Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Absorbing boundary conditions
for electromagnetic wave propagation

Author: Xiaobing Feng
Journal: Math. Comp. 68 (1999), 145-168
MSC (1991): Primary 65M99; Secondary 35L50
MathSciNet review: 1613707
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 conditions

References [Enhancements On Off] (What's this?)

  • 1. A. Bendali and L. Halpern, Conditions aux limites absorbantes pour le système de Maxwell dans le vide en dimension $3$, C.R.A.S. Paris, Tome 307, Série I, n$^{o}$ 20 (1988), 1011-1013. MR 90f:35172
  • 2. B. Chalinder, Conditions aux limites absorbantes pour les équations de l' élastodynamique linéaire, Ph.D. Thesis, Université de Saint-Etienne, 1988.
  • 3. R. Dautray and J. L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, I, Springer-Verlag, New York, 1990. MR 90k:00004
  • 4. 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).
  • 5. B. Engquist and A. Majda, Absorbing boundary conditions for the numerical simulation of waves, Math. Comp. 31 (1977), 629-651. MR 55:9555
  • 6. -, Radiation boundary conditions for acoustic and elastic wave calculations, Comm. Pure Appl. Math. 32 (1979), 313-357. MR 80e:76041
  • 7. R. Hersh, Mixed problems in several variables, J. Math. Mech. 12 (1963), 317-334. MR 26:5304
  • 8. R. L. Higdon, Initial-boundary value problems for linear hyperbolic systems, SIAM Rev. 28 (1986), 177-217. MR 88a:35138
  • 9. -, Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation, Math. Comp. 47 (1986), 437-459. MR 87m:65131
  • 10. -, Numerical absorbing boundary conditions for the wave equation, Math Comp 49 (1987), 65-90. MR 88f:65168
  • 11. -, Radiation boundary conditions for elastic wave propagation, SIAM J. Numer. Anal. 27 (1990), 831-870. MR 91h:73017
  • 12. 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).
  • 13. H. O. Kreiss, Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math. 23 (1970), 277-298. MR 55:10862
  • 14. L. Landau and E. Lifschitz, The Classical Theory of Fields, Pergamon, Oxford, 1959. MR 13:289i
  • 15. A. Majda and S. Osher, Initial-boundary value problems for hyperbolic equations with uniformly characteristic boundary, Comm. Pure Appl. Math. 28 (1975), 607-675. MR 53:13857
  • 16. 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.
  • 17. M. Sesquès, Conditions aux limites absorbantes pour le système de Maxwell, Ph. D. thesis, Université de Bordeaux, 1990.
  • 18. A. Taflove, Computational Electromagnetics, the Finite-Difference Time-Domain Method, Artech House, 1995.
  • 19. H. F. Tiersten, A Development of the Equations of Electromagnetism in Material Continua, Springer Tracts in Natural Philosophy Volume 36, Springer-Verlag, New York, 1990. MR 91e:78012
  • 20. L. N. Trefethen, Instability of difference models for hyperbolic initial boundary value problems, Comm. Pure Appl. Math. 37 (1984), 329-367. MR 86f:65162
  • 21. L. N. Trefethen and L. Halpern, Well-posedness of one-way wave equations and absorbing boundary conditions, Math. Comp. 47 (1986), 421-435. MR 88b:65148
  • 22. 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.

Similar Articles

Retrieve articles in Mathematics of Computation of the American Mathematical Society with MSC (1991): 65M99, 35L50

Retrieve articles in all journals with MSC (1991): 65M99, 35L50

Additional Information

Xiaobing Feng
Affiliation: Department of Mathematics, The University of Tennessee, Knoxville, TN 37996

Keywords: Maxwell system, absorbing boundary conditions, Laplace--Fourier transform, Kreiss criterion
Received by editor(s): January 11, 1994
Received by editor(s) in revised form: June 27, 1994, and May 24, 1997
Article copyright: © Copyright 1999 American Mathematical Society

American Mathematical Society