论文标题
基于间/外推的多进取方案
Inter/extrapolation-based multirate schemes -- a dynamic-iteration perspective
论文作者
论文摘要
普通微分方程（ODE）和微分 - 代码方程（DAE）的多段行为的特征是在解决方案的不同组件或右侧的不同添加剂项中广泛分离的时间常数。在这里，经典的多条方案是专用求解器，它适用（例如）微观和宏步骤，以相应地解决瞬态模拟中的快速和缓慢变化。推断和插值程序的使用是耦合不同部分的真正方法，这些零件是在不同的时间网格上定义的。 本文首次包含了作者的最佳知识，这是针对基于索引的ODE和DAE的基于/外推的多条计划的完整收敛理论，这些方案基于完全耦合的方法，最慢的第一和最快的方法。收敛理论是基于将这些方案与多条动态迭代方案联系起来的，即动态迭代方案而没有进一步的迭代。此链接定义了DAE情况的自然稳定条件。
Multirate behavior of ordinary differential equations (ODEs) and differential-algebraic equations (DAEs) is characterized by widely separated time constants in different components of the solution or different additive terms of the right-hand side. Here, classical multirate schemes are dedicated solvers, which apply (e.g.) micro and macro steps to resolve fast and slow changes in a transient simulation accordingly. The use of extrapolation and interpolation procedures is a genuine way for coupling the different parts, which are defined on different time grids. This paper contains for the first time, to the best knowledge of the authors, a complete convergence theory for inter/extrapolation-based multirate schemes for both ODEs and DAEs of index one, which are based on the fully-decoupled approach, the slowest-first and the fastest-first approach. The convergence theory is based on linking these schemes to multirate dynamic iteration schemes, i.e., dynamic iteration schemes without further iterations. This link defines naturally stability conditions for the DAE case.
