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Impedance matrix compression with the use of wavelet expansions
Author(s) -
Baharav Z.,
Leviatan Y.
Publication year - 1996
Publication title -
microwave and optical technology letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.304
H-Index - 76
eISSN - 1098-2760
pISSN - 0895-2477
DOI - 10.1002/(sici)1098-2760(19960805)12:5<268::aid-mop7>3.0.co;2-8
Subject(s) - impedance parameters , wavelet , matrix (chemical analysis) , basis function , thresholding , mathematics , mathematical analysis , basis (linear algebra) , wavelet transform , sparse matrix , electrical impedance , scattering , integral equation , algorithm , computer science , physics , geometry , optics , engineering , materials science , artificial intelligence , electrical engineering , quantum mechanics , composite material , gaussian , image (mathematics)
Wavelet expansions have been used recently in numerical solutions of integral equations encountered in various electromagnetic scattering problems. In these solutions one utilizes the power of the wavelet basis functions to localize the problem impedance matrix. Thus, after the impedance matrix has been computed, it can be rendered sparse via a thresholding procedure, and the resultant matrix equation can be solved in more quickly without any significant loss in accuracy. In this article we propose a novel approach, where instead of thresholding the impedance matrix in a conventional manner, it is compressed to a reduced‐size form. This is effected by first singling out a small number of basis functions, which are expected to accurately represent the unknown, and keeping only the matrix elements needed for finding the coefficients of these basis functions. A method to carry out this matrix compression automatically is described. Numerical examples are given for the case of TM scattering by perfectly conducting cylinders of triangular and square cross sections. The advantages of the proposed approach are shown. © 1996 John Wiley & Sons, Inc.