Approximate inverse preconditioner for near resonant scattering problems

To solve the method of moments (MoM) matrix calculation, iterative methods are becoming popular as a solution technique for such problems. These methods require one or two matrix-vector multiplications per iteration. To speed up the matrix-vector multiplications in the iterative solvers, the fast multipole method (FMM) and its multilevel extension, multilevel fast multipole algorithm (MLFMA) are developed to obtain fast solution for scattering problems. But they are more advantageous if the number of iterations for convergence is much smaller than the number of unknowns. However, for strongly resonant problems and/or strong multiple reflection problems, these methods require a very large number of iterations for convergence. In this paper, to account for these near interactions, the approximate inverse of the block banded coefficient matrix is introduced as a preconditioner. By means of the matrix partitioning method, the computing time required to set up this preconditioner is O(N), which is indispensable for applying to O(Nlog N) fast algorithms.