On the approximation of the Dirichlet to Neumann map for high contrast two phase composites and its applications to domain decomposition methods
Doctor of Philosophy
An asymptotic approximation of the Dirichlet to Neumann (DtN) map of high contrast composite media with perfectly conducting inclusions that are close to touching is presented. 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 in order to obtain more computational efficiency.
Asymptotic approximation; high contrast; Dirichlet to Neumann Map; domain decomposition methods; preconditioner