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In this paper we revisit the Restricted Additive Schwarz method for solvingdiscretized Helmholtz problems, using impedance boundary conditions onsubdomains (sometimes called ORAS). We present this method in its variationalform and show that it can be seen as a finite element discretization of aparallel overlapping domain decomposition method defined at the PDE level. In afourthcoming paper, the authors have proved certain contractive properties ofthe error propagation operator for this method at the PDE level, under certaingeometrical assumptions. We illustrate computationally that these propertiesare also enjoyed by its finite element approximation, i.e., the ORAS method.

A variational interpretation of Restricted Additive Schwarz with impedance transmission condition for the Helmholtz problem