New nonoverlapping domain decomposition methods for the harmonic Maxwell system

We study a non--overlapping domain decomposition method for the harmonic Maxwell equations with a new kind of interface condition. Using Fourier analysis we derive suitable families of transmission conditions in $\R^3$ that involve second order tangential differential operators and that guarantee convergence for both propagative and evanescent modes. Such families depend upon parameters that are chosen in order to optimize the convergence rate of the corresponding iterative algorithm. We then propose iterative solvers for the Maxwell equations based on a domain decomposition procedure where such conditions are enforced on the interface. Some numerical results for a two domain decomposition show the effectiveness of the optimized interface conditions.