DETERMINATION OF THE GREEN-FUNCTIONS FOR SYSTEMS WITH LARGE ASYMMETRIC MATRICES BY THE MOMENTS METHOD

In this paper we develop applications of the spectral moments method t o the study of the propagation of sound waves and electromagnetic wave s in heterogeneous systems with or without energy dissipation. In thes e systems the matrices are often asymmetric. We show that the moments method can be very useful for determining the Green functions of such systems. For a matrix with real eigenvalues the method requires only t he introduction of a 1D auxiliary density function while for a matrix with complex eigenvalues it needs the introduction of a 2D density fun ction. These functions can be calculated by the moments technique and lead to computation of the Green functions. For systems involving slig htly asymmetric matrices, we found that the method is particularly sta ble while, for strongly asymmetric matrices, it is better to calculate directly a response function which is a bilinear combination of Green functions.