Stable simulation of conservation laws, such as those used to model fluid dynamics and plasma physics applications, requires the satisfaction of the so-called Courant-Friedrichs-Lewy condition. By allowing regions of the mesh to advance with different timesteps that locally satisfy this stability constraint, significant work reduction can be attained when compared to a time integration scheme using a single timestep size. However, parallelizing this algorithm presents considerable difficulty. Since the stability condition depends on the state of the system, dependencies become dynamic and potentially non-local. In this article, we present an adaptive local timestepping algorithm using an optimistic (Timewarp-based) parallel discrete event simulation. We introduce waiting heuristics to limit misspeculation and a semi-static load balancing scheme to eliminate load imbalance as parts of the mesh require finer or coarser timesteps. Last, we outline an interface for separating the physics of the specific conservation law from the temporal integration allowing for productive adoption of our proposed algorithm. We present a misspeculation study for three conservation laws, demonstrating both the productivity of the local timestepping API, for which 74% of the lines of code are reused across different conservation laws, and the robustness of the waiting heuristics—at most 1.5% of element updates are rolled back. Our performance studies demonstrate up to a 2.8× speedup versus a baseline unoptimized local timestepping approach, a 4x improvement in per-node throughput compared to an MPI parallelization of synchronous timestepping, and scalability up to 3,072 cores on NERSC’s Cori Haswell partition.

守恒定律的稳定模拟，例如用于模拟流体动力学和等离子体物理应用的守恒定律，需要满足所谓的 Courant-Friedrichs-Lewy 条件。通过允许网格区域以局部满足此稳定性约束的不同时间步长前进，与使用单个时间步长大小的时间积分方案相比，可以显着减少工作量。然而，并行化该算法存在相当大的困难。由于稳定性条件取决于系统的状态，因此依赖性变得动态且可能是非局部的。在本文中，我们提出了一种使用乐观（基于时间扭曲）并行离散事件模拟的自适应本地时间步长算法。我们引入等待启发式来限制错误推测和半静态负载平衡方案来消除负载不平衡，因为网格的某些部分需要更精细或更粗略的时间步长。最后，我们概述了一个接口，用于将特定守恒定律的物理与时间积分分开，从而可以有效地采用我们提出的算法。我们对三个守恒定律进行了错误推测研究，展示了本地时间步 API 的生产力，其中 74% 的代码行在不同的守恒定律中重复使用，以及等待启发式的鲁棒性 - 最多 1.5% 的元素更新被回滚。我们的性能研究表明，与基准未优化的本地时间步长方法相比，速度提升高达 2.8 倍，