  The convergence rate of domain decomposition methods (DDMs) strongly depends
on the transmission condition at the interfaces between subdomains. Thus, an
important aspect in improving the efficiency of such solvers is careful design
of appropriate transmission conditions. In this work, we will develop an
efficient solver for Helmholtz equations based on perfectly matched layers
(PMLs) as transmission conditions at the interfaces within an optimised
restricted additive Schwarz (ORAS) domain decomposition preconditioner, in both
two and three dimensional domains. We perform a series of numerical simulations
on a model problem and will assess the convergence rate and accuracy of our
solutions compared to the situation where impedance boundary conditions are
used.
