JefiFast: Accelerating Jefimenko’s Equations with Memory-Centric Optimizations and Multi-GPU Parallelism

As a foundation for numerical solvers in computational electromagnetics, particularly for multiphysics and electromagnetic compatibility applications, Jefimenko’s equations offer a generalized solution to Maxwell’s equations, enabling the direct computation of electromagnetic fields from time-dependent source distributions without the boundary-condition artifacts inherent to grid-based methods. However, the numerical integration of these equations is computationally intensive, typically scaling as O(NsNo) for Ns source points and No observation points. In this paper, we present JefiFast, a highly optimized graphics processing unit (GPU) implementation that significantly outperforms the state-of-the-art JefiGPU algorithm. We identify that previous implementations are strictly memory-bound due to inefficient global memory transactions and a lack of data reuse. JefiFast addresses these bottlenecks through four key optimizations: (i) a packed memory layout (PML) using an array-of-structures approach to ensure coalesced memory access for source densities and their derivatives; (ii) geometry-aware shared memory tiling strategies that maximize L2 (level-2) cache hit rates and on-chip data reuse; (iii) pre-computation of time derivatives to minimize redundant arithmetic operations; and (iv) a robust observation domain decomposition strategy that enables linear scaling across multiple GPUs. Benchmarks demonstrate that JefiFast achieves speedups ranging from 4.08 times (for 303 grids on a single NVIDIA V100 graphic processor) to 84.51 times (for 503 grids on 4 NVIDIA V100 processors) compared to the baseline. Notably, for a 503 grid on a single GPU, JefiFast reduces execution time from about 51 min to just about 2.6 min (19.54 times speedup). These performance advances make high-resolution relativistic heavy-ion collision simulations feasible in near real-time.