An <i>N</i>² algorithm for the multiple scattering solution of <i>N</i> scatterers

Abstract

Abstract The scattering solution from N scatterers, each of whose scattered field is approximated by M harmonics is an NM unknown problem. A straightforward solution to this problem can be obtained by casting it into an NM linear algebraic equation. The solution of the linear algebraic equation will involve order N 3 M 3 flouting point operations. However, via the use of a recursive algorithm and the translation formula, an order N 2 M 3 algorithm to solve such a problem is possible.