Chapter 3 - The Multiple Multipole Program (MMP) and the Generalized Multipole Technique (GMT)

Abstract

The Multiple Multipole Program (MMP) was developed in the late 1970s and early 1980s starting from the Point Matching (PM) technique in conjunction with the Circular Harmonic Analysis (CHA). To obtain efficient and reliable codes, the numerical problems of both the CHA and the PM had to be removed. This goal was achieved by a careful analysis and a generalization of both methods. The resulting code was called Multiple Multipole Program (MMP) and the corresponding method was called Multiple Multipole (MMP) method. In 1989, the SPEX code was presented, which was very similar to the 3D MMP code for EM scattering. Moreover, it was recognized that several groups were working on techniques that could be considered as special cases of the MMP method. Therefore, Generalized Multipole Technique (GMT) was proposed as a new generic name. This chapter begins by discussing the expansion from CHA to MMP. All of the MMP expansions are analytic solutions of the Maxwell equations. These equations are linear and only linear material properties are admitted in the MMP code. Therefore, any linear combination of MMP expansions is again an analytic solution of the Maxwell equations. The chapter further discusses special MMP features such as weighting, fictitious boundaries, periodic problems, eigenvalue computation, and ill-conditioned matrix methods.