I will talk about an asymptotic approximation of the Dirichlet to Neumann (DtN) map of high contrast composite media with perfectly conducting inclusions that are close to touching.  The result is an explicit characterization of the DtN map in the asymptotic limit of the distance between the inclusions tending to zero. The approximation of DtN map is applied directly to nonoverlapping domain decomposition methods as preconditioners. I have coupled theoretical results into numerical methods successfully in order to obtain more computational efficiency.