文章基本信息

标题：The Interaction of Iteration Error and Stability for Linear Partial Differential Equations Coupled through an Interface
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作者：B. Sheehan ; D. Estep ; S. Tavener 等
期刊名称：Advances in Mathematical Physics
印刷版ISSN：1687-9120
电子版ISSN：1687-9139
出版年度：2015
卷号：2015
DOI：10.1155/2015/787198
出版社：Hindawi Publishing Corporation
摘要：We investigate properties of algorithms that are used to solve coupled evolutionary partial differential equations posed on neighboring, nonoverlapping domains, where the solutions are coupled by continuity of state and normal flux through a shared boundary. The algorithms considered are based on the widely used approach of iteratively exchanging boundary condition data on the shared boundary at each time step. There exists a significant and sophisticated numerical analysis of such methods. However, computations for practical applications are often carried out under conditions under which it is unclear if rigorous results apply while relatively few iterations are used per time step. To examine this situation, we derive exact matrix expressions for the propagation of the error due to incomplete iteration that can be readily evaluated for specific discretization parameters. Using the formulas, we show that the universal validity of several tenants of the practitioner’s conventional wisdom are not universally valid.