论文标题
平行隐式阐释一般线性方法
Parallel implicit-explicit general linear methods
论文作者
论文摘要
部分微分方程（PDE）的高阶离散化需要高阶时间整合方案，能够有效地处理僵硬和非固定操作员。基于一般线性方法（GLM）的隐式解释（IMEX）集成，由于其高阶段和方法顺序以及出色的稳定性属性，提供了一个有吸引力的解决方案。 IMEX的特征允许隐式术语被隐式处理，并有效地将非固定项处理。这项工作开发了两种系统的方法，用于开发任意顺序的IMEX GLM，并可以并行解决。第一种方法是基于类型3和4的对角隐式多阶段积分方法（DIMSIMS）。第二种是IMEX Euler的并行概括，并具有有趣的特征，即线性稳定性与准确性无关。数值实验证实了收敛的理论速率，并表明新方案比串行IMEX GLM和IMEX runge-kutta方法更有效。
High-order discretizations of partial differential equations (PDEs) necessitate high-order time integration schemes capable of handling both stiff and nonstiff operators in an efficient manner. Implicit-explicit (IMEX) integration based on general linear methods (GLMs) offers an attractive solution due to their high stage and method order, as well as excellent stability properties. The IMEX characteristic allows stiff terms to be treated implicitly and nonstiff terms to be efficiently integrated explicitly. This work develops two systematic approaches for the development of IMEX GLMs of arbitrary order with stages that can be solved in parallel. The first approach is based on diagonally implicit multistage integration methods (DIMSIMs) of types 3 and 4. The second is a parallel generalization of IMEX Euler and has the interesting feature that the linear stability is independent of the order of accuracy. Numerical experiments confirm the theoretical rates of convergence and reveal that the new schemes are more efficient than serial IMEX GLMs and IMEX Runge-Kutta methods.
