A fast direct solver for scattering problems involving elongated structures

A fast solver is presented for the solution of scattering problems in which the scatterer is a relatively thin, elongated object. The scheme presented here is a version of an algorithm previously published by the authors, and is based on the observation that under certain conditions and with certain modifications, the scheme will retain its O(n) CPU time estimate independently of the size of the scatterer in wavelengths. The performance of the scheme is illustrated with numerical examples.