Analysis of the Schwarz Domain Decomposition Method for the Conductor-like Screening Continuum Model

We study the Schwarz overlapping domain decomposition method applied to Poisson problem on a special family of domains, which by construction consist union large number fixed-size subdomains. These domains are motivated applications in computational chemistry where subdomains van der Waals balls. As is usual theory methods, rate convergence related stable subspace decomposition. derive such for this and analyze how stability "constant" depends relevant geometric properties domain. For this, we introduce new descriptors that used formalize geometry domains. show how, an increasing subdomains, specific local one global descriptor. The analysis also naturally provides lower bounds terms smallest eigenvalue Laplace