arXivDaily arXiv每日学术速递 周一至周五更新
arXiv周末暂无论文更新,休息一下吧,周末愉快~~

超越快速收缩:高阶有限元中矩阵引擎加速的衰减与恢复

Beyond Fast Contractions: Attenuation and Recovery of Matrix-Engine Speedups in High-Order Finite Elements

Yinuo Wang, Lin Gan, Tianqi Mao, Zeyu Song, Wubing Wan, Jiayu Fu, Zekun Yin, Yuyang Jin, Xiaohui Duan, Wei Xue, Guangwen Yang

arXiv 2608.09175首次发表:更新:

AI 中文总结

该研究针对Arm LX2 CPU上的SPECFEM3D刚度算子,发现矩阵引擎加速因多种因素衰减,通过优化可恢复部分加速,表明需协同设计整个算子路径。

AI 中文摘要

现代处理器越来越多地提供矩阵引擎,其峰值算术吞吐量远超传统SIMD,但科学应用很少能端到端实现这一优势。我们在支撑旗舰Lineshine超级计算机的Arm LX2 CPU上,针对SPECFEM3D的主导刚度算子研究这一差距。与相同核心上匹配的高性能SVE基线相比,SME的4倍单精度峰值优势,在孤立张量收缩中降至2.2倍,在完整算子中降至1.1倍。我们的分解诊断将损失归因于逐点计算、间接场移动与同步,以及不规则系数传递。显式SIMD缓解了逐点工作,将完整算子加速提升至1.3倍;场布局变更缓解了间接移动与同步,而向量块系数流减少了不规则访问成本,二者共同将高阶下的加速提升至1.6倍;无收缩控制将仅收缩的增益限制在1.11至1.32倍之间。因此,实现矩阵引擎性能需要协同设计整个算子路径,而非仅替换其收缩内核。

英文摘要

Modern processors increasingly provide matrix engines whose peak arithmetic throughput greatly exceeds conventional SIMD, but scientific applications rarely realize this advantage end to end. We examine this gap in SPECFEM3D's dominant stiffness operator on the Arm LX2 CPUs that power the flagship Lineshine supercomputer. Against a matched, high-performance SVE baseline on the same cores, SME's $4\times$ single-precision peak advantage falls to $2.2\times$ for isolated tensor contractions and $1.1\times$ for the complete operator. Our factorized diagnostic attributes the loss to pointwise computation, indirect field movement and synchronization, and irregular coefficient delivery. Explicit SIMD mitigates pointwise work, raising the full-operator speedup to $1.3\times$. Field-layout changes mitigate indirect movement and synchronization, while vector-blocked coefficient streaming reduces irregular-access costs; together they raise speedup to $1.6\times$ at high order. A contraction-free control bounds further contraction-only gains at $1.11$--$1.32\times$. Realizing matrix-engine performance therefore requires co-designing the entire operator path, not merely replacing its contraction kernel.

论文原文

arXiv 摘要页 · PDF 原文 · HTML 原文

↑