dorsal/arxiv
View SchemaMatrix-PIC: Harnessing Matrix Outer-product for High-Performance Particle-in-Cell Simulations
| Authors | Yizhuo Rao, Xingjian Cui, Jiabin Xie, Shangzhi Pang, Guangnan Feng, Jinhui Wei, Zhiguang Chen, Yutong Lu |
|---|---|
| Categories | |
| ArXiv ID | 2601.08277vv1 |
| URL | https://arxiv.org/abs/2601.08277 |
| DOI | 10.1145/3767295.3769378 |
| License | http://creativecommons.org/licenses/by/4.0/ |
Abstract
Particle-in-Cell (PIC) simulations spend most of their execution time on particle--grid interactions, where fine-grained atomic updates become a major bottleneck on traditional many-core CPUs. Recent CPU architectures integrate specialized Matrix Processing Units (MPUs) that efficiently support matrix outer-product operations, offering new opportunities to overcome this limitation. Leveraging this architectural shift, this work focuses on redesigning the current deposition step of PIC simulations under a matrix-centric execution model. We present MatrixPIC, the first holistic co-design of the deposition kernel, data layout, and incremental particle sorting tailored to the hybrid MPU--VPU SIMD model on modern CPUs. MatrixPIC introduces: (i)~a block-matrix formulation of the current deposition algorithm that maps naturally to MPU outer-product primitives; (ii)~a hybrid execution pipeline that combines MPU-based high-density accumulation with VPU-based data preparation and control flow; and (iii)~an $O(1)$-amortized incremental sorter based on a gapped packed-memory array to preserve data locality for efficient MPU execution. Evaluated on a next-generation HPC platform, MatrixPIC achieves significant performance gains. In Laser-Wakefield Acceleration (LWFA) simulations, it delivers up to $2.63\times$ speedup in total runtime. For third-order deposition, the core kernel is accelerated by $8.7\times$ over the baseline and $2.0\times$ over the best hand-optimized VPU implementation. Moreover, MatrixPIC reaches $83.08\%$ of theoretical CPU peak performance, nearly $2.8\times$ higher than a highly optimized CUDA kernel on a data center GPU. These results demonstrate the effectiveness of matrix-oriented co-design for accelerating PIC simulations on emerging CPU architectures.
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"abstract": "Particle-in-Cell (PIC) simulations spend most of their execution time on particle--grid interactions, where fine-grained atomic updates become a major bottleneck on traditional many-core CPUs. Recent CPU architectures integrate specialized Matrix Processing Units (MPUs) that efficiently support matrix outer-product operations, offering new opportunities to overcome this limitation. Leveraging this architectural shift, this work focuses on redesigning the current deposition step of PIC simulations under a matrix-centric execution model.\n We present MatrixPIC, the first holistic co-design of the deposition kernel, data layout, and incremental particle sorting tailored to the hybrid MPU--VPU SIMD model on modern CPUs. MatrixPIC introduces: (i)~a block-matrix formulation of the current deposition algorithm that maps naturally to MPU outer-product primitives; (ii)~a hybrid execution pipeline that combines MPU-based high-density accumulation with VPU-based data preparation and control flow; and (iii)~an $O(1)$-amortized incremental sorter based on a gapped packed-memory array to preserve data locality for efficient MPU execution.\n Evaluated on a next-generation HPC platform, MatrixPIC achieves significant performance gains. In Laser-Wakefield Acceleration (LWFA) simulations, it delivers up to $2.63\\times$ speedup in total runtime. For third-order deposition, the core kernel is accelerated by $8.7\\times$ over the baseline and $2.0\\times$ over the best hand-optimized VPU implementation. Moreover, MatrixPIC reaches $83.08\\%$ of theoretical CPU peak performance, nearly $2.8\\times$ higher than a highly optimized CUDA kernel on a data center GPU. These results demonstrate the effectiveness of matrix-oriented co-design for accelerating PIC simulations on emerging CPU architectures.",
"arxiv_id": "2601.08277",
"authors": [
"Yizhuo Rao",
"Xingjian Cui",
"Jiabin Xie",
"Shangzhi Pang",
"Guangnan Feng",
"Jinhui Wei",
"Zhiguang Chen",
"Yutong Lu"
],
"categories": [
"cs.DC"
],
"doi": "10.1145/3767295.3769378",
"license": "http://creativecommons.org/licenses/by/4.0/",
"title": "Matrix-PIC: Harnessing Matrix Outer-product for High-Performance Particle-in-Cell Simulations",
"url": "https://arxiv.org/abs/2601.08277",
"version": "v1"
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