Some composite boundary value problems in electromagnetics and their applications
Liu, Qinghuo
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Permalink
https://hdl.handle.net/2142/20152
Description
Title
Some composite boundary value problems in electromagnetics and their applications
Author(s)
Liu, Qinghuo
Issue Date
1989
Doctoral Committee Chair(s)
Chew, Weng Cho
Department of Study
Electrical and Computer Engineering
Discipline
Electrical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Geophysics
Engineering, Electronics and Electrical
Language
eng
Abstract
In this thesis, some composite boundary value problems of stratified media with various types of discontinuities are discussed. These problems fall into three categories: (i) a disk on top of a stratified medium; (ii) a general multiregion vertically stratified medium; and (iii) a slantingly stratified half-space with junction discontinuity.
The resonant frequency problem of a rectangular microstrip patch on top of a stratified medium is solved in this thesis by the vector Fourier transforms with Galerkin's method in the spectral domain, where the Green's function is diagonal. Sinusoidal functions are used as basis functions. The results are compared with those for the perturbation approach and experiments. Furthermore, a curve-fitting formula based on the data obtained via Galerkin's method is developed to reproduce the resonant frequencies rapidly. A curve-fitting formula for the resonant frequencies of circular microstrip antennas is also developed based on the earlier work.
The radiation of a source in the presence of an N-region, vertically stratified medium is solved in this thesis using the numerical mode matching method, which reduces the two-dimensional problem to many one-dimensional problems which are solved by the one-dimensional finite element method, which saves computer storage and computation time as compared to the two-dimensional finite element method. Some typical numerical results are obtained for the illustration of the method. This theory is applied to study the high frequency dielectric logging tool in a complicated borehole environment.
The radiation of a source in the presence of a slantingly stratified half-space is studied in this thesis using the surface integral equation method. An extended extinction theorem for the slantingly stratified half-space problem is derived. The Green's functions for a stratified medium are found by a semianalytical method. Using the surface integral equations, the rather complicated two-dimensional problem can be solved by the one-dimensional finite element method. For some special cases, the results obtained by this method are compared with those obtained by the numerical mode matching method and the Fourier integral technique.
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