sTiles：一种面向结构化矩阵稀疏分解的加速计算框架
sTiles: An Accelerated Computational Framework for Sparse Factorizations of Structured Matrices
AI总结：
本文提出GPU加速框架sTiles，通过tile算法、结构感知任务调度和left-looking Cholesky变体高效分解箭头形稀疏对称矩阵，相比CHOLMOD等实现最高11.08倍加速。
摘要：
本文介绍了sTiles，一个GPU加速的框架，用于对稀疏结构化对称矩阵进行分解。通过利用tile算法进行细粒度计算，sTiles采用结构感知的任务执行流程来处理具有可变带宽的具有挑战性的箭头形稀疏矩阵，这类矩阵在科学和工程领域中很常见。它利用置换技术在Cholesky分解过程中最小化填充，并采用静态调度器在带有GPU加速器的共享内存系统上管理任务。sTiles在tile大小和并行性之间取得平衡，其中较大的tile能增强算法强度，但会增加浮点运算量和内存使用量，而并行性则受到箭头形结构的制约。为了暴露更多的并行性，一种left-looking Cholesky变体通过树归约打破了尾随子矩阵更新中的顺序依赖。评估结果表明，与CHOLMOD、SymPACK、MUMPS和PARDISO相比，sTiles分别实现了高达8.41倍、9.34倍、5.07倍和11.08倍的加速，并且在NVIDIA A100 GPU上相比32核AMD EPYC CPU实现了5倍的加速。我们的通用软件框架引入了稠密矩阵计算中成熟的概念，但在混合架构上的部署都需要进行定制化，以最佳地处理具有箭头形结构的稀疏矩阵分解。
英文摘要：
This paper introduces sTiles, a GPU-accelerated framework for factorizing sparse structured symmetric matrices. By leveraging tile algorithms for fine-grained computations, sTiles uses a structure-aware task execution flow to handle challenging arrowhead sparse matrices with variable bandwidths, common in scientific and engineering fields. It minimizes fill-in during Cholesky factorization using permutation techniques and employs a static scheduler to manage tasks on shared-memory systems with GPU accelerators. sTiles balances tile size and parallelism, where larger tiles enhance algorithmic intensity but increase floating-point operations and memory usage, while parallelism is constrained by the arrowhead structure. To expose more parallelism, a left-looking Cholesky variant breaks sequential dependencies in trailing submatrix updates via tree reductions. Evaluations show sTiles achieves speedups of up to 8.41X, 9.34X, 5.07X, and 11.08X compared to CHOLMOD, SymPACK, MUMPS, and PARDISO, respectively, and a 5X speedup compared to a 32-core AMD EPYC CPU on an NVIDIA A100 GPU. Our generic software framework imports well-established concepts from dense matrix computations but they all require customizations in their deployments on hybrid architectures to best handle factorizations of sparse matrices with arrowhead structures.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
