Resolution of coupled Helmholtz equation in the inhomogeneous coaxial waveguides by the finite element method

Issue		Eur. Phys. J. Appl. Phys. Volume 38, Number 1, April 2007


Page(s)		61 - 67
Section		Characterization of Materials: Imaging,\ Microscopy and Spectroscopy
DOI		10.1051/epjap:2007046
Published online		14 March 2007

Eur. Phys. J. Appl. Phys. 38, 61-67 (2007)
DOI: 10.1051/epjap:2007046

Resolution of coupled Helmholtz equation in the inhomogeneous coaxial waveguides by the finite element method

M. Bour^{1, 2}, A. Toumanari² and D. Khatib²

¹ Laboratoire Matériaux, Systèmes et Technologie de l'Informations, Université Ibn Zohr, ESTA, BP 33/S, 80000 Agadir, Morocco
² Laboratoire de la Physique Théorique de Solide, Université Ibn Zohr, Faculté des Sciences, Agadir, Morocco

bour@esta.ac.ma

(Received: 16 April 2006 / Received in final form: 14 November 2006 / Accepted: 24 January 2007 / Published online: 14 March 2007)

Abstract
This paper presents the application of the Finite Element Method FEM to the resolution of system Helmholtz coupled equations that has been obtained in the coaxial waveguides containing magnetic anisotropic materials with loss. This application is based on variational method which necessitates the construction of functional stationary written in the form of integral equation and dependent on the electromagnetic fields. After being minimized, this functional leads to algebraic equation system to which we can apply many numerical resolution algorithms. The electromagnetic study of the waveguide led us to a system of Helmholtz coupled equations which is difficult to be solved analytically. Our software code allows us to determine the electromagnetic field distribution in all points of the coaxial waveguide. The result has been validated when the coaxial waveguide was entirely loaded with air. This software has later been applied when the waveguide was partially filled with a magnetic anisotropic material with loss ( $\varepsilon_r$ , $\overline{\overline{\mu_r}}$ ).

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