Heterogeneous optimized schwarz methods for coupling helmholtz and laplace equations

Optimized Schwarz methods have increasingly drawn attention over the last decades because of their improvements in terms of robustness and computational cost compared to the classical Schwarz method. Optimized Schwarz methods are also a natural framework to study heterogeneous phenomena, where the spatial decomposition is provided by the multi-physics of the problem, because of their good convergence properties in the absence of overlap. We propose here zeroth order optimized transmission conditions for the coupling between the Helmholtz equation and the Laplace equation, giving asymptotically optimized choices for the parameters, and illustrating our analytical results with numerical experiments.