Development and Application of a Fast Multipole Method in a Hybrid FEM/MoM Field Solver

Abstract

Hybrid FEM/MoM methods combine the finite element method (FEM) and the method of moments (MoM) to model inhomogeneous unbounded problems. These two methods are coupled by enforcing the continuity of tangential fields on the boundary that separates the FEM and MoM regions. When modeling complex geometries with many elements on the boundary, the MoM part of the problem is the bottleneck of the hybrid method since it requires O(N^2) memory and O(N^3) computation time. This paper presents a hybrid FEM/MoM formulation applying the fast multipole method (FMM) that greatly reduces the memory requirement associated with MoM part. Two practical electromagnetic problems are presented to validate this method.