As noted in the previous chapter, standard method of moments (MoM) implementations quickly reach the limits of computer time and memory resources. Even though better geometry modeling methods can enable solutions of the same problem using less computer resources, fast and low-memory solution methods must be employed in connection with iterative solvers to tackle electrically large real-life problems. In this chapter, we outline the FMM and its multilevel version. We will particularly focus on curvilinear elements and conformal basis functions.

Chapter Contents:

• 7.1 Fast Multipole Method
• 7.2 Multilevel Fast Multipole Method
• 7.3 MLFMM Formulation
• 7.4 Radiation and Scattering Examples
• 7.5 MLFMM for Volume Integral Equations
• Bibliography

Inspec keywords: iterative methods; computational electromagnetics; electromagnetic field theory; method of moments

Other keywords: method of moments; FMM; MoM; geometry modeling method; iterative solver; fast multipole method; curvilinear element; conformal basis function

Subjects: Numerical approximation and analysis; Electric and magnetic fields; Interpolation and function approximation (numerical analysis); Electromagnetic waves: theory