Computational Electromagnetics Research Laboratory
A Time-Domain Haar-Wavelet-Based Multiresolution Technique for Electromagnetic Field Analysis
Masafumi Fujii, University of Victoria, June 1999.
In this thesis, we propose a time-domain electromagnetic field modeling technique based onHaar wavelets. The multiresolution nature of the wavelets was used in the formulation, and a time stepping algorithm that is similar to the conventional finite-difference time-domain (FDTD) method was obtained. The proposed technique effectively models realistic structures by virtue of the multiresolution property; the number of floating point operations is reduced approximately by half compared to the conventional FDTD method.
In order to provide a comprehensive understanding of the proposed method,algorithms for one, two and three space dimensions were formulated, validated in terms of the accuracy, and actually applied to various realistic problems. Various boundary conditions have been formulated and implemented, and in addition, the following applications are addressed: S-parameter extraction for two-dimensional waveguide problems, combined with field singularity correction at metal edges and corners, resonant cavity analyses for validation purposes, and analyses of microwave passive devices with open boundaries such as microstrip low-pass filters and spiral inductors.
An algorithm that needs half the computational effort is equivalent to hardware that is twiceas fast. The purpose of this thesis is to make a contribution to the improvement of computational speed in electromagnetic time domain solutions.
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