The Interaction of Iteration Error and Stability for Linear Partial Differential Equations Coupled through an Interface

B. Sheehan, D. Estep, S. Tavener, J. Cary, S. Kruger, A. Hakim, A. Pletzer, J. Carlsson and S. Vadlamani

Advances in Mathematical Physics, 2015, vol. 2015, issue 1

Abstract: 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.

Date: 2015
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2015/787198

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2015:y:2015:i:1:n:787198

Access Statistics for this article

More articles in Advances in Mathematical Physics from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().