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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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Numerical analysis of the exterior boundary value problem for the time-harmonic Maxwell equations by a boundary finite element method. I. The continuous problem
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by A. Bendali PDF
Math. Comp. 43 (1984), 29-46 Request permission

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
    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. A. Bendali, D. Clair & J. Tourneur, "Finite element approximation of electromagnetic diffraction by arbitrarily-shaped surfaces," Electron. Lett., v. 28, 1982, pp. 641-642.
  • F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers, Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge 8 (1974), no. R-2, 129–151 (English, with French summary). MR 365287
  • Manfredo P. do Carmo, Differential geometry of curves and surfaces, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1976. Translated from the Portuguese. MR 0394451
  • G. Duvaut and J.-L. Lions, Les inéquations en mécanique et en physique, Travaux et Recherches Mathématiques, No. 21, Dunod, Paris, 1972 (French). MR 0464857
  • G. J. Fix and R. A. Nicolaides, An analysis of mixed finite element approximations for periodic acoustic wave propagation, SIAM J. Numer. Anal. 17 (1980), no. 6, 779–786. MR 595443, DOI 10.1137/0717065
    • J. Giroire, Integral Equation Methods for Exterior Problems for the Helmholtz Equation, Rapport Interne no. 40, Centre de Mathématiques Appliquées, Ecole Polytechnique, Palaiseau, 1978.
  • J. Giroire and J.-C. Nédélec, Numerical solution of an exterior Neumann problem using a double layer potential, Math. Comp. 32 (1978), no. 144, 973–990. MR 495015, DOI 10.1090/S0025-5718-1978-0495015-8
    • 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.
  • J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. Vol. 1, Travaux et Recherches Mathématiques, No. 17, Dunod, Paris, 1968 (French). MR 0247243
  • Claus Müller, Foundations of the mathematical theory of electromagnetic waves, Die Grundlehren der mathematischen Wissenschaften, Band 155, Springer-Verlag, New York-Heidelberg, 1969. Revised and enlarged translation from the German. MR 0253638, DOI 10.1007/978-3-662-11773-6
    • 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.
  • J.-C. Nédélec, Computation of eddy currents on a surface in $\textbf {R}^{3}$ by finite element methods, SIAM J. Numer. Anal. 15 (1978), no. 3, 580–594. MR 495761, DOI 10.1137/0715038
  • J.-C. Nédélec and J. Planchard, Une méthode variationnelle d’éléments finis pour la résolution numérique d’un problème extérieur dans $R^{3}$, Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge 7 (1973), no. R-3, 105–129 (French, with English summary). MR 424022
    • 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. 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.
  • P.-A. Raviart and J. M. Thomas, A mixed finite element method for 2nd order elliptic problems, Mathematical aspects of finite element methods (Proc. Conf., Consiglio Naz. delle Ricerche (C.N.R.), Rome, 1975) Lecture Notes in Math., Vol. 606, Springer, Berlin, 1977, pp. 292–315. MR 0483555
  • Franz Rellich, Über das asymptotische Verhalten der Lösungen von $\Delta u+\lambda u=0$ in unendlichen Gebieten, Jber. Deutsch. Math.-Verein. 53 (1943), 57–65 (German). MR 17816
  • V. H. Rumsey, Reaction concept in electromagnetic theory, Phys. Rev. (2) 94 (1954), 1483–1491. MR 63933, DOI 10.1103/PhysRev.94.1483
    • A. Sankar & T. C. Tong, "Current computation on complex structures by finite element method," Electron. Lett., v. 11, 1975, pp. 481-482. W. L. Stutzman & G. A. Thiele, Antenna Theory and Design, Wiley, New York, 1981. J. van Bladel, Electromagnetic Fields, McGraw-Hill, New York, 1964.
  • Calvin H. Wilcox, Scattering theory for the d’Alembert equation in exterior domains, Lecture Notes in Mathematics, Vol. 442, Springer-Verlag, Berlin-New York, 1975. MR 0460927, DOI 10.1007/BFb0070581
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • 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