Chapter 4 - Multipole Methods

Abstract

The room impulse response is a quantity that characterizes the reverberant structure of a room. A method to approximate this quantity was proposed by Allen and Berkley, by using the image method. This method has been used by many authors to compute the impulse response. By using multipole methods, this computation can be performed much faster. This chapter presents several problems to illustrate how multipole reexpansion/translation theory can be applied to obtain their solution. It describes the speeding up of summation of sources with the aid of multipole expansions and solution of boundary value problems for spherical scatterers. It also introduces the T-matrix method, which can be used for computation of fields in multiple scattering problems with arbitrary scatterers. Comparisons of the multipole methods for these cases with other methods based on direct summation or boundary discretization show efficiency of the multipole methods. However, the use of the direct multipole methods for problems where the number of scatterers is large requires development of faster algorithms.