Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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

 
 

 

Numerical analysis of the exterior boundary value problem for the time-harmonic Maxwell equations by a boundary finite element method. I. The continuous problem


Author: A. Bendali
Journal: Math. Comp. 43 (1984), 29-46
MSC: Primary 65N30; Secondary 78-08, 78A45
DOI: https://doi.org/10.1090/S0025-5718-1984-0744923-1
MathSciNet review: 744923
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A general finite element method is applied to compute the skin currents flowing on a perfectly conducting surface when it is illuminated by a time-harmonic incident electromagnetic wave. In this paper, we introduce and study the framework in which the continuous problem can be stated in order to make possible the numerical analysis which will follow in a second part.


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

  • [1] A. Bendali, Problème aux Limites Extérieur et Intérieur pour le Système de Maxwell en Régime Harmonique, Rapport Interne no. 50, Centre de Mathématiques Appliquées, Ecole Polytechnique, Palaiseau, 1980.
  • [2] A. Bendali, D. Clair & J. Tourneur, "Finite element approximation of electromagnetic diffraction by arbitrarily-shaped surfaces," Electron. Lett., v. 28, 1982, pp. 641-642.
  • [3] F. Brezzi, "On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers,"RAIRO Ser. Rouge, v. 8, No. R-2, 1974, pp. 129-151. MR 0365287 (51:1540)
  • [4] M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, Englewood Cliffs, N.J., 1976. MR 0394451 (52:15253)
  • [5] G. Duvaut & J. L. LIONS, Les Inéquations en Mécanique el en Physique, Dunod, Paris, 1972. MR 0464857 (57:4778)
  • [6] G. J. Fix & R. A. Nicolaides, "An analysis of mixed finite element approximations for periodic acoustic wave propagation," SIAM J. Numer. Anal., v. 17, 1980, pp. 779-786. MR 595443 (82f:76029)
  • [7] J. Giroire, Integral Equation Methods for Exterior Problems for the Helmholtz Equation, Rapport Interne no. 40, Centre de Mathématiques Appliquées, Ecole Polytechnique, Palaiseau, 1978.
  • [8] J. Giroire & J. C. Nedelec, "Numerical solution of an exterior Neumann problem using a double-layer potential," Math. Comp., v. 32, 1978, pp. 973-990. MR 0495015 (58:13783)
  • [9] R. F. Harrington, "Characteristic modes for antennas and scatterers," in Numerical and Asymptotic Techniques in Electromagnetics (R. Mittra, ed.), Topics in Applied Physics, Vol. 3, Springer-Verlag, Berlin, Heidelberg, New York, 1975.
  • [10] J. L. Lions & E. Magenes, Problèmes aux Limites Non Homogènes et Applications, Vol. 1, Dunod, Paris, 1968. MR 0247243 (40:512)
  • [11] C. Muller, Foundations of the Mathematical Theory of Electromagnetic Waves, Springer-Verlag, Berlin, 1969. MR 0253638 (40:6852)
  • [12] J. C. Nedelec, Approximation des Équations Intégrales en Mécanique et en Physique, Cours de l'Ecole d'Eté d'Analyse Numérique EDF-CEA-IRIA, Centre de Mathématiques Appliquées, Ecole Polytechnique, Palaiseau, 1977.
  • [13] J. C. Nedelec, "Computation of eddy currents on a surface in $ {{\mathbf{R}}^3}$ by finite element methods," SIAM J. Numer. Anal., v. 15, 1978, pp. 580-595. MR 0495761 (58:14409)
  • [14] J. C. Nedelec & J. Planchard, "Une méthode variationnelle d'éléments finis pour la résolution numérique d'un problème extérieur dans $ {{\mathbf{R}}^3}$, RAIRO Ser. Rouge, v. 7, R3, 1973, pp. 105-129. MR 0424022 (54:11992)
  • [15] D. J. Poggio & E. K. Miller, "Solutions of three-dimensional scattering problems," in Computer Techniques for Electromagnetics (R. Mittra, ed.), Permagon Press, New York, 1973.
  • [16] S. S. M. Rao, D. R. Wilton & A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas and Propagation, v. AP-30, 1982, pp. 409-418.
  • [17] P. A. Raviart & J. M. Thomas, A Mixed Finite Element Method for 2nd Order Elliptic Problems, Lecture Notes in Math., Vol. 606, Springer-Verlag, Berlin and New York, 1977, pp. 292-315. MR 0483555 (58:3547)
  • [18] F. Rellich, "Über das asymptotische Verhalten der Lösungen von $ \Delta u + \lambda u = 0$ in unendlichen Gebieten," Jber. Deutsch. Math. Verein., v. 53, 1943, pp. 57-65. MR 0017816 (8:204c)
  • [19] V. H. Rumsey, "Reaction concept in electromagnetic theory," Phys. Rev., v. 94, 1954, pp. 1483-1491. MR 0063933 (16:202b)
  • [20] A. Sankar & T. C. Tong, "Current computation on complex structures by finite element method," Electron. Lett., v. 11, 1975, pp. 481-482.
  • [21] W. L. Stutzman & G. A. Thiele, Antenna Theory and Design, Wiley, New York, 1981.
  • [22] J. van Bladel, Electromagnetic Fields, McGraw-Hill, New York, 1964.
  • [23] C. H. Wilcox, Scattering Theory for the d'Alembert Equation in Exterior Domains, Lecture Notes in Math., Vol. 442, Springer-Verlag, Berlin, 1975. MR 0460927 (57:918)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65N30, 78-08, 78A45

Retrieve articles in all journals with MSC: 65N30, 78-08, 78A45


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1984-0744923-1
Article copyright: © Copyright 1984 American Mathematical Society

American Mathematical Society