A wavelet-packet based preconditioner for iterative solution of electromagnetic integral equations

It has been demonstrated that the pre-defined wavelet packet (PWP) basis is very efficient for representing the electromagnetic integral equation. We construct an effective preconditioner for moment equations from the PWP-transformed moment matrix. The preconditioning can be implemented in either the transform domain or the regular space domain. However, the computational complexity and memory requirement are at least on the order of O(N/sup 2/) to transform the moment equation from the space domain to the wavelet packet domain. Therefore, we devise a scheme to compute the PWP preconditioner directly from the PWP basis functions and implement the preconditioning operation in the space domain. Numerical results show that the PWP preconditioner is effective in accelerating the convergence rate of iterative solution for deep cavity structures. We also demonstrate that the total computational complexity and memory costs for the preconditioner can be kept to O(NlogN), making it compatible with fast matrix-vector multiplication algorithms such as the multi-level fast multiple method (MLFMM).