An efficient wavelet preconditioner for iterative solution of three-dimensional electromagnetic integral equations

A wavelet-based preconditioning method is proposed to facilitate the iterative solution of three-dimensional (3-D) electromagnetic integral equations. The preconditioner is derived from the wavelet transform of the moment matrix. It is based on the observation that both the moment matrix and its inverse exhibit a sparse, multilevel finger structure. A method based on the Forbenius-norm minimization is used to solve the inverse of the matrix under the multilevel finger structure. Numerical results on a 3-D cavity show that the iteration numbers are significantly reduced with the wavelet-preconditioned system. The computational cost of the preconditioner is kept under O(NlogN).