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The convergence rate of domain decomposition methods (DDMs) strongly dependson the transmission condition at the interfaces between subdomains. Thus, animportant aspect in improving the efficiency of such solvers is careful designof appropriate transmission conditions. In this work, we will develop anefficient solver for Helmholtz equations based on perfectly matched layers(PMLs) as transmission conditions at the interfaces within an optimisedrestricted additive Schwarz (ORAS) domain decomposition preconditioner, in bothtwo and three dimensional domains. We perform a series of numerical simulationson a model problem and will assess the convergence rate and accuracy of oursolutions compared to the situation where impedance boundary conditions areused.

Numerical assessment of PML transmission conditions in a domain decomposition method for the Helmholtz equation