Finite element/dipole moment method for efficient solution of multiscale electromagnetic problems

In this paper, we introduce a novel method, which we call Finite Element / Dipole Moment Method (FEDM), with two alternative (iterative and self-consistent) implementations, for handling the multiscale problem mentioned above. In this method, the conventional FEM is modified through the use of dipole moments in such a way that the region around the thin/small object is extracted and the object is represented by a number of unmeshed overlapping spheres whose centers contain dipole(s) characterized by their dipole moments. In this way, the local mesh refinement along the object is not needed since the volume mesh around the object is eliminated. The coupling of the object with the remaining part of the computational domain is achieved by using the fields radiated by the dipoles whose dipole moments are unknowns that are yet to be determined. Similar to the conventional Method of Moments (MoM), the unknown dipole moments are obtained by solving the matrix system constructed by appropriately imposing the boundary conditions for conducting objects or by matching polarization currents for dielectric objects. The FEDM can be implemented either in an iterative or self-consistent (namely, non-iterative) manner, both of which are described below. The proposed method is especially useful for modeling of wire antennas located in the vicinity of inhomogeneous structures, as well as for simulating interconnect structures in integrated circuits, which typically have fine features. We present the results of some numerical experiments to demonstrate the performance of the method in 3D electromagnetic scattering problems.