interpolation to a (semi-)structured phase-space mesh (i.e., bins), and subsequent resampling within bins. Some of these approaches [39] explicitly embed arbitrary moment conservation in their formulation, which is a desirable property. However, to our knowledge, the use of Gaussian-mixture techniques for this purpose remains unexplored.…”

Electromagnetic Fireworks: Fast Radio Bursts from Rapid Reconnection in the Compressed Magnetar Wind

“…12 Conservative PIC particle merging algorithms are one way to down-sample the particle load and were initially reviewed by Assous et al (2003). Weight optimization techniques for merged particles have since been developed to conserve essential moments of the distribution function (Welch et al 2007;Faghihi et al 2020). Vranic et al (2015) and Luu et al (2016) hold a credible benchmark for their particle merging algorithm based on the proximity of particles in 6D phase space to simultaneously conserve charge, momentum, and energy of particles.…”

Implementation of higher-order velocity mapping between marker particles and grid in the particle-in-cell code XGC

“…In XGC simulations, with a realistic number of marker particles and a typical 5-D grid size, we expect that a fraction ∼ 1 % of all velocity cells are not appropriately populated during a time step, and particularly cells at high kinetic energy. To remedy this issue, XGC is equipped with a particle resampling technique which is used to create, annihilate or redistribute particles in configuration space while preserving a desired number of moments (Faghihi et al 2020). (More details of the XGC resampling can be found in Dominski et al (2021).)…”