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The Interaction of Iteration Error and Stability for Linear Partial Differential Equations Coupled through an Interface
Joint Authors
Sheehan, B.
Estep, D.
Tavener, S.
Cary, J.
Kruger, S.
Hakim, A.
Pletzer, A.
Carlsson, J.
Vadlamani, S.
Source
Advances in Mathematical Physics
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-01-14
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Sheehan, B.& Estep, D.& Tavener, S.& Cary, J.& Kruger, S.& Hakim, A.…[et al.]. 2015. The Interaction of Iteration Error and Stability for Linear Partial Differential Equations Coupled through an Interface. Advances in Mathematical Physics،Vol. 2015, no. 2015, pp.1-13.
https://search.emarefa.net/detail/BIM-1053023
Modern Language Association (MLA)
Sheehan, B.…[et al.]. The Interaction of Iteration Error and Stability for Linear Partial Differential Equations Coupled through an Interface. Advances in Mathematical Physics No. 2015 (2015), pp.1-13.
https://search.emarefa.net/detail/BIM-1053023
American Medical Association (AMA)
Sheehan, B.& Estep, D.& Tavener, S.& Cary, J.& Kruger, S.& Hakim, A.…[et al.]. The Interaction of Iteration Error and Stability for Linear Partial Differential Equations Coupled through an Interface. Advances in Mathematical Physics. 2015. Vol. 2015, no. 2015, pp.1-13.
https://search.emarefa.net/detail/BIM-1053023
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1053023