The null field method and modified Green functions

Abstract

Abstract A relation is established between the null field or T-matrix method and the method of modified Green functions for solving the Dirichlet and Neumann problems for the Helmholtz equation in an exterior domain. It is shown that elements of the T-matrix, formed by using appropriately chosen expansion functions, are precisely the coefficients of a representation of the Green function in terms of these same expansion functions. The linear independence of these functions is established together with the invertibility of a number of infinite dimensional matrices and their finite dimensional approximations, which is crucial to the T -matrix approach.