Solving Maxwell equations in 3D prismatic domains

Patrick Ciarlet; Emmanuelle Garcia; Jun Zou

doi:10.1016/j.crma.2004.09.032

Numerical Analysis/Partial Differential Equations

Solving Maxwell equations in 3D prismatic domains
[Résolution des équations de Maxwell dans des domaines prismatiques tridimensionnels.]

Présenté par : Roland Glowinski

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

Comptes Rendus. Mathématique, Volume 339 (2004) no. 10, pp. 721-726.

Résumé
Abstract

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.

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.

Reçu le : 2004-09-02
Accepté le : 2004-09-28
Publié le : 2004-11-05

DOI : 10.1016/j.crma.2004.09.032

Affiliations des auteurs :

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

@article{CRMATH_2004__339_10_721_0,
     author = {Patrick Ciarlet and Emmanuelle Garcia and Jun Zou},
     title = {Solving {Maxwell} equations in {3D} prismatic domains},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {721--726},
     publisher = {Elsevier},
     volume = {339},
     number = {10},
     year = {2004},
     doi = {10.1016/j.crma.2004.09.032},
     language = {en},
}

TY  - JOUR
AU  - Patrick Ciarlet
AU  - Emmanuelle Garcia
AU  - Jun Zou
TI  - Solving Maxwell equations in 3D prismatic domains
JO  - Comptes Rendus. Mathématique
PY  - 2004
SP  - 721
EP  - 726
VL  - 339
IS  - 10
PB  - Elsevier
DO  - 10.1016/j.crma.2004.09.032
LA  - en
ID  - CRMATH_2004__339_10_721_0
ER  -

%0 Journal Article
%A Patrick Ciarlet
%A Emmanuelle Garcia
%A Jun Zou
%T Solving Maxwell equations in 3D prismatic domains
%J Comptes Rendus. Mathématique
%D 2004
%P 721-726
%V 339
%N 10
%I Elsevier
%R 10.1016/j.crma.2004.09.032
%G en
%F CRMATH_2004__339_10_721_0

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/

Bibliographie
Cité par

[1] F. Assous; P. Ciarlet; E. Garcia Solution of the time-dependent Maxwell equations with charges in a two-dimensional singular domain, C. R. Acad. Sci. Paris, Ser. I, Volume 330 (2000), pp. 391-396

[2] F. Assous; P. Ciarlet; J. Segré Numerical solution to the time-dependent Maxwell equations in two-dimensional singular domain: The Singular Complement Method, J. Comput. Phys., Volume 161 (2000), pp. 218-249

[3] F. Assous; P. Degond; E. Heintzé; P.A. Raviart; J. Segré On a finite element method for solving the three-dimensional Maxwell equations, J. Comput. Phys., Volume 109 (1993), pp. 222-237

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

[5] M.Sh. Birman; M.Z. Solomyak Maxwell operator in regions with nonsmooth boundaries, Sib. Math. J., Volume 28 (1987), pp. 12-24

[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

[11] E. Jamelot, Nodal finite element methods for Maxwell's equations, C. R. Acad. Sci. Paris, Ser. I, in press

Cité par Sources :

Commentaires - Politique