Chapter 3Iterative Solutions of Electromagnetics Problems with MLFMA
This chapter is devoted to iterative solutions of electromagnetics problems with MLFMA. Starting from the factorization and diagonalization, MLFMA is discussed in detail. Local interpolations and anterpolations are particularly focused for accurate and efficient implementations. Iterative solutions of metallic and dielectric objects are investigated and compared for different formulations and iterative algorithms. Finally, low-frequency MLFMA (LF-MLFMA) implementations based on multipoles are presented for rigorous analysis of small objects discretized with large numbers of unknowns.
3.1 Factorization and Diagonalization of the Green's Function
FMM and its multilevel version MLFMA are derived from the factorization and diagonalization of the Green's function. As detailed in this section, the factorization of the Green's function is based on the addition theorem.
3.1.1 Addition Theorem
Consider the decomposition of an arbitrary three-dimensional vector 
into three vectors as
where
and . The addition ...
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