The domain decomposition method of Bank and Jimack as an optimized Schwarz method

The aim of this thesis is to introduce the Bank-Jimack domain decomposition method and study its convergence behavior. We are interested in understanding what the precise contribution of the outer coarse mesh is to the convergence behavior of the domain decomposition method proposed by Bank and Jimack. We show for a two subdomain decomposition that the outer coarse mesh can be interpreted as computing an approximation to the optimal transmission condition represented by the Dirichlet to Neumann map, and thus the method of Bank and Jimack can be viewed as an optimized Schwarz method, i.e. a Schwarz method that uses Robin or higher order transmission conditions instead of the classical Dirichlet ones