In an electrostatic field, all charge distributions and currents may be represented by a multipolar expansion using only electric and magnetic
multipoles. Instead, in a multipolar expansion of an electrodynamic field new terms appear.
Then, the low-frequency multilevel fast
multipole algorithm (LF-MLFMA) [30,31] is employed to produce an H-matrix representation of the A-EFIE system matrix.
Several numerical examples are given to show the priority of the proposed method compared to the conventional multilevel fast
multipole algorithm (MLFMA) [13] for periodic structures.
The first term in (23) can be considered as the quantized rotation energy of the drop; the second one is the quantized electrostatic energy due to the
multipole moments of the charged drop.
Advanced Classical Electrodynamics: Green Functions, Regularizations,
Multipole Decompositions
Meanwhile, many researchers [27-30] have adopted the fast
multipole method (FMM) (Rokhlin [31]) in their BEM because of FMM's ability to reduce memory requirement and calculation scale.
Moreover, structured low-rank approximations for integral transforms with smooth kernels have been developed as fast
multipole methods [15, 25, 28] and hierarchical matrices [3, 4, 14, 16, 17].