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
- Semyon V. Tsynkov, Numerical solution of problems on unbounded domains. A review, Appl. Numer. Math. 27 (1998), no. 4, 465–532. Absorbing boundary conditions. MR 1644674, DOI https://doi.org/10.1016/S0168-9274%2898%2900025-7
- Allen Taflove (ed.), Advances in computational electrodynamics, Artech House Antenna Library, Artech House, Inc., Boston, MA, 1998. The finite-difference time-domain method. MR 1639352
- Jean-Pierre Berenger, A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys. 114 (1994), no. 2, 185–200. MR 1294924, DOI https://doi.org/10.1006/jcph.1994.1159
- S. Abarbanel, D. Gottlieb, and J. S. Hesthaven, Long time behavior of the perfectly matched layer equations in computational electromagnetics, Proceedings of the Fifth International Conference on Spectral and High Order Methods (ICOSAHOM-01) (Uppsala), 2002, pp. 405–422. MR 1910579, DOI https://doi.org/10.1023/A%3A1015141823608
- K. O. Friedrichs, Symmetric hyperbolic linear differential equations, Comm. Pure Appl. Math. 7 (1954), 345–392. MR 62932, DOI https://doi.org/10.1002/cpa.3160070206
- K. O. Friedrichs, Symmetric positive linear differential equations, Comm. Pure Appl. Math. 11 (1958), 333–418. MR 100718, DOI https://doi.org/10.1002/cpa.3160110306
- Bertil Gustafsson, Heinz-Otto Kreiss, and Joseph Oliger, Time dependent problems and difference methods, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1995. A Wiley-Interscience Publication. MR 1377057
- Heinz-Otto Kreiss and Jens Lorenz, Initial-boundary value problems and the Navier-Stokes equations, Pure and Applied Mathematics, vol. 136, Academic Press, Inc., Boston, MA, 1989. MR 998379
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)
- J.-P. Berenger, A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys. 114 (1994) 185-200. MR 1294924 (95e:78002)
- S. Abarbanel, D. Gottlieb, and J. S. Hesthaven, Long time behavior of the perfectly matched layer equations in computational electromagnetics, Proceedings of the Fifth International Conference on Spectral and High Order Methods (ICOSAHOM-01) (Uppsala). J. Sci. Comput. 17 (2002), no. 1-4, 405–422 MR 1910579
- K. O. Friedrichs, Symmetric hyperbolic linear differential equations, CPAM 7 (1954), pp 345-392. MR 0062932 (16:44c)
- K. O. Friedrichs, Symmetric positive linear differential equations, CPAM 11 (1958), pp. 333-418. MR 0100718 (20:7147)
- B. Gustafsson, H.-O. Kreiss, and J Oliger. Time Dependent Problems and Difference Methods. Pure and Applied Mathematics. John Wiley & Sons Inc., New York 1995. A Wiley-Interscience Publication. MR 1377057 (97c:65145)
- H.-O. Kreiss and J. Lorenz. Initial-Boundary Value Problems and the Navier-Stokes Equations, Volume 136 of Pure and Applied Mathematics. Academic Press Inc., Boston, MA, 1989. MR 998379 (91a:35138)
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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.
