通过粗网格重分布将结构化多网格扩展到50万+核心
Scaling Structured Multigrid to 500K+ Cores through Coarse-Grid Redistribution
AI总结：
本文提出通过增量聚类实现粗网格问题的重分布算法，提升结构化多网格的并行扩展性，通过二维扩散问题验证性能提升，并在大规模计算系统上展示可扩展性。
摘要：
稀疏线性系统高效求解对许多基于物理的模拟性能至关重要。多级方法在常见离散化中的算法最优性使其成为高效并行求解器的候选。然而，高性能计算系统现代架构仍挑战多级求解器的并行可扩展性。虽然代数多网格方法对各种问题具有鲁棒性，但现代架构中数据局部性和数据移动成本的重要性促使需要仔细利用问题结构。鲁棒的逻辑结构变分多网格方法，如Black Box Multigrid（BoxMG），在多网格层次中保持结构，避免了并行代数多网格中常见的间接性和增加的粗网格通信成本。然而，结构化多网格的并行可扩展性受到粗网格问题的挑战，其中通信开销主导计算。本文提出一种算法，通过增量聚类重分布粗网格问题。该算法由预测性能模型引导，为结构化多级求解器提供稳健的重分布决策。通过二维扩散问题验证该算法相对于之前使用聚类到一个处理器的方法的显著性能提升。此外，在两个大规模计算系统上展示了该方法的并行可扩展性，解决了高达50万+核心的问题。
英文摘要：
The efficient solution of sparse, linear systems resulting from the discretization of partial differential equations is crucial to the performance of many physics-based simulations. The algorithmic optimality of multilevel approaches for common discretizations makes them a good candidate for an efficient parallel solver. Yet, modern architectures for high-performance computing systems continue to challenge the parallel scalability of multilevel solvers. While algebraic multigrid methods are robust for solving a variety of problems, the increasing importance of data locality and cost of data movement in modern architectures motivates the need to carefully exploit structure in the problem. Robust logically structured variational multigrid methods, such as Black Box Multigrid (BoxMG), maintain structure throughout the multigrid hierarchy. This avoids indirection and increased coarse-grid communication costs typical in parallel algebraic multigrid. Nevertheless, the parallel scalability of structured multigrid is challenged by coarse-grid problems where the overhead in communication dominates computation. In this paper, an algorithm is introduced for redistributing coarse-grid problems through incremental agglomeration. Guided by a predictive performance model, this algorithm provides robust redistribution decisions for structured multilevel solvers. A two-dimensional diffusion problem is used to demonstrate the significant gain in performance of this algorithm over the previous approach that used agglomeration to one processor. In addition, the parallel scalability of this approach is demonstrated on two large-scale computing systems, with solves on up to 500K+ cores.
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