Eigenanalysis of Electromagnetic Structures Based on the Finite Element Method (original) (raw)
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Finite element solution for a class of unbounded geometrics (EM scattering)
IEEE Transactions on Antennas and Propagation, 1991
An efficient and systematic procedure is described for the finite element solution of a class of electromagnetic radiation and scattering problems involving unbounded geometries. The numerical procedure is well suited for analyzing infinite metallic structures with cavity regions filled with inhomogeneous and anisotropic media. The formulation is based upon an approach that combines the finite element method @EM) with the surface integral equation to truncate the mesh region. The efficiency of the proposed technique arises from the use of the Green's function of the first kind in the surface integral. Illustrative numerical representations that demonstrate the validity, versatility, and efficiency of the method are included.
A Finite element formulation for the solution of the two-dimensional eigenvalue problem for open radiating structures is proposed. The semi-infinite solution domain that occurs in such problem is modelled using an expansion in an infinite sum of cylindrical harmonics, while the structure itself is described by the finite element method. The two mathematical models are coupled by exploiting the tangential field continuity condition. In fact for the truncation of the finite element mesh a fictitious cylindrical domain boundary is used which encloses the opening of our structure. On that fictitious boundary we impose the field continuity condition formulating in that way a generalized eigenvalue problem taking in to account Sommerfeld radiation condition. This final eigenvalue problem is solved using the Arnoldi subspace iterative technique, [5].
The Journal of the Acoustical Society of America, 2012
In this paper, a three-dimensional boundary element method for the eigenanalysis of complex-shaped cavity is presented. A particular integral method is proposed with general absorbing boundary conditions, well suited for determination of the lower modes. In this approach, a polynomial approximation of surface admittance is used with a recent class of compactly supported radial basis function. Two common absorbent models are employed in order to demonstrate the relevance of high-order approximation of the admittance. Resulting eigenproblems of several order (linear to cubic) are thus performed on basic geometries and a car interior. Results show significant improvements for the computed damped eigenfrequencies and the associated modal reverberation time while using an approximation polynomial matching the surface admittance variation order.
The paper presents an optimizationprocedure for the distribution of the electromagneticfield in a microwave applicator used for the drying of adielectric. There are shown various applications ofnumerical modelling 3D, using the Method of theFinite Elements, for the study of the heating of somedielectrics with losses, of parallelepiped shape, situatedin a multimode applicator, excited with energy througha wave guide. To determine the electromagnetic fieldwe used the Ansoft HFSS 10.1 programme. Thisprogramme uses the finite elements method and thenodal functions of the first order. The calculationdomain is divided into tetrahedral subdomains and thefield in each subdomain is properly defined by thevalues in the nodes of the tetrahedron. In this paper wepresent the optimization of the distribution of theelectromagnetic field from the following point of view:the placing mode of the wave guide on the applicator.The main problem which appears is represented by thehomogeneity of the field ...
International Workshop on Finite Elements for Microwave Engineering
Proceedings e report, 2016
When Courant prepared the text of his 1942 address to the American Mathematical Society for publication, he added a two-page Appendix to illustrate how the variational methods first described by Lord Rayleigh could be put to wider use in potential theory. Choosing piecewise-linear approximants on a set of triangles which he called elements, he dashed off a couple of two-dimensional examples and the finite element method was born. … Finite element activity in electrical engineering began in earnest about 1968-1969. A paper on waveguide analysis was published in Alta Frequenza in early 1969, giving the details of a finite element formulation of the classical hollow waveguide problem. It was followed by a rapid succession of papers on magnetic fields in saturable materials, dielectric loaded waveguides, and other well-known boundary value problems of electromagnetics. … In the decade of the eighties, finite element methods spread quickly. In several technical areas, they assumed a domi...
Journal de Mathématiques Pures et Appliquées, 2019
We consider a spectral problem for the Laplacian operator in a planar T-like shaped thin structure Ω ε , where ε denotes the transversal thickness of both branches. We assume the homogeneous Dirichlet boundary condition on the ends of the branches and the homogeneous Neumann boundary condition on the remaining part of the boundary of Ω ε. We study the asymptotic behavior, as ε tends to zero, of the high frequencies of such a problem. Unlike the asymptotic behavior of the low frequencies where the limit problem involves only longitudinal vibrations along each branch of the T-like shaped thin structure (i.e. 1D limit spectral problems), we obtain a two dimensional limit spectral problem which allows us to capture other kinds of vibrations. We also give a characterization of the asymptotic form of the eigenfunctions originating these vibrations. Résumé: On considère le problème spectral pour le Laplacien, dans une structure mince bidimensionnelle Ω ε en forme de T, où ε désigne l'épaisseur des deux branches du T. Les conditions aux limites sont du type Neumann homogène sur tout le bord sauf aux extrémités des branches où une condition de Dirichlet homogène est imposée. Onétudie le comportement asymptotique des hautes fréquences lorsque ε tend vers zéro. Contrairement au comportement asymptotique des basses fréquences, pour lesquelles le problème limite ne fait apparaître que des vibrations longitudinales le long de chaque branche de la structure (c'est-à-dire, des problèmes spectraux limites 1D), on obtientà la limite un problème spectral bidimensionnel, qui nous permet de capter d'autres types de vibrations. On donneégalement une caractérisation de la forme asymptotique des fonctions propres qui sontà l'origine de ces vibrations.
Asymptotic estimates for localized electromagnetic modes in doubly periodic structures with defects
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2007
The paper presents analytical and numerical models describing localized electromagnetic defect modes in a doubly periodic structure involving closely located inclusions of elliptical and circular shapes. Two types of localized modes are considered: (i) an axi-symmetric mode for the case of transverse electric polarization with an array of metallic inclusions; (ii) a dipole type localized mode that occurs in problems of waveguide modes confined in a defect region of an array of cylindrical fibres, and propagating perpendicular to the plane of the array. A thin bridge asymptotic analysis is used for case (i) to establish double-sided bounds for the frequencies of localized modes in macro-cells with thin bridges. For the case (ii), the electric and magnetic fields independently satisfy Helmholtz equations, but are coupled through the boundary conditions. We show that the model problem associated with localized vibration modes is the Dirichlet problem for the Helmholtz operator. We characterize defect modes by introducing a parameter called the 'effective diameter'. We show that for circular inclusions in silica matrix, the effective diameter is accurately represented by a linear function of the inclusion radius.