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In this paper we discuss the convergence of state-of-the-art optimizedSchwarz transmission conditions for Helmholtz problems defined on closeddomains (i.e. setups which do not exhibit an outgoing wave condition), ascommonly encountered when modeling cavities. In particular, the impact ofback-propagating waves on the Dirichlet-to-Neumann map is analyzed. Afterwards,the performance of the well-established optimized 0th-order, evanescent modesdamping, optimized 2nd-order and Pad\'e-localized square-root transmissionconditions is discussed.

Convergence of classical optimized non-overlapping Schwarz method for Helmholtz problems in closed domains