We introduce a new domain decomposition strategy for time harmonic Maxwell's
equations that is valid in the case of automatically generated subdomain
partitions with possible presence of cross-points. The convergence of the
algorithm is guaranteed and we present a complete analysis of the matrix form
of the method. The method involves transmission matrices responsible for
imposing coupling between subdomains. We discuss the choice of such matrices,
their construction and the impact of this choice on the convergence of the
domain decomposition algorithm. Numerical results and algorithms are provided