×

Analysis of electromagnetic scattering from an overfilled cavity in the ground plane. (English) Zbl 1100.78014

This article aims to develop a mathematical method in order to investigate the electromagnetic scattering by overfilled protruding cavities embedded in the perfect electrically conducting infinite ground plane in the frequency domain. An artificial boundary condition is imposed on a semicircle enclosing the cavity, which couples the fields from the infinite exterior domain to those inside. Variational formulations for the TM and TE polarizations are derived, existence and uniqueness of weak solutions are established, and the finite element error analysis is performed as well. Their results indicate that the scattering problem in both TM and TE polarizations attains a unique weak solution for a general cavity medium. In addition, they numerically tried to demonstrate the efficiency of the method.

MSC:

78A45 Diffraction, scattering
78M30 Variational methods applied to problems in optics and electromagnetic theory
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
78-02 Research exposition (monographs, survey articles) pertaining to optics and electromagnetic theory
78A40 Waves and radiation in optics and electromagnetic theory
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Gunzburger, M.; Bayliss, A.; Turkel, E., Boundary conditions for the numerical solution of elliptic equations in exterior regions, SIAM J. Appl. Math., 42, 430-451 (1982) · Zbl 0479.65056
[2] (Abramowitz, M.; Stegun, I., Handbook of Mathematical Functions. Handbook of Mathematical Functions, Applied Mathematics Series, 55 (1972), US Government Printing Office: US Government Printing Office Washington, DC)
[3] Ammari, H.; Bao, G.; Wood, A., An integral equation method for the electromagnetic scattering from cavities, Math. Meth. Appl. Sci., 23, 1057-1072 (2000) · Zbl 0991.78012
[4] Ammari, H.; Bao, G.; Wood, A., Analysis of the electromagnetic scattering from a cavity, Jpn. J. Indus. Appl. Math., 19, 2, 301-308 (2001)
[5] Ammari, H.; Bao, G.; Wood, A., A cavity problem for Maxwell’s equations, Meth. Math. Appl., 9, 2, 249-260 (2002) · Zbl 1170.78335
[6] Burkholder, R. J., Two ray shooting methods for computing the em scattering by large open-ended cavities, Comput. Phys. Commun., 68, 1-3, 353-365 (1991)
[7] Diaz, J.; Joly, P., An analysis of higher order boundary conditions for the wave equation, SIAM J. Appl. Math, 65, 5, 1547-1575 (2005) · Zbl 1078.35062
[8] Engquist, B.; Majda, A., Absorbing boundary conditions for numerical simulation of waves, Math. Comput., 31, 629-651 (1977) · Zbl 0367.65051
[9] Grote, M.; Keller, J. B., Exact nonreflecting boundary conditions for the time dependent wave equation, SIAM J. Appl. Math., 55, 280-297 (1995) · Zbl 0817.35049
[10] Grote, M.; Keller, J. B., Nonreflecting boundary conditions for time dependent wave equation, J. Comput. Phys., 127, 52-65 (1996) · Zbl 0860.65080
[11] Grote, M.; Keller, J. B., Nonreflecting boundary conditions for Maxwell’s equations, J. Comput. Phys., 139, 327-342 (1998) · Zbl 0908.65118
[12] Hansen, T. B.; Yaghjian, A. D., Low-frequency scattering from two-dimensional perfect conductors, IEEE Trans. Antennas Propag., 40, 11, 1389-1402 (1992)
[13] Jin, J. M., Electromagnetic scattering from large, deep, and arbitrarily-shaped open cavities, Electromagnetics, 18, 1, 3-34 (1998)
[14] Jin, J. M.; Ni, S.; Lee, S. W., Hybridization of SBR and FEM for scattering by large bodies with cracks and cavities, IEEE Trans. Antennas Propag., 43, 1130-1139 (1995)
[15] Jin, J. M.; Volakis, J. L., A hybrid finite element method for scattering and radiation by micro strip patch antennas and arrays residing in a cavity, IEEE Trans. Antennas Propag., 39, 1598-1604 (1991)
[16] Ling, H.; Chou, R. C.; Lee, S. W., Shooting and bouncing rays: calculating the RCS of an arbitrarily shaped cavity, IEEE Trans. Antennas Propag., 37, 2, 194-205 (1989)
[17] Liu, J.; Jin, J. M., A special higher order finite-element method for scattering by deep cavities, IEEE Trans. Antennas Propag., 48, 694-703 (2000) · Zbl 1113.78316
[18] Reuster, D. H.; Thiele, G. A., A field iterative method for computing the scattered electric fields at the apertures of large perfectly conducting cavities, IEEE Trans. Antennas Propag., 43, 3, 286-290 (1995)
[19] Van, T.; Wood, A., Finite element analysis for 2-D cavity problem, IEEE Trans. Antennas Propag., 51, 1, 1-8 (2003)
[20] Wang, T. M.; Ling, H., Electromagnetic scattering from three-dimensional cavities via a connection scheme, IEEE Trans. Antennas Propag., 39, 1505-1513 (1991)
[21] Wood, W. D.; Wood, A. W., Development and numerical solution of integral equations for electromagnetic scattering from a trough in a ground plane, IEEE Trans. Antennas Propag., 47, 8, 1318-1322 (1999) · Zbl 0955.78007
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.