Nowadays, electrically large complex electromagnetic problems exist in modern defence and communication industry. Accurate and efficient calculation for such electromagnetic radiation and scattering is a high computational complex task and a challenge to conventional electromagnetic solvers such as Method of Moment (MOM) where high memory and long computational time are required owing to its large size compared to operating wavelength. This paper presents the fast solution method with wavelet transform in the computation of scattering from large scale complex objects. Because of the vanishing moments, the moment matrices arising in these problems are sparsified by wavelet, and consequently, the induced current and equivalent magnetic current can be obtained quickly. Moreover, a precondition method is postulated and implemented in the fast solution of the transformed moment matrix equation with iteration methods.
2. Steinberg, B. Z. and Y. Leviatan, "On the use of wavelet expansions in the method of moments," IEEE Trans. Antennas Propagat., Vol. 41, 610-619, 1993.
3. Wei, X. C., "Application of wavelet analysis to computational electromagnetics,", Ph.D. thesis, Xi’an, P.R.C., 2001.
4. Wagner, R. L. and W. C. Chew, "A study of wavelets for the solution of electromagnetic integral equations," IEEE Trans. Antennas Propagat., Vol. 43, 802-810, 1995.
5. Golik, W. L., "Wavelet packets for fast solution of electromagnetic integral equations," IEEE Trans. Antennas Propagat., Vol. 46, 618-624, 1998.
6. Chui, C. K., An Introduction to Wavelets, San Diego, Academic Press, USA, 1992.
7. Daubechies, I., Ten Lectures on Wavelets, SIAM Publ., Philadelphia, 1992.
8. Wei, X. C. and C. H. Liang, "A comparison between the applications of orthonormal wavelet and dualorthonormal wavelet for the wavelet moment methods," Journal of Microwave (Chinese), Vol. 16, 384-388, 2000.
9. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surface of arbitrary shape," IEEE Trans. Antennas Propagat., Vol. 30, 409-418, 1982.
10. Wang, T. M. and H. Ling, "Electromagnetic scattering from three-dimension cavities via a connection scheme," IEEE Trans. Antennas Propagat., Vol. 39, 1505-1513, 1991.
11. Peterson, A. F., C. F. Smith, and R. Mittra, "Eigenvalues of the moment-method matrix and their effect on the convergence of the conjugate gradient algorithm," IEEE Trans. Antennas Propagat., Vol. 36, 1177-1179, 1988.