A nonconforming domain decomposition method with a high order basis for the time-harmonic Maxwell equation

We propose a mathematically equivalent formulation but computationally more efficient than the one used in Vouvakis et al. (2004). It is formulated in a way that the traditional programs for the curl-conforming finite element method can be used without further modification. The field continuity between the mismatching meshes on the interfaces is imposed through a supplementary equation derived front the Robin boundary condition. To achieve high-order accuracy and subdue the numerical dispersion, we employ a high-order curl-conforming vector basis. We study the effects of mismatching meshes and the orders of basis vectors on the solution accuracy and iteration counts, and examine how the sequences of solving subdomain problems affect the iteration counts, and formulate when the elimination of interior unknowns leading to a smaller dense matrix is advantageous.