A sparse approximate inverse preconditioner for the method of moments accelerated with the multilevel fast multipole method

When solving the electric or combined field integral equation (EFIE or CFIE) using the multilevel fast multipole method (MLFMM), an iterative solver has to be used for the solution of the resulting very large system of linear equations, because the MLFMM provides a matrix-vector product only. It is essential to combine the iterative method with a suitable preconditioner to accelerate the convergence or enable convergence at all. Since the MLFMM has an asymptotic complexity of O(N·log(N)) if implemented carefully, it is necessary that the construction and application of the preconditioner is at most of this complexity. We resent a sparse approximate inverse preconditioner (SPAI) adjusted to the MLFMM with complexity O(N) and a factor which is smaller than the one for the standard approach.