Efficient representation of electromagnetic integral equations using pre-defined wavelet packet basis

Abstract

We proposed a pre-defined wavelet packet (PWP) basis that can be used for the efficient representation of electrodynamic moment equations. The PWP basis is designed from the wavelet packet decomposition tree that zooms in along the oscillatory frequency k/sub 0/ of the kernel function in the integral equation. This is in contrast to the zero frequency zoom-in used in the conventional wavelet transform. In comparison with the adaptive wavelet packet transform (AWPT) we reported on previously, the PWP basis can be designed without resorting to any adaptive search procedure that is both scatterer dependent and computationally costly. The resulting non-zero elements grow as O(N/sup 1.3/), or O(NlogN) for large-scale problems, in the PWP-transformed moment matrix. Thus the complexity of solving the moment equations in the transform domain is significantly reduced when combined with an iterative solver. Furthermore, with this pre-defined basis, it is possible to form the sparse transformed matrix directly, without resorting to first generating the original moment matrix using conventional subsectional basis. By thresholding the transformed matrix element-by-element on the fly, the N/sup 2/ memory bottleneck associated with the AWPT algorithm can thus be eliminated.