Impedance matrix compression with the use of wavelet expansions

✍ Scribed by Z. Baharav; Y. Leviatan

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 514 KB
• Volume: 12
• Category: Article
• ISSN: 0895-2477
• DOI: 10.1002/(sici)1098-2760(19960805)12:5<268::aid-mop7>3.0.co;2-8

✦ Synopsis

Wavelet expansions have been used recently in numerical solutions of integral equations encountered in various electromagnetic scatteringproblems. 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. Zn 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 tiangular and square cross sections. The advantages of the proposed approach are shown.