Determination of the Green functions for systems with large asymmetric matrices by the moments method

摘要

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