A Hybrid Finite Element and Integral Equation Domain Decomposition Method for the Solution of the 3-D Scattering Problem

A domain decomposition method (DDM) is presented for the solution of the time-harmonic electromagnetic scattering problem by inhomogeneous 3-D objects. The computational domain is partitioned into concentric subdomains on the interfaces of which Robin-type transmission conditions are prescribed. On the outer boundary terminating the computational domain, the radiation condition is accounted for by employing an integral equation (IE) formulation. The DDM decouples the interior problems, that correspond to the solution of Maxwellʹs equations inside each subdomain and are formulated by using a finite element method, from the exterior problem solved by employing the IE. It has been shown that the solutions of this DDM algorithm converge to those of the original problem. A particular IE is used that allows the implementation of a very simple and fully iterative solver. The main advantage offered by this technique is a reduction in memory requirements. Various numerical examples are presented that illustrate its potential.