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Super‐hyper singularity treatment for solving 3D electric field integral equations
Author(s) -
Tong Mei Song,
Chew Weng Cho
Publication year - 2007
Publication title -
microwave and optical technology letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.304
H-Index - 76
eISSN - 1098-2760
pISSN - 0895-2477
DOI - 10.1002/mop.22443
Subject(s) - electric field integral equation , singularity , mathematics , mathematical analysis , singular integral , integral equation , method of moments (probability theory) , kernel (algebra) , boundary element method , matrix (chemical analysis) , principal value , physics , finite element method , pure mathematics , statistics , materials science , estimator , composite material , thermodynamics
The super‐hyper singularity treatment is developed for solving three‐dimensional (3D) electric field integral equations (EFIE). EFIE usually takes two forms: one of which includes a super‐hyper singular kernel generated by the double gradient of the Green's function. So far, there is no way to evaluate these super‐hyper singular integrals needed for constructing the pertinent matrix equation. We apply the series expansion of the Green's function to the super‐hyper singular kernel and derive closed‐form expressions for their evaluations in the Cauchy principal‐value sense. The derivation is based on the constant current approximation over a flat triangle patch, but it can be extended easily to higher‐order approximations of the current. The scheme can be used to accurately calculate the near and self interaction terms in the impedance matrix for the method of moments (MoM), Nyström method or boundary element method (BEM). © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1383–1388, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI.10.1002/mop.22443