Comptes Rendus
Numerical Analysis/Partial Differential Equations
Solving Maxwell equations in 3D prismatic domains
Comptes Rendus. Mathématique, Volume 339 (2004) no. 10, pp. 721-726.

In this Note, we introduce the Fourier Singular Complement Method, for solving Maxwell equations in a 3D prismatic domain. The numerical implementation of this method provides a continuous approximation of the electromagnetic field. It can be applied to the computation of propagating and evanescent modes in prismatic stub filters, thus generalizing 2D approaches.

Dans cette Note, nous introduisons la Méthode du Complément Singulier avec Fourier, pour résoudre les équations de Maxwell dans des domaines prismatiques tridimensionnels. La mise en œuvre numérique de cette méthode permet de calculer une approximation continue du champ électromagnétique. Elle peut être appliquée à la détermination des modes propagatifs ou bloquants dans un filtre à stubs prismatique, ce qui constitue une généralisation des méthodes applicables en domaine bidimensionnel.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.09.032
Patrick Ciarlet 1; Emmanuelle Garcia 1; Jun Zou 2

1 ENSTA–CNRS–INRIA UMR 2706 POEMS, 32, boulevard Victor, 75739 Paris cedex 15, France
2 Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong
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Patrick Ciarlet; Emmanuelle Garcia; Jun Zou. Solving Maxwell equations in 3D prismatic domains. Comptes Rendus. Mathématique, Volume 339 (2004) no. 10, pp. 721-726. doi : 10.1016/j.crma.2004.09.032. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.09.032/

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[4] F. Ben Belgacem; C. Bernardi Spectral element discretization of the Maxwell equations, Math. Comp., Volume 68 (1999), pp. 1497-1520

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[6] P. Ciarlet, Jr., Augmented formulations for solving Maxwell equations, Comput. Methods Appl. Mech. Engrg., in press

[7] P. Ciarlet, Jr., B. Jung, S. Kaddouri, S. Labrunie, J. Zou, The Fourier Singular Complement Method for the Poisson problem. Part I: prismatic domains, Numer. Math., submitted for publication

[8] E. Garcia, PhD Thesis, Paris 6 University, France, 2002 (in French)

[9] E. Garcia; S. Labrunie Space–time regularity of the solution to Maxwell's equations in non-convex domains, C. R. Acad. Sci. Paris, Ser. I, Volume 334 (2002), pp. 293-298

[10] C. Hazard; S. Lohrengel A singular field method for Maxwell's equations: numerical aspects for 2D magnetostatics, SIAM J. Appl. Math., Volume 40 (2002), pp. 1021-1040

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