Multipole placement rules for the multiple multipole technique
The focus of this dissertation work is on the development of a unified set of rules and guidelines for placement of the multipole sources in the multiple multipole (MMP) technique. The placement scheme is applicable to solving electromagnetic scattering problems involving two-dimensional perfectly conductive or dielectric cylinders having flat or smoothly varying surfaces. Multipole order and placement is based on the localized radius of curvature, and the curvature rate of change, at prescribed matching points along the boundary interface of the scatterer. The number of boundary matching points used and their spacing interval is also dictated by the object's curvature. The rules and guidelines stem from the accumulated knowledge of some 10,000 computer simulations of various scatterer geometries, and a theoretical foundation based on classical multipole expansion methods. Conclusions are drawn using canonical geometries and other numerical techniques as benchmarks to test the rules and guidelines. Contributions are made by uniquely comparing analytic and MMP solutions, and by showing that a greater rate of curvature requires multipoles of higher order to match the boundary. Advantages to placement of higher order multipoles, each at their own expansion center, is demonstrated. This suggests that higher order multipoles are linked to the higher order derivatives of the curvature on a scatterer surface, which in turn draws on the connection between geometry and electromagnetic scattering.
Francis William Forest,
"Multipole placement rules for the multiple multipole technique"
(January 1, 1998).
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