In this work, we consider the challenges of developing a distributed solver for models based on nonlocal interactions. In nonlocal models, in contrast to the local model, such as the wave and heat partial differential equation, the material interacts with neighboring points on a larger-length scale compared to the mesh discretization. In developing a fully distributed solver, the interaction over a length scale greater than mesh size introduces additional data dependencies among the compute nodes and communication bottleneck. In this work, we carefully look at these challenges in the context of nonlocal models; to keep the presentation specific to the computational issues, we consider a nonlocal heat equation in a 2d setting. In particular, the distributed framework we propose pays greater attention to the bottleneck of data communication and the dynamic balancing of loads among nodes with varying compute capacity. For load balancing, we propose a novel framework that assesses the compute capacity of nodes and dynamically balances the load so that the idle time among nodes is minimal. Our framework relies heavily on HPX library, an asynchronous many-task run time system. We present several results demonstrating the effectiveness of the proposed framework.
翻译:在这项工作中,我们考虑开发一个基于非本地互动模型的分布式求解器的挑战。在非本地模型中,与本地模型(如波和热部分差异方程式)不同的是,材料与相邻点的相互作用比网状分解法大得多。在开发一个完全分布式求解器时,大于网状尺寸的相互作用增加了计算节点和通信瓶颈之间的数据依赖度。在这项工作中,我们仔细研究非本地模型背景下的这些挑战;为了保持对计算问题的具体介绍,我们考虑在2D环境中的非本地热方程式。特别是,我们提议的分布式框架更加关注数据通信的瓶颈和不同计算能力节点之间负载的动态平衡。关于工作量平衡,我们提出了一个新的框架,用以评估节点的计算能力和动态平衡负荷,以便节点之间的闲置时间是最小的。我们的框架大量依赖HPX图书馆,这是一个同步的多塔时间运行系统。我们提出的若干成果展示了拟议框架的有效性。