Solution of arbitrarily dimensional matrix equation in computational electromagnetics by fast lifting wavelet-like transform

Abstract

A new wavelet matrix transform (WMT), operated by lifting wavelet-like transform (LWLT), is applied to the solution of matrix equations in computational electromagnetics. The method can speedup the WMT without allocating auxiliary memory for transform matrices and can be implemented with the absence of the fast Fourier transform. Furthermore, to handle the matrix equation of arbitrarily dimension, a new in-space preprocessing technique based on LWLT is constructed to eliminate the limitation in matrix dimension. Complexity analysis and numerical simulation show the superiority of the proposed algorithm in saving CPU time. Numerical simulations for scattering analysis of differently shaped objects are considered to validate the effectiveness of the proposed method. In particular, due to its generality, the proposed preprocessing technique can be extended to other engineering areas and therefore can pave a broad way for the application of the WMT. © 2009 John Wiley & Sons, Ltd.