Stephen Copplestone | Searcharxiv

arXiv2026

A P-Adaptive Hybridizable Discontinuous Galerkin Spectral Element Method for Electrostatic Particle-in-Cell Simulations

This paper presents a p-adaptive high-order hybridizable discontinuous Galerkin spectral element method (HDG-SEM) for solving the Poisson equation in electrostatic plasma simulations using particle-in-cell (PIC) schemes. This approach enables element-local refinement of the polynomial degree, concentrating computational effort specifically in regions with strong gradients. Thus, the method significantly reduces the global number of degrees of freedom compared to uniform high-order methods. The proposed method is implemented in the open-source framework PICLas and validated through a series of benchmark test cases, including a dielectric sphere and a one-dimensional plasma sheath. Finally, a two-dimensional axisymmetric simulation of an ion optic demonstrates the method's capability to efficiently model complex plasma phenomena but also highlights current limitations.

physics.comp-ph↗

arXiv2022

Hybrid Parallelization of Euler-Lagrange Simulations Based on MPI-3 Shared Memory

The use of Euler-Lagrange methods on unstructured grids extends their application area to more versatile setups. However, the lack of a regular topology limits the scalability of distributed parallel methods, especially for routines that perform a physical search in space. One of the most prominent slowdowns is the search for halo elements in physical space for the purpose of runtime communication avoidance. In this work, we present a new communication-free halo element search algorithm utilizing the MPI-3 shared memory model. This novel method eliminates the severe performance bottleneck of many-to-many communication during initialization compared to the distributed parallelization approach and extends the possible applications beyond those achievable with the previous approach. Building on these data structures, we then present methods for efficient particle emission, scalable deposition schemes for particle-field coupling, and latency hiding approaches. The scaling performance of the proposed algorithms is validated through plasma dynamics simulations of an open-source framework on a massively parallel system, demonstrating an efficiency of up to 80% on 131000 cores.

physics.comp-ph↗