论文标题
迭代平行算法的统一分析框架
A unified analysis framework for iterative parallel-in-time algorithms
论文作者
论文摘要
在过去的二十年中，由于大规模平行的计算机架构和纯粹的空间并行化的缩放限制，并平行的整合一直是密集研究工作的重点。已经提出了各种迭代平行时间（PINT）算法，例如Parareal，PFASST，MGRIT和时空多网格（STMG）。这些方法已经使用不同的符号进行了描述，并且很难比较可用的收敛估计值。我们使用共同的符号来描述Dahlquist模型问题的Parareal，PFASST，MGRIT和STMG，并使用生成功能给出精确的收敛估计。这使我们首次可以直接比较它们的收敛性。我们证明，所有四种方法最终都会超级线性收敛，并以数字进行比较。生成功能框架提供了进一步的机会来探索和分析现有方法和新方法。
Parallel-in-time integration has been the focus of intensive research efforts over the past two decades due to the advent of massively parallel computer architectures and the scaling limits of purely spatial parallelization. Various iterative parallel-in-time (PinT) algorithms have been proposed, like Parareal, PFASST, MGRIT, and Space-Time Multi-Grid (STMG). These methods have been described using different notations, and the convergence estimates that are available are difficult to compare. We describe Parareal, PFASST, MGRIT and STMG for the Dahlquist model problem using a common notation and give precise convergence estimates using generating functions. This allows us, for the first time, to directly compare their convergence. We prove that all four methods eventually converge super-linearly, and also compare them numerically. The generating function framework provides further opportunities to explore and analyze existing and new methods.
