On the Effect of Boundary Conditions on the Scalability of Schwarz Methods

It is well known that one-level Schwarz methods are not weakly scalable, if the number of subdomains increases and the whole domain Ω is fixed. However, the recent work [2], published in the field of implicit solvation models used in computational chemistry, has drawn attention to the opposite case in which the number of subdomains increases, but their size remains unchanged, and, as a result, the size of the whole domain Ω increases