An effective wavelet matrix transform approach for efficient solutions of electromagnetic integral equations

Abstract

An effective numerical method based on wavelet matrix transforms for efficient solution of electromagnetic (EM) integral equations is proposed. Using the wavelet matrix transform produces highly sparse moment matrices which can be solved efficiently. A fast construction method for various orthonormal or nonorthonormal wavelet basis matrices is also given. It has been found that using nonsimilarity wavelet matrix transforms such as nonsimilarity nonorthonormal cardinal spline wavelet (NSNCSW) transform, one can obtain a much higher compression rate and much better accuracy of the approximate solutions than using similarity wavelet transforms such as Daubechies' (1992) orthonormal wavelet (DOW) transform. Numerical examples are given to show the validity and effectiveness of the method.