Efficient Parallel and Sequential Domain Decomposition Methods for High-Frequency Helmholtz Problems with Variable Wave Speed

The authors develop and analyze parallel and sequential overlapping Schwarz methods for solving high-frequency Helmholtz problems with variable wave speed, using Cartesian perfectly-matched layers (PML) at the subdomain boundaries. They prove that the error decays smoothly and exponentially quickly in the number of iterations, with the number of iterations depending on the behavior of the geometric-optic rays.