Author: Cao, Qunsheng
Title: Development of multiresolution time domain method for electromagnetic communication applications
Degree: Ph.D.
Year: 2001
Subject: Electromagnetism
Hong Kong Polytechnic University -- Dissertations
Department: Department of Electronic and Information Engineering
Pages: xvii, 258 leaves : ill. ; 30 cm
Language: English
Abstract: In order to accurately solve electromagnetic problems in engineering, with the aid of modern computer technologies and techniques, various computational methods are developed in predicting characteristics of electromagnetic fields. The finite difference time domain (FDTD) technique, introduced by K. S. Yee in 1966, is one of the most widely using methods. The FDTD method has been shown to be relatively straightforward to implement; it easily accommodates complex geometries and different materials; it efficiently handles wide-bandwidth waveforms; and it can be applied nonlinear devices. A diversity of modifications and extensions of the FDTD have been developed, such as hybrid FDTD technique and high-order FDTD scheme, which are used to solve electromagnetic problems in a more efficient and accurate way. In spite of its simplicity and versatility, the FDTD technique suffers from serious limitations because of its substantial computer resource it requires to model electromagnetic problems with large computational volumes. This is due to inability of the existing technique to calculate large-scale models with sufficiently fine resolution. The FDTD method requires a relatively high node density, usually 10-20 cells per minimum wavelength, to achieve reasonably good accuracy. Although evolving computer technology has enabled applications of the original FDTD technique to large problems, it remains a key goal to increase the computational efficiency of the method in a manner that retains its many desirable features. In 1996, Krumpholz and Katehi first introduced the multiresolution time domain (MRTD) scheme, which is based on the multiresolution analysis. The application of multiresolution analysis in the method of moments (MoM) for discretization of Maxwell's equations led to the generation of the MRTD scheme. In the scheme the electromagnetic fields are expanded using the scaling and wavelet functions with respect to space and the pulse functions with respect to time. The MRTD scheme has great potential and is very promising in reducing the grid density close to the Nyquist sampling rate. The MRTD scheme has been successfully applied for the analysis of fundamental microwave structures. It has been reported that the MRTD can significantly save computer resource for both computational CPU time and memory capacity. This research work aims at developing a systematic multiresolution time domain (MRTD) scheme from prospective views of both theories and practical applications. A generalized MRTD scheme, on the basis of the cubic spline Battle-Lemarie scaling and high-level resolution wavelet functions has been developed. The MRTD scheme has been applied in conjunction with an adjustable multiple image technique (MIT) for the truncation of a boundary with a perfect electric conductor (PEC) or perfectly magnetic conductor, and an anisotropic perfectly matched layer (APML) for the truncation an open space, including face, edge, and corner APML boundaries. The MRTD formulations retain the content of the leapfrog algorithm as that applied in the conventional FDTD method. Meanwhile, the MRTD scheme, as a generalized Maxwell's solver, has been successfully applied to the analysis of a number of practical electromagnetic applications, such as electromagnetic wave propagation in layered spaces, monolithic millimetre-wave integrated circuits (MMICs), and scattering radar cross sections (RCSs) for different targets. This research has been extensively validated for a variety of applications through comparisons with the available results published in literature. This research showed that the MRTD scheme is a full wave tool with great potential in solving complicated electromagnetic problems in efficient way, due to its flexibility in modelling complex-shaped geometry, broadband computation with leapfrog time-stepping algorithm; and low sampling rate fitting for large objects. It is can conclude that the MRTD techniques represent a significant generalization of the original FDTD method. It has been shown the MRTD scheme has great advantages over the conventional Yee's FDTD method with respect to computer memory requirements and CPU time for a large amount of practical applications. Undoubtedly, the MRTD will be further investigated and explored and it will be found to have more applications in near future.
Rights: All rights reserved
Access: open access

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