On O(n) algebraic preconditioners for the fast multipole method

In this paper we present the framework of preconditioners based on sparsification strategies for solving electromagnetic scattering problems expressed in an integral formulation. We review some recent results with sparse approximate inverse and multilevel techniques combined with the fast multipole method for large-scale surface integral equations. When computed from the near-part of the coefficient matrix, both classes of methods can maintain the algorithmic complexity of the matrix-vector product operation.