A domain decomposition preconditioner for time-harmonic electromagnetics

In this article we introduce a new domain decomposition (DD) based iterative method for the solution of the time-harmonic vector wave equation. The method derives its efficiency by decomposing large problems into several smaller, more manageable pieces. It differs from previous non-overlapping DD methods in two significant respects: (1) it does not introduce any auxiliary variables, and (2) the method is applied to a decomposition of the computational mesh. After briefly summarizing the formulation of the method we provide numerical results which verify the accuracy of the method. We then examine its convergence behavior with respect to varying mesh size, partition number, problem size, and frequency. Finally, we apply the method to two challenging problems.