# Effect of subdomain topologies on overlapping additive Schwarz?

Is there a reference on the effect of subdomain topology on performance of the overlapping additive Schwarz method for (high order) finite elements? For example, taking subdomains to be vertex patches (elements directly connected through a vertex) differs from taking a subdomain to be an element + all its neighbors connected through faces (the former I believe gave me iteration counts independent of subdomain size, the former did not for high order).

• Hi Hui - thanks for the response, I'll take a look. I thought that Luca Pavarino showed for higher $p$ that convergence depended on the number of total number of subdomains contributing to an overlap region. Is that result consistent with Martin's work? – Jesse Chan Feb 16 '15 at 15:24