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A singular integral equation approach to electromagnetic fields for circular boundaries with slots

A singular integral equation approach to electromagnetic fields for circular boundaries with slots SummaryIt is shown that for the case of a single cylinder which has any number of axial slots of arbitrary width and infinite length, or for the case of coaxial cylinders where one of the cylindrical boundaries has such slots, the Dirichlet and Neumann problems for the Helmholtz equation (which correspond respectively to E and H waves) can be reduced to that of solving a singular integral equation. It is also shown that the resulting singular integral equation is formally the same for both the Dirichlet and Neumann problems for various kinds of circular boundaries. The exact solution of the integral equation is given and applied to the Dirichlet and Neumann problems. The following three simple cases: (1) a single narrow slot in a cylinder; (2) a single narrow slot in a coaxial cylinder; and (3) narrow circular strips are considered to illustrate the applicability of the method. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Scientific Research, Section B Springer Journals

A singular integral equation approach to electromagnetic fields for circular boundaries with slots

Hayashi, Yoshio
Applied Scientific Research, Section B , Volume 12 (5-6) – Oct 1, 1965
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29 pages

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Publisher
Springer Journals
Copyright
Copyright © Martinus Nijhoff 1965
ISSN
0365-7140
DOI
10.1007/bf02933508
Publisher site
See Article on Publisher Site

Abstract

SummaryIt is shown that for the case of a single cylinder which has any number of axial slots of arbitrary width and infinite length, or for the case of coaxial cylinders where one of the cylindrical boundaries has such slots, the Dirichlet and Neumann problems for the Helmholtz equation (which correspond respectively to E and H waves) can be reduced to that of solving a singular integral equation. It is also shown that the resulting singular integral equation is formally the same for both the Dirichlet and Neumann problems for various kinds of circular boundaries. The exact solution of the integral equation is given and applied to the Dirichlet and Neumann problems. The following three simple cases: (1) a single narrow slot in a cylinder; (2) a single narrow slot in a coaxial cylinder; and (3) narrow circular strips are considered to illustrate the applicability of the method.

Journal

Applied Scientific Research, Section B – Springer Journals

Published: Oct 1, 1965

Keywords: Electromagnetic Field; Circular Cylinder; Singular Integral Equation; Neumann Problem; Helmholtz Equation

References