Treatment of cement variables in the domain decomposition method for Maxwell’s equations

In this contribution we focus our attention on the cement variables of the DDM and consider their theoretical and practical treatment. We first determine the correct functional space of the continuous variables and then examine two possible representations in the VFEM. One choice is shown to provide superior solver convergence though its use results in sub-optimal error convergence. We then propose and validate a remedy to this problem by special treatment of non-planar interfaces. Finally, we demonstrate the scalability of the resulting method.