论文标题
使用多级快速多极算法对Helmholtz电位的高性能评估
High Performance Evaluation of Helmholtz Potentials using the Multi-Level Fast Multipole Algorithm
论文作者
论文摘要
在许多物理领域中,对配对电位的评估至关重要。经典的人体问题具有评估拉普拉斯电位的根源,并且已经产生了树 - 偏这,快速多极方法(FMM)以及内核独立的方法。多年来,Laplace潜力的FMM对许多学科产生了深远的影响,因为可以为这些潜在评估者开发高度可扩展的并行算法。这与Helmholtz(振荡)电势的平行算法形成鲜明对比。主要的瓶颈和可扩展的并行性是在树上上下穿越,影响计算和通信所需的操作。在本文中,我们描述了克服瓶颈的技术,并对Helmholtz的高性能评估进行了广泛的几何形状。我们证明,由此产生的实现具有负载平衡效应,可大大减少时间到解决的时间,并增强可以使用全波物理学处理的问题的规模。
Evaluation of pair potentials is critical in a number of areas of physics. The classicalN-body problem has its root in evaluating the Laplace potential, and has spawned tree-algorithms, the fast multipole method (FMM), as well as kernel independent approaches. Over the years, FMM for Laplace potential has had a profound impact on a number of disciplines as it has been possible to develop highly scalable parallel algorithm for these potential evaluators. This is in stark contrast to parallel algorithms for the Helmholtz (oscillatory) potentials. The principal bottleneck to scalable parallelism are operations necessary to traverse up, across and down the tree, affecting both computation and communication. In this paper, we describe techniques to overcome bottlenecks and achieve high performance evaluation of the Helmholtz potential for a wide spectrum of geometries. We demonstrate that the resulting implementation has a load balancing effect that significantly reduces the time-to-solution and enhances the scale of problems that can be treated using full wave physics.