On the intersection of sets of incoming and outgoing waves
Authors:
Adi Ditkowski and Michael Sever
Journal:
Quart. Appl. Math. 66 (2008), 1-26
MSC (2000):
Primary 35Lxx, 35Qxx, 78Axx
DOI:
https://doi.org/10.1090/S0033-569X-07-01080-3
Published electronically:
January 10, 2008
MathSciNet review:
2396650
Full-text PDF Free Access
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Abstract:
In the neighborhood of a boundary point, the solution of a first-order symmetric homogenous hyperbolic system is conveniently decomposed into fundamental waves solutions that are readily classified as outgoing, incoming, and stationary, or tangential.
Under a broad hypothesis, we show that the spans of the sets of outgoing and incoming waves have nontrivial intersection. Under these conditions, local, linear, perfectly nonreflecting local boundary conditions are shown to be an impossibility.
References
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References
- S. V. Tsynkov, Numerical solution of problems on unbounded domains. A review. Absorbing boundary conditions, Appl. Numer. Math. 27 (1998), no. 4, 465–532. MR 1644674 (99i:65116)
- Advances in computational electrodynamics. The finite-difference time-domain method. Edited by Allen Taflove. Artech House Antenna Library. Artech House, Inc., Boston, MA, 1998 MR 1639352 (99c:78001)
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Additional Information
Adi Ditkowski
Affiliation:
School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
Michael Sever
Affiliation:
Department of Mathematics, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel
Received by editor(s):
February 17, 2006
Published electronically:
January 10, 2008
Additional Notes:
This research was supported by the Israel Science Foundation (grant No. 1364/04).
Article copyright:
© Copyright 2007
Brown University
The copyright for this article reverts to public domain 28 years after publication.