A Space and Bandwidth Efficient Multicore Algorithm for the Particle-in-Cell Method

Abstract

Abstract. The Particle-in-Cell (PIC) method allows solving partial differential equation through simulations, with important applications in plasma physics. To simulate thousands of billions of particles on clusters of multicore machines, prior work has proposed hybrid algorithms that combine domain decomposition and particle decomposition with carefully optimized algorithms for handling particles processed on each multicore socket. Regarding the multicore processing, existing algorithms either suffer from suboptimal execution time, due to sorting operations or use of atomic instructions, or suffer from suboptimal space usage. In this paper, we propose a novel parallel algorithm for two-dimensional PIC simulations on multicore hardware that features asymptotically-optimal memory consumption, and does not perform unnecessary accesses to the main memory. In practice, our algorithm reaches 65% of the maximum bandwidth, and shows excellent scalability on the classical Landau damping and two-stream instability test cases.

Efficient Strict-Binning Particle-in-Cell Algorithm for Multi-core SIMD Processors

“…The strict-binning approach to implementing the PIC method enables significant reduction in the number of random accesses and cache misses [21,7,17,1]: at every time step, particles that fall in the same cell are stored together. Doing so brings two main benefits.…”

“…For example, in a parallel execution using 64 cores, having as little as 0.5% of fast-moving particles can result in a 32% slowdown on the total execution time due to the sequential processing of these particles. 1 We propose an algorithm implementing strict-binning for the PIC method that addresses the aforementioned limitations, while still supporting efficient OpenMP/SIMD parallelization of all critical loops. Our algorithm leverages the use of chunk bags, i.e.…”

“…Particles are stored in fixed-capacity arrays (chunks, e.g., [1]). Several chunks might be needed to store all the particles contained in a same cell.…”

“…( The chunk bag data structure supports O(1) insertion of a particle (adding a fresh chunk if needed), O(1) merge of two bags thanks to the back field (note that chunk compaction is not needed), and O(n) iteration over the contents, all with excellent constant factors. Furthermore, unlike chunks introduced by prior work [1], our chunk bags are devised to support a thread-safe atomic insertion operation. Atomic insertions are central to the handling of fast-moving particles.…”