Chapter 2 - Review of the Generalized Multipole Technique Literature

Abstract

The Generalized Multipole Technique (GMT) is a new and fast advancing method, developed by different research groups. In Mie theory and in the T-matrix method, the fields inside and outside a scatterer are expanded by a set of spherical multipoles having their origin at the centre of the sphere. With the GMT method, many origins are applied for multipole expansion. The coefficients of these expansions are the unknown values to be determined by applying the boundary conditions on the particle surface. The coefficients may be found by point matching, that is, fulfilling the boundary conditions at a discrete number of surface points, or fulfilling the boundary conditions in a least squares sense, or by a surface integral similar to the extended boundary condition method. Other “equivalent sources” for field expansion may be of any type, as long as they are solutions of the wave equation. Spherical waves, dipoles, and Gabor functions have been applied as expansion functions. Therefore, other names for similar concepts have been given like Multiple MultiPole Method (MMP), Discrete Sources Method (DSM), Method of Auxiliary Sources (MAS), and Fictitious Sources Method or Yasuura method. This chapter discusses the related methods that are Point Matching Method and the Extended Boundary Condition Method and reviews the different variants of the GMT methods.