Premium
Well‐posedness of integral equations for modeling electromagnetic scattering from cavities
Author(s) -
Xu Yuan
Publication year - 2008
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/2007rs003758
Subject(s) - integral equation , scattering , mathematical analysis , aperture (computer memory) , singular integral , mathematics , computational electromagnetics , resonance (particle physics) , plane (geometry) , physics , electromagnetic field , optics , geometry , acoustics , quantum mechanics
Integral equations for modeling electromagnetic scattering from indented screens or cavity structures are proposed using a symmetric equivalent current model, which is based on image theory with a perfect electrically conducting (PEC) ground plane. The well posedness of the proposed integral equations is theoretically established in this paper. It is known that all resonance modes for cavity problems either due to the presence of a perfect magnetically conducting (PMC) open aperture or a PEC open aperture. In this paper, it is proved that both kinds of resonance modes cannot exist for the proposed integral equations without excitation. To numerically examine this well posedness, the condition numbers of resultant matrices from the generalized network formulation and proposed integral equations are analyzed as functions of frequency and the depth of cavity. The numerical analysis of the condition numbers obtained also shows that the integral equations proposed in this paper are immune to the problem of the interior resonance for three‐dimensional cavity problems. Moreover, simulation of scattering from standard cavity structures verifies the validity of the proposed integral equations.