Optimized Schwarz Methods for Maxwell Equations with Discontinuous Coefficients

We study non-overlapping Schwarz methods for solving time-harmonic Maxwell’s equations in heterogeneous media. We show that the classical Schwarz algorithm is always divergent when coefficient jumps are present along the interface. In the case of transverse magnetic or transverse electric two dimensional formulations, convergence can be achieved in specific configurations only. We then develop optimized Schwarz methods which can take coefficient jumps into account in their transmission conditions. These methods exhibit rapid convergence, and sometimes converge independently of the mesh parameter, even without overlap. We illustrate our analysis with numerical experiments.