Optimal Interface Conditions for an Arbitrary Decomposition into Subdomains
نویسندگان
چکیده
The use of Dirichlet-to-Neumann operators as transmission conditions is known to yield optimal Schwarz methods that converge in a finite number of iterations when the subdomain decomposition has tree-like connectivity. However, it remains an open problem whether it is possible to construct a finitely terminating algorithm for arbitrary decompositions. In this article, we construct a Schwarz method that converges in exactly two steps for any decomposition into subdomains with minimal overlap. In this method, every subdomain must communicate with all other subdomains, but only data along subdomain boundaries need to be exchanged.
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