Scattering of time-harmonic electromagnetic waves by anisotropic inhomogeneous scatterers or impenetrable obstacles

We investigate an overlapping solution technique to compute the scattering of time-harmonic electromagnetic waves in two dimensions. The technique can be used to compute waves scattered by penetrable anisotropic inhomogeneous scatterers or impenetrable obstacles. The major focus is on implementing t he method using finite elements. We prove existence of a unique solution to the discretized problem and derive an optimal convergence rate for the sch eme, which is verified by numerical examples.