A fast multiresolution moment method algorithm using wavelet concepts

It is well known that the application of the conventional moment method to boundary integral equations results in a dense matrix equation that is very time-consuming to solve. To speed up the moment method calculation, a number of fast algorithms have been developed. There is also interest in applying wavelet concepts to solve integral equations arising in electromagnetics. However, direct application of wavelet basis to sparsify the moment matrix still results in the same order of computational complexity. The reason is that the electromagnetic Green´s function is an oscillatory kernel. We present a method of reducing the computational complexity using a different wavelet concept. The idea is to take advantage of the multiscale nature of the k-space Green´s function. In the far field it has small-scale features around k/sub 0/ and in the near field it has large-scale features over all k.