Absorbing boundary conditions for electromagnetic wave propagation
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- Math. Comp. 68 (1999), 145-168 Request permission
Abstract:
In this paper, the theoretical perfectly absorbing boundary condition on the boundary of a half–space domain is developed for the Maxwell system by considering the system as a whole instead of considering each component of the electromagnetic fields individually. This boundary condition allows any wave motion generated within the domain to pass through the boundary of the domain without generating any reflections back into the interior. By approximating this theoretical boundary condition a class of local absorbing boundary conditions for the Maxwell system can be constructed. Well–posedness in the sense of Kreiss of the Maxwell system with each of these local absorbing boundary conditions is established, and the reflection coefficients are computed as a plane wave strikes the artificial boundary. Numerical experiments are also provided to show the performance of these local absorbing boundary conditionsReferences
- Abderrahmane Bendali and Laurence Halpern, Conditions aux limites absorbantes pour le système de Maxwell dans le vide en dimension $3$, C. R. Acad. Sci. Paris Sér. I Math. 307 (1988), no. 20, 1011–1013 (French, with English summary). MR 978263
- B. Chalinder, Conditions aux limites absorbantes pour les équations de l’ élastodynamique linéaire, Ph.D. Thesis, Université de Saint–Etienne, 1988.
- Robert Dautray and Jacques-Louis Lions, Mathematical analysis and numerical methods for science and technology. Vol. 1, Springer-Verlag, Berlin, 1990. Physical origins and classical methods; With the collaboration of Philippe Bénilan, Michel Cessenat, André Gervat, Alain Kavenoky and Hélène Lanchon; Translated from the French by Ian N. Sneddon; With a preface by Jean Teillac. MR 1036731
- E. Duceau and B. Mercier, Approche instationnaire pour la réflexion des ondes électromagnétiques, Communication aux journées “Aspects Mathématiques des Phénomènes de Propagation d’ondes", INRIA, Nice 16 (1988).
- Bjorn Engquist and Andrew Majda, Absorbing boundary conditions for the numerical simulation of waves, Math. Comp. 31 (1977), no. 139, 629–651. MR 436612, DOI 10.1090/S0025-5718-1977-0436612-4
- Björn Engquist and Andrew Majda, Radiation boundary conditions for acoustic and elastic wave calculations, Comm. Pure Appl. Math. 32 (1979), no. 3, 314–358. MR 517938, DOI 10.1002/cpa.3160320303
- Reuben Hersh, Mixed problems in several variables, J. Math. Mech. 12 (1963), 317–334. MR 0147790
- Robert L. Higdon, Initial-boundary value problems for linear hyperbolic systems, SIAM Rev. 28 (1986), no. 2, 177–217. MR 839822, DOI 10.1137/1028050
- Robert L. Higdon, Absorbing boundary conditions for difference approximations to the multidimensional wave equation, Math. Comp. 47 (1986), no. 176, 437–459. MR 856696, DOI 10.1090/S0025-5718-1986-0856696-4
- Robert L. Higdon, Numerical absorbing boundary conditions for the wave equation, Math. Comp. 49 (1987), no. 179, 65–90. MR 890254, DOI 10.1090/S0025-5718-1987-0890254-1
- Robert L. Higdon, Radiation boundary conditions for elastic wave propagation, SIAM J. Numer. Anal. 27 (1990), no. 4, 831–869. MR 1051110, DOI 10.1137/0727049
- P. Joly and B. Mercier, Une nouvelle condition transparente d’order $2$ pour les équations de Maxwell en dimension $3$, Rapport INRIA, n$^{0}$ 1047 (1989).
- Heinz-Otto Kreiss, Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math. 23 (1970), 277–298. MR 437941, DOI 10.1002/cpa.3160230304
- C. J. Everett Jr., Annihilator ideals and representation iteration for abstract rings, Duke Math. J. 5 (1939), 623–627. MR 13
- Andrew Majda and Stanley Osher, Initial-boundary value problems for hyperbolic equations with uniformly characteristic boundary, Comm. Pure Appl. Math. 28 (1975), no. 5, 607–675. MR 410107, DOI 10.1002/cpa.3160280504
- G. Mur, Absorbing boundary conditions for the finite–difference approximation of the time–domain electromagnetic–field equations, IEEE Trans. Electromag. Comp. EMC 23 (1981), 377.
- M. Sesquès, Conditions aux limites absorbantes pour le système de Maxwell, Ph. D. thesis, Université de Bordeaux, 1990.
- A. Taflove, Computational Electromagnetics, the Finite–Difference Time–Domain Method, Artech House, 1995.
- Harry F. Tiersten, A development of the equations of electromagnetism in material continua, Springer Tracts in Natural Philosophy, vol. 36, Springer-Verlag, New York, 1990. MR 1070100, DOI 10.1007/978-1-4613-9679-6
- Lloyd N. Trefethen, Instability of difference models for hyperbolic initial-boundary value problems, Comm. Pure Appl. Math. 37 (1984), no. 3, 329–367. MR 739924, DOI 10.1002/cpa.3160370305
- Lloyd N. Trefethen and Laurence Halpern, Well-posedness of one-way wave equations and absorbing boundary conditions, Math. Comp. 47 (1986), no. 176, 421–435. MR 856695, DOI 10.1090/S0025-5718-1986-0856695-2
- K. S. Yee, Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media, IEEE Trans. Ant. Prop. AP-14 (1966), 302–307.
Additional Information
- Xiaobing Feng
- Affiliation: Department of Mathematics, The University of Tennessee, Knoxville, TN 37996
- MR Author ID: 351561
- Email: xfeng@math.utk.edu
- Received by editor(s): January 11, 1994
- Received by editor(s) in revised form: June 27, 1994, and May 24, 1997
- © Copyright 1999 American Mathematical Society
- Journal: Math. Comp. 68 (1999), 145-168
- MSC (1991): Primary 65M99; Secondary 35L50
- DOI: https://doi.org/10.1090/S0025-5718-99-01028-5
- MathSciNet review: 1613707