504

IGPM504.pdf June 2020 
TITLE 
Analysis of the Schwarz domain decomposition method for the conductorlike screening continuum model 
AUTHORS 
Arnold Reusken, Benjamin Stamm 
ABSTRACT 
We study the Schwarz overlapping domain decomposition method applied to the Poisson problem on a special family of domains, which by construction consist of a union of a large number of fixedsize subdomains. These domains are motivated by applications in computational chemistry where the subdomains consist of van der Waals balls. As is usual in the theory of domain decomposition methods, the rate of convergence of the Schwarz method is related to a stable subspace decomposition. We derive such a stable decomposition for this family of domains and analyze how the stability “constant” depends on relevant geometric properties of the domain. For this, we introduce new descriptors that are used to formalize the geometry for the family of domains. We show how, for an increasing number of subdomains, the rate of convergence of the Schwarz method depends on specific local geometry descriptors and on one global geometry descriptor. The analysis also naturally provides lower bounds in terms of the descriptors for the smallest eigenvalue of the Laplace eigenvalue problem for this family of domains. 
KEYWORDS 
Schwarz domain decomposition method, conductorlike screening continuum model, convergence analysis
