面向现代大规模并行架构的并发多波前求解器研究
A study of concurrent multi-frontal solvers for modern massively parallel architectures
AI总结：
该研究利用迹理论探究大型线性方程组多波前直接求解器的并行化，提出近最优调度方法并严格验证，还基于有限元法矩阵在GPU、CPU平台测试评估性能。
摘要：
利用迹理论（Trace Theory），我们研究了大型线性方程组直接求解器的高效并行化方法。我们的研究聚焦于多波前（multi-frontal）算法，并提出了一种在现代大规模并行机器上实现近最优调度的方法。通过结合Diekert图（Diekert Graphs）与Foata范式（Foata Normal Form）的迹理论，我们严格验证了所提方案的有效性。为建立多波前求解器的网格与消去树之间的强关联，我们对来自有限元法（FEM）的矩阵开展了大量测试。此外，我们还采用实用的实现策略，评估了GPU和CPU平台上的计算性能。
英文摘要：
Leveraging Trace Theory, we investigate the efficient parallelization of direct solvers for large linear equation systems. Our focus lies on a multi-frontal algorithm, and we present a methodology for achieving near-optimal scheduling on modern massively parallel machines. By employing trace theory with Diekert Graphs and Foata Normal Form, we rigorously validate the effectiveness of our proposed solution. To establish a strong link between the mesh and elimination tree of the multi-frontal solver, we conduct extensive testing on matrices derived from the Finite Element Method (FEM). Furthermore, we assess the performance of computations on both GPU and CPU platforms, employing practical implementation strategies.
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