We report new developments in the analytical evaluation of the near-field contribution to the matrix elements of the electric and magnetic field operators for planar conducting structures embedded in a layered medium. The method is applicable to Rao-Wilton-Glisson (RWG) basis functions supported on parallel interfaces in the medium. Our method is an extension of the approach described in [1] of representing a Green function as a two-dimensional Laplacian of an auxiliary function. Such Laplacian representations can be obtained for the asymptotic forms of the Green functions, which are being subtracted in order to regularize the behavior of the Sommerfeld-type integrals. Matrix elements resulting from these asymptotic forms, given originally as quadruple surface integrals with singular integrands, are then reduced to double contour integrals over the perimeters of the surface elements, involving simple closed-form non-singular auxiliary functions.
New Simplified Analytic Expressions for the Matrix Elements of the Asymptotic Part of the Layered Medium Green Function in the Mixed Potential Formulation / Bleszynski, E.; Bleszynski, M.; Jaroszewicz, T.; Johnson, W.; Rivero, J.; Vipiana, F.; Wilton, D.. - ELETTRONICO. - (2021). (Intervento presentato al convegno 22nd International Conference on Electromagnetics in Advanced Applications, ICEAA 2021 tenutosi a Honolulu, HI, USA nel 09-13 August 2021) [10.1109/ICEAA52647.2021.9539713].
New Simplified Analytic Expressions for the Matrix Elements of the Asymptotic Part of the Layered Medium Green Function in the Mixed Potential Formulation
Vipiana F.;
2021
Abstract
We report new developments in the analytical evaluation of the near-field contribution to the matrix elements of the electric and magnetic field operators for planar conducting structures embedded in a layered medium. The method is applicable to Rao-Wilton-Glisson (RWG) basis functions supported on parallel interfaces in the medium. Our method is an extension of the approach described in [1] of representing a Green function as a two-dimensional Laplacian of an auxiliary function. Such Laplacian representations can be obtained for the asymptotic forms of the Green functions, which are being subtracted in order to regularize the behavior of the Sommerfeld-type integrals. Matrix elements resulting from these asymptotic forms, given originally as quadruple surface integrals with singular integrands, are then reduced to double contour integrals over the perimeters of the surface elements, involving simple closed-form non-singular auxiliary functions.File | Dimensione | Formato | |
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New_Simplified_Analytic_Expressions_for_the_Matrix_Elements_of_the_Asymptotic_Part_of_the_Layered_Medium_Green_Function_in_the_Mixed_Potential_Formulation.pdf
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https://hdl.handle.net/11583/2982125