  In this paper we discuss different transmission operators for the
non-overlapping Schwarz method which are suited for solving the time-harmonic
Helmholtz equation in cavities (i.e. closed domains which do not feature an
outgoing wave condition). Such problems are heavily impacted by
back-propagating waves which are often neglected when devising optimized
transmission operators for the Schwarz method. This work explores new operators
taking into account those back-propagating waves and compares them with
well-established operators neglecting these contributions. Notably, this paper
focuses on the case of rectangular cavities, as the optimal (non-local)
transmission operator can be easily determined. Nonetheless, deviations from
this ideal geometry are considered as well. In particular, computations of the
acoustic noise in a three-dimensional model of the helium vessel of a beamline
cryostat with optimized Schwarz schemes are discussed. Those computations show
a reduction of 46% in the iteration count, when comparing an operator optimized
for cavities with those optimized for unbounded problems.
