Wavelet-like basis functions for efficient waveguide mode computation

The authors demonstrate the use of the wavelet-like basis functions of B. Alpert et al. to reduce the MoM (method of moments) impedance matrix Z for a hollow cylindrical waveguide from N/sup 2/ nonzero elements in the pulse basis to /spl alpha/N/sup 2/ nonzero elements in the wavelet-like basis, where /spl alpha/ /spl ap/ 0.2 for the example considered. The reduction in the expense of computing the determinant of the MoM matrix Z comes about because many of the wavelet-like basis functions are subdomain functions with only high spatial frequencies. These high spatial frequency sources do not radiate well and hence do not interact with one another. Thus, the impedance matrix Z has many zero elements when represented in such a basis. This allows the use of sparse matrix methods for efficient calculation of the determinant. The new sparse matrix can be factored and its determinant computed much more rapidly than the original full matrix. For the example considered, the speedup factor is about 10.<>