  In contrast with classical Schwarz theory, recent results have shown that for
special domain geometries, one-level Schwarz methods can be scalable. This
property has been proved for the Laplace equation and external Dirichlet
boundary conditions. Much less is known if mixed boundary conditions are
considered. This short manuscript focuses on the convergence and scalability
analysis of one-level parallel Schwarz method and optimized Schwarz method for
several different external configurations of boundary conditions, i.e., mixed
Dirichlet, Neumann and Robin conditions.
