Particle-in-Cell Simulations of Relativistic Magnetic Reconnection with Advanced Maxwell Solver Algorithms

TL;DR

This paper evaluates advanced Maxwell solver algorithms, CKC and PSATD, within GPU-accelerated PIC simulations of relativistic magnetic reconnection, demonstrating their accuracy and potential for improved computational efficiency over traditional methods.

Contribution

It introduces and compares CKC and PSATD algorithms in PIC simulations, highlighting their stability and performance benefits over standard Yee-grid methods.

Findings

CKC and PSATD match standard Yee-grid results in reconnection simulations.

CKC and PSATD allow 40% longer time steps, reducing simulation time.

PSATD remains stable at larger time steps, offering potential for further performance gains.

Abstract

Relativistic magnetic reconnection is a non-ideal plasma process that is a source of non-thermal particle acceleration in many high-energy astrophysical systems. Particle-in-cell (PIC) methods are commonly used for simulating reconnection from first principles. While much progress has been made in understanding the physics of reconnection, especially in 2D, the adoption of advanced algorithms and numerical techniques for efficiently modeling such systems has been limited. With the GPU-accelerated PIC code WarpX, we explore the accuracy and potential performance benefits of two advanced Maxwell solver algorithms: a non-standard finite difference scheme (CKC) and an ultrahigh-order pseudo-spectral method (PSATD). We find that for the relativistic reconnection problem, CKC and PSATD qualitatively and quantitatively match the standard Yee-grid finite-difference method. CKC and PSATD both admit a time step that is 40% longer than Yee, resulting in a ~40% faster time to solution for CKC, but no performance benefit for PSATD when using a current deposition scheme that satisfies Gauss's law. Relaxing this constraint maintains accuracy and yields a 30% speedup. Unlike Yee and CKC, PSATD is numerically stable at any time step, allowing for a larger time step than with the finite-difference methods. We found that increasing the time step 2.4-3 times over the standard Yee step still yields accurate results, but only translates to modest performance improvements over CKC due to the current deposition scheme used with PSATD. Further optimization of this scheme will likely improve the effective performance of PSATD.