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

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.