1. The proposed research is to conduct new and novel approaches for solving EM problems in deep-sub-micro chip designs faster and much more efficient than the current existing ones. The proposed approach tackles both frequency and time domain approaches: one will be a new/novel Discontinuous Galerkin time domain method using a locally divergence-free basis functions; and the other will be the interiori penalty domain decomposition method (IPDDM) preconditioner in the frequency domain. The breakthrough of these time and frequency domain approaches comes from the knowledge of the interior penalty formulation, which lays down the foundation of non-conformal finite and boundary element computations. Formulating our time and frequency domain methods using the new found insights gained from the interior penalty formulation, we are conducting research needed for the next generation computational electromagnetic (CEM) tools for solving full wave Maxwell equations with orders of magnitude improvements over the current existing