On wavelet transforms for the effective solution of electromagnetic integral equations

• Main Author: Xiang, Zhong Gui
• Other Authors: Lu, Yilong
• Format: Theses and Dissertations
• Language: English
• Published: 2009
• Subjects: DRNTU::Engineering::Electrical and electronic engineering::Control and instrumentation
• Online Access: http://hdl.handle.net/10356/19590
• Institution: Nanyang Technological University

In the study, an effective wavelet matrix transform method for effective solutions of electromagnetic (EM) problems is developed. In order to overcome the so-called "edge effect" in wavelet expansion methods, a wrapped-around (circulant) wavelet expansion method is proposed. Based on the proposed wrapped-around recipe, a fast iterative algorithm to construct various circulant orthonormal or non-orthonormal wavelet basis matrices is developed. Applying the circulant wavelet matrix transform one can obtain highly sparse moment matrices which can be solved efficiently in only O(NlogN) or even O(N) operations. This is in contrast with a cost of O(N3) for a dense matrix inversion or O(N2) per dense matrix-vector multiplication in an iterative solution.