arXiv subjects

Guangye Chen

Publications and source records attributed to Guangye Chen.

16 recordsLinked to original sources

arXiv2026

Comment on "Impact of particle number and cell-size in fully implicit charge- and energy-conserving particle-in-cell schemes" by N. Savard et al., Phys. Plasmas 32, 073903 (2025)

We take issue with the conclusions in the recent publication by Savard et al. In the study, the authors implement a fully nonlinear charge- and energy-conserving implicit particle-in-cell method (ECC-IPIC), and use it to study the impact of particle number in the quality of the ECC-IPIC solutions for several problems, including an ion acoustic shockwave (IASW) problem and several sheath problems in bounded plasmas. From the study, the authors concluded that ``to reproduce highly resolved convergent solutions, a higher amount of particles per cell need to be used in the implicit scheme for both periodic and bounded simulations when the cell size exceeds the Debye length.'' We demonstrate that, according to our analysis for the IASW test, this conclusion does not survive independent scrutiny. We have identified several diagnostics procedural issues that are at the root of their conclusion, which when fixed dramatically change the outcome of the study.

physics.plasm-ph↗

arXiv2025

Novel Methods for Simulating Astrophysical Plasmas and the Coherent Emission in Fast Radio Bursts

We present particle-in-cell simulations of one dimensional relativistic electromagnetic shocks in a uniform magnetic field, for a range of magnetic field strengths, plasma temperatures and numerical initial conditions. We show that the particle energy distributions of these shocks can develop a state of population inversion in the precursor and shock regions, which may allow for synchrotron maser (or maser-like, coherent) emission. Our set-up is applicable to conditions expected in models of fast radio bursts and therefore lends credence to the synchrotron maser model for these transients. We also show, for the first time, how a newly developed ``analytic particle pusher'' for kinetic simulations gives similar results to the commonly-used Boris pusher, but for larger timesteps and without the need to resolve the gyro-radius and gyro-period of the system. This has important implications for modeling astrophysical plasmas in extreme magnetic fields as well as for bridging scales between kinetic and fluid regimes.

astro-ph.HE↗

arXiv2024

Exact local conservation of energy in fully implicit PIC algorithms

We consider the issue of strict, fully discrete \emph{local} energy conservation for a whole class of fully implicit local-charge- and global-energy-conserving particle-in-cell (PIC) algorithms. Earlier studies demonstrated these algorithms feature strict global energy conservation. However, whether a local energy conservation theorem exists (in which the local energy update is governed by a flux balance equation at every mesh cell) for these schemes is unclear. In this study, we show that a local energy conservation theorem indeed exists. We begin our analysis with the 1D electrostatic PIC model without orbit-averaging, and then generalize our conclusions to account for orbit averaging, multiple dimensions, and electromagnetic models (Darwin). In all cases, a temporally, spatially, and particle-discrete local energy conservation theorem is shown to exist, proving that these formulations (as originally proposed in the literature), in addition to being locally charge conserving, are strictly locally energy conserving as well. In contrast to earlier proofs of local conservation in the literature \citep{xiao2017local}, which only considered continuum time, our result is valid for the fully implicit time-discrete version of all models, including important features such as orbit averaging. We demonstrate the local-energy-conservation property numerically with a paradigmatic numerical example.

math.NA↗

arXiv2023

An implicit, conservative and asymptotic-preserving electrostatic particle-in-cell algorithm for arbitrarily magnetized plasmas in uniform magnetic fields

We introduce a new electrostatic particle-in-cell algorithm capable of using large timesteps compared to particle gyro-period under a uniform external magnetic field. The algorithm extends earlier electrostatic fully implicit PIC implementations with a new asymptotic-preserving particle-push scheme that allows timesteps much larger than particle gyroperiods. In the large-timestep limit, the integrator preserves all particle drifts, while recovering the full orbit for small timesteps. The scheme allows for a seamless, efficient treatment of particles with coexisting magnetized and unmagnetized species, and conserves energy and charge exactly without spoiling implicit solver performance. We demonstrate by numerical experiment with several problems of variable species magnetization (diocotron instability, modified two-stream instability, and drift instability) that orders of magnitude wall-clock-time speedups vs. the standard fully implicit electrostatic PIC algorithm are possible without sacrificing solution accuracy.

physics.comp-ph↗

arXiv2021

Enabling particle applications for exascale computing platforms

The Exascale Computing Project (ECP) is invested in co-design to assure that key applications are ready for exascale computing. Within ECP, the Co-design Center for Particle Applications (CoPA) is addressing challenges faced by particle-based applications across four sub-motifs: short-range particle-particle interactions (e.g., those which often dominate molecular dynamics (MD) and smoothed particle hydrodynamics (SPH) methods), long-range particle-particle interactions (e.g., electrostatic MD and gravitational N-body), particle-in-cell (PIC) methods, and linear-scaling electronic structure and quantum molecular dynamics (QMD) algorithms. Our crosscutting co-designed technologies fall into two categories: proxy applications (or apps) and libraries. Proxy apps are vehicles used to evaluate the viability of incorporating various types of algorithms, data structures, and architecture-specific optimizations and the associated trade-offs; examples include ExaMiniMD, CabanaMD, CabanaPIC, and ExaSP2. Libraries are modular instantiations that multiple applications can utilize or be built upon; CoPA has developed the Cabana particle library, PROGRESS/BML libraries for QMD, and the SWFFT and fftMPI parallel FFT libraries. Success is measured by identifiable lessons learned that are translated either directly into parent production application codes or into libraries, with demonstrated performance and/or productivity improvement. The libraries and their use in CoPA's ECP application partner codes are also addressed.

cs.DC↗

arXiv2021

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

We propose an unsupervised machine-learning checkpoint-restart (CR) lossy algorithm for particle-in-cell (PIC) algorithms using Gaussian mixtures (GM). The algorithm features a particle compression stage and a particle reconstruction stage, where a continuum particle distribution function is constructed and resampled, respectively. To guarantee fidelity of the CR process, we ensure the exact preservation of charge, momentum, and energy for both compression and reconstruction stages, everywhere on the mesh. We also ensure the preservation of Gauss' law after particle reconstruction. As a result, the GM CR algorithm is shown to provide a clean, conservative restart capability while potentially affording orders of magnitude savings in input/output requirements. We demonstrate the algorithm using a recently developed exactly energy- and charge-conserving PIC algorithm on physical problems of interest, with compression factors $\gtrsim75$ with no appreciable impact on the quality of the restarted dynamics.

cs.DC↗

arXiv2021

Particle integrator for particle-in-cell simulations of ultra-high intensity laser-plasma interactions

Particle-in-cell codes are the most widely used simulation tools for kinetic studies of ultra-intense laser-plasma interactions. Using the motion of a single electron in a plane electromagnetic wave as a benchmark problem, we show surprising deterioration of the numerical accuracy of the PIC algorithm with increasing normalized wave amplitude for typical time-step and grid sizes. Two significant sources of errors are identified: strong acceleration near stopping points and the temporal field interpolation. We propose adaptive electron sub-cycling coupled with a third order temporal interpolation of the magnetic field and electric field as an efficient remedy that dramatically improves the accuracy of the particle integrator.

physics.plasm-ph↗

arXiv2020

An Adaptive EM Accelerator for Unsupervised Learning of Gaussian Mixture Models

We propose an Anderson Acceleration (AA) scheme for the adaptive Expectation-Maximization (EM) algorithm for unsupervised learning a finite mixture model from multivariate data (Figueiredo and Jain 2002). The proposed algorithm is able to determine the optimal number of mixture components autonomously, and converges to the optimal solution much faster than its non-accelerated version. The success of the AA-based algorithm stems from several developments rather than a single breakthrough (and without these, our tests demonstrate that AA fails catastrophically). To begin, we ensure the monotonicity of the likelihood function (a the key feature of the standard EM algorithm) with a recently proposed monotonicity-control algorithm (Henderson and Varahdan 2019), enhanced by a novel monotonicity test with little overhead. We propose nimble strategies for AA to preserve the positive definiteness of the Gaussian weights and covariance matrices strictly, and to conserve up to the second moments of the observed data set exactly. Finally, we employ a K-means clustering algorithm using the gap statistic to avoid excessively overestimating the initial number of components, thereby maximizing performance. We demonstrate the accuracy and efficiency of the algorithm with several synthetic data sets that are mixtures of Gaussians distributions of known number of components, as well as data sets generated from particle-in-cell simulations. Our numerical results demonstrate speed-ups with respect to non-accelerated EM of up to 60X when the exact number of mixture components is known, and between a few and more than an order of magnitude with component adaptivity.

cs.LG↗

arXiv2019

A semi-implicit, energy- and charge-conserving particle-in-cell algorithm for the relativistic Vlasov-Maxwell equations

Conventional explicit electromagnetic particle-in-cell (PIC) algorithms do not conserve discrete energy exactly. Time-centered fully implicit PIC algorithms can conserve discrete energy exactly, but may introduce large dispersion errors in the light-wave modes. This can lead to intolerable simulation errors where accurate light propagation is needed (e.g. in laser-plasma interactions). In this study, we selectively combine the leap-frog and Crank-Nicolson methods to produce an exactly energy- and charge-conserving relativistic electromagnetic PIC algorithm. Specifically, we employ the leap-frog method for Maxwell's equations, and the Crank-Nicolson method for the particle equations. The semi-implicit algorithm admits exact global energy conservation, exact local charge conservation, and preserves the dispersion properties of the leap-frog method for the light wave. The algorithm employs a new particle pusher designed to maximize efficiency and minimize wall-clock-time impact vs. the explicit alternative. It has been implemented in a code named iVPIC, based on the Los Alamos National Laboratory VPIC code (\url{https://github.com/losalamos/vpic}). We present numerical results that demonstrate the properties of the scheme with sample test problems: relativistic two-stream instability, Weibel instability, and laser-plasma instabilities.

physics.comp-ph↗

arXiv2015

A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov-Darwin particle-in-cell algorithm

For decades, the Vlasov-Darwin model has been recognized to be attractive for particle-in-cell (PIC) kinetic plasma simulations in non-radiative electromagnetic regimes, to avoid radiative noise issues and gain computational efficiency. However, the Darwin model results in an elliptic set of field equations that renders conventional explicit time integration unconditionally unstable. Here, we explore a fully implicit PIC algorithm for the Vlasov-Darwin model in multiple dimensions, which overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. The finite-difference scheme for Darwin field equations and particle equations of motion is space-time-centered, employing particle sub-cycling and orbit-averaging. The algorithm conserves total energy, local charge, canonical-momentum in the ignorable direction, and preserves the Coulomb gauge exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large time steps and cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. We demonstrate the accuracy and efficiency properties of the algorithm with various numerical experiments in 2D-3V.

physics.comp-ph↗

arXiv2014

Temporal resolution criterion for correctly simulating relativistic electron motion in a high-intensity laser field

Particle-in-cell codes are now standard tools for studying ultra-intense laser-plasma interactions. Motivated by direct laser acceleration of electrons in sub-critical plasmas, we examine temporal resolution requirements that must be satisfied to accurately calculate electron dynamics in strong laser fields. Using the motion of a single electron in a perfect plane electromagnetic wave as a test problem, we show surprising deterioration of the numerical accuracy with increasing wave amplitude $a_0$ for a given time-step. We go on to show analytically that the time-step must be significantly less than $λ/c a_ 0$ to achieve good accuracy. We thus propose adaptive electron sub-cycling as an efficient remedy.

physics.plasm-ph↗

arXiv2013

An energy- and charge-conserving, nonlinearly implicit, electromagnetic 1D-3V Vlasov-Darwin particle-in-cell algorithm

A recent proof-of-principle study proposes a nonlinear electrostatic implicit particle-in-cell (PIC) algorithm in one dimension (Chen, Chacon, Barnes, J. Comput. Phys. 230 (2011) 7018). The algorithm employs a kinetically enslaved Jacobian-free Newton-Krylov (JFNK) method, and conserves energy and charge to numerical round-off. In this study, we generalize the method to electromagnetic simulations in 1D using the Darwin approximation of Maxwell's equations, which avoids radiative aliasing noise issues by ordering out the light wave. An implicit, orbit-averaged time-space-centered finite difference scheme is applied to both the 1D Darwin field equations (in potential form) and the 1D-3V particle orbit equations to produce a discrete system that remains exactly charge- and energy-conserving. Furthermore, enabled by the implicit Darwin equations, exact conservation of the canonical momentum per particle in any ignorable direction is enforced via a suitable scattering rule for the magnetic field. Several 1D numerical experiments demonstrate the accuracy and the conservation properties of the algorithm.

physics.plasm-ph↗

arXiv2013

Fluid preconditioning for Newton-Krylov-based, fully implicit, electrostatic particle-in-cell simulations

A recent proof-of-principle study proposes an energy- and charge-conserving, nonlinearly implicit electrostatic particle-in-cell (PIC) algorithm in one dimension [Chen et al, J. Comput. Phys., 230 (2011) 7018]. The algorithm in the reference employs an unpreconditioned Jacobian-free Newton-Krylov method, which ensures nonlinear convergence at every timestep (resolving the dynamical timescale of interest). Kinetic enslavement, which is one key component of the algorithm, not only enables fully implicit PIC a practical approach, but also allows preconditioning the kinetic solver with a fluid approximation. This study proposes such a preconditioner, in which the linearized moment equations are closed with moments computed from particles. Effective acceleration of the linear GMRES solve is demonstrated, on both uniform and non-uniform meshes. The algorithm performance is largely insensitive to the electron-ion mass ratio. Numerical experiments are performed on a 1D multi-scale ion acoustic wave test problem.

physics.plasm-ph↗

arXiv2011

An efficient mixed-precision, hybrid CPU-GPU implementation of a fully implicit particle-in-cell algorithm

Recently, a fully implicit, energy- and charge-conserving particle-in-cell method has been proposed for multi-scale, full-f kinetic simulations [G. Chen, et al., J. Comput. Phys. 230,18 (2011)]. The method employs a Jacobian-free Newton-Krylov (JFNK) solver, capable of using very large timesteps without loss of numerical stability or accuracy. A fundamental feature of the method is the segregation of particle-orbit computations from the field solver, while remaining fully self-consistent. This paper describes a very efficient, mixed-precision hybrid CPU-GPU implementation of the implicit PIC algorithm exploiting this feature. The JFNK solver is kept on the CPU in double precision (DP), while the implicit, charge-conserving, and adaptive particle mover is implemented on a GPU (graphics processing unit) using CUDA in single-precision (SP). Performance-oriented optimizations are introduced with the aid of the roofline model. The implicit particle mover algorithm is shown to achieve up to 400 GOp/s on a Nvidia GeForce GTX580. This corresponds to 25% absolute GPU efficiency against the peak theoretical performance, and is about 300 times faster than an equivalent serial CPU (Intel Xeon X5460) execution. For the test case chosen, the mixed-precision hybrid CPU-GPU solver is shown to over-perform the DP CPU-only serial version by a factor of \sim 100, without apparent loss of robustness or accuracy in a challenging long-timescale ion acoustic wave simulation.

physics.plasm-ph↗

arXiv2011

An Energy- and Charge-conserving, Implicit, Electrostatic Particle-in-Cell Algorithm

This paper discusses a novel fully implicit formulation for a 1D electrostatic particle-in-cell (PIC) plasma simulation approach. Unlike earlier implicit electrostatic PIC approaches (which are based on a linearized Vlasov-Poisson formulation), ours is based on a nonlinearly converged Vlasov-Ampère (VA) model. By iterating particles and fields to a tight nonlinear convergence tolerance, the approach features superior stability and accuracy properties, avoiding most of the accuracy pitfalls in earlier implicit PIC implementations. In particular, the formulation is stable against temporal (CFL) and spatial (aliasing) instabilities. It is charge- and energy-conserving to numerical roundoff for arbitrary implicit time steps. While momentum is not exactly conserved, errors are kept small by an adaptive particle sub-stepping orbit integrator, which is instrumental to prevent particle tunneling. The VA model is orbit-averaged along particle orbits to enforce an energy conservation theorem with particle sub-stepping. As a result, very large time steps, constrained only by the dynamical time scale of interest, are possible without accuracy loss. Algorithmically, the approach features a Jacobian-free Newton-Krylov solver. A main development in this study is the nonlinear elimination of the new-time particle variables (positions and velocities). Such nonlinear elimination, which we term particle enslavement, results in a nonlinear formulation with memory requirements comparable to those of a fluid computation, and affords us substantial freedom in regards to the particle orbit integrator. Numerical examples are presented that demonstrate the advertised properties of the scheme. In particular, long-time ion acoustic wave simulations show that numerical accuracy does not degrade even with very large implicit time steps, and that significant CPU gains are possible.

physics.comp-ph↗

arXiv2009

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

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.

physics.comp-ph↗