Absorbing Boundary Conditions on Arbitrary Boundaries for the Scalar and Vector Wave Equations

IEEE Transactions on Antennas and Propagation

Volumn 42, Issue 6, 1994, Pages 773-780

  Stupfel, Bruno ^a  

^a CEA DIF   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ANTENNAS; APPROXIMATION THEORY; DIFFERENTIAL EQUATIONS; ELECTROMAGNETIC WAVE ABSORPTION; ELECTROMAGNETIC WAVE REFLECTION; FINITE ELEMENT METHOD; TIME DOMAIN ANALYSIS; VECTORS;

ABSORBING BOUNDARY CONDITIONS; ARBITRARY BOUNDARIES; SCALAR AND VECTOR WAVE EQUATIONS;

ELECTROMAGNETIC WAVE SCATTERING;

EID: 0028445572     PISSN: 0018926X     EISSN: 15582221     Source Type: Journal    
DOI: 10.1109/8.301695     Document Type: Article

References (32)

1. T. C. Jurgens, A. Taflove, K. R. Umashankar, and T. G. Moore, “FDTE modeling of curved surfaces,” IEEE Trans. Antennas Propagat., vol 13, pp. 357-366, 1992.
2. X. Yuan, “Three-dimensional electromagnetic scattering from inhomogeneous objects by the hybrid moment and finite element method,” IEEE Trans. Microwave Theory Tech., vol. 38, pp. 1053-1058, 1990.
3. B. Stupfel, R. Le Martret, P. Bonnemason, and B. Scheurer, “Solution of the scattering problem by axisymmetrical penetrable objects with a mixed boundary-element and finite-element method,” in Proc. JINA ‘90 Nice, France, pp. 116-119, Nov. 1990.
4. J. M. Jin, J. L. Volakis, and J. D. Collins, “A finite element-boundary integral method for scattering and radiation by two- and three-dimensional structures,” IEEE Trans. Antennas Propagat. Mag., vol. 33, pp. 22-32 1991.
5. W. E. Boyse and A. A. Seidl, “A hybrid finite element method for near bodies of revolution,” IEEE Trans. Magnetics, vol. 27, pp. 3833-3836 1991.
6. P. Bonnemason, R. Le Martret, and B. Stupfel, “Oblique incidence scattering by large, coated cylinders of arbitrary cross-section,” in URSi Dig. Joint Symp. IEEE-APS/URSI/NEM, Chicago, p. 26, July 1992.
7. C. H. Wilcox, “A generalization of theorems of Rellich and Atkinson,” Proc. Amer. Math. Soc., pp. 271-276, 1955.
8. “An expansion theorem for electromagnetic fields,” Comm. Pun Appl. Math., vol. 9, pp. 115-134, 1956.
9. T. G. Moore, J. G. Blashack, A. Taflove, and G. A. Kriegsmann, “Theory and application of radiation boundary operators,” IEEE Trans. Antennas Propagat., vol. 36, pp. 1797-1811, 1988.
10. F. R. Cooray and G. I. Costache, “An overview of the absorbing boundary conditions,” J. Electromag. Waves and Appl., vol. 5, pp 1041-1054, 1991.
11. A. Bayliss, M. Gunzburger, and E. Turkel, “Boundary conditions for the numerical solution of elliptic equations in exterior regions,” SIAk J. Appl. Math., vol. 42, pp. 430-451, 1982.
12. A. F. Peterson, “Absorbing boundary conditions for the vector wave equation,” Microwave Opt. Tech. Lett., vol. 1, pp. 62-64, 1988.
13. J. P. Webb and V. N. Kanellopoulos, “Absorbing boundary conditions for the finite element solution of the vector wave equation,” Microwave Opt. Tech. Lett., vol. 2, pp. 370-372, 1989.
14. A. Khebir, O. M. Ramahi, and R. Mittra, “An efficient partial differentia equation technique for solving the problem of scattering by objects of arbitrary shape,” Microwave Opt. Tech. Lett., vol. 2, pp. 229-233, 1989
15. R. Janaswamy, “2-D radiation boundary conditions on an arbitrary outer boundary,” Microwave Opt. Tech. Lett., vol. 5, pp. 393-395, 1992.
16. D. B. Meade, G. W. Slade, A. F. Peterson, and K. J. Webb, “Analytic evaluation of the accuracy of several conformable local absorbing boundary conditions,” in AP Dig. Joint Symp. IEEE-APS/URSI/NEM Chicago, pp. 540-543, July 1992.
17. B. Engquist and A. Majda, “Absorbing boundary conditions for the numerical simulation of waves,” Math. Comp., vol. 31, pp. 421-135 1977.
18. R. L. Higdon, “Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation,” Math. Comp., vol 47, pp. 437-459, 1986.
19. E. L. Lindman, “Free space boundary conditions for the time dependen wave equation,” J. Comp. Phys., vol. 18, pp. 66-78, 1975.
20. P. Joly and B. Mercier, “Une nouvelle condition transparente d'ordre 2 pour les équations de Maxwell en dimension 3,” INRIA, BP 105, 78135 Le Chesnay, France, Rapport de recherche 1047, 1989.
21. C. F. Lee, R. T. Shin and J. A. Kong, “Absorbing boundary conditions on circular and elliptical boundaries,” J. Electromag. Waves Appl. vol. 4, pp. 945-962, 1990.
22. Y. C. Ma, “A note on the radiation boundary conditions for the Helmholtz equation,” IEEE Trans. Antennas Propagat., vol. 39, pp. 1526-1530, 1991.
23. M. Sesques, “Conditions aux limites absorbantes pour le systemè de Maxwell,” Ph.D. dissertation, Université de Bordeaux I, France, 1990.
24. M. Sesques and B. Hanouzet, “Absorbing boundary conditions for Maxwell's equations,” in Proc. 4th Int. Conf. Hyperbolic Problems, Numerical Methods and Applications, Taormina, Italy, Apr. 1992.
25. J. D'Angelo and I.D. Mayergoyz, “Finite element method for the solution of RF radiation and scattering problems,” Electromagn., vol. 10, pp. 177-199, 1990.
26. A. Chaterjee, J. M. Jin, and J. L. Volakis, “Robust finite element solution for three-dimensional scattering,” Electron. Lett., vol. 28, pp. 966-967, 1992.
27. G. A. Kriegsmann, A. Taflove, and K. R. Umashankar, “A new formulation of electromagnetic wave scattering using an on-surface radiation boundary condition approach,” IEEE Trans. Antennas Propagat., vol. AP-35, pp.153-161, 1987.
28. D. S. Jones, “Surface radiation conditions,” IMA J. Appl. Math., vol. 41, pp. 21-30, 1988.
29. J. B. Keller, R. M. Lewis, and B. D. Seckler, “Asymptotic solution of some diffraction problems,” Comm. Pure Appl. Math., vol. 9, pp. 207-265, 1956.
30. J. A. Stratton, Electromagnetic Theory. New York: McGraw-Hill, 1941, pp. 49-50.
31. A. Erdélyi, Asymptotic Expansions. New York: Dover, 1956.
32. H. O. Kreiss, “Initial boundary value problems for linear hyperbolic systems,” Comm. Pure Appl. Math., vol. 23, pp. 277-298, 1970.