Wavelet packets for fast solution of electromagnetic integral equations

This paper considers the problem of wavelet sparsification of matrices arising in the numerical solution of electromagnetic integral equations by the method of moments. Scattering of plane waves from two-dimensional (2-D) cylinders is computed numerically using a constant number of test functions per wavelength. Discrete wavelet packet (DWP) similarity transformations and thresholding are applied to system matrices to obtain sparsity. If thresholds are selected to keep the relative residual error constant the matrix sparsity is of order O(N^P) with p<2. This stands in contrast with O(N² ) sparsities obtained with standard wavelet transformations. Numerical tests also show that the DWP method yields faster matrix-vector multiplication than some fast multipole algorithms