A Domain Embedding Method for Scattering Problems with an Absorbing Boundary or a Perfectly Matched Layer

Abstract

The efficient numerical solution of the exterior Helmholtz equation modeling the acoustic scattering by an obstacle is considered. The exterior problem is approximated by truncating the domain with a rectangular boundary and using either a perfectly matched layer or a second-order absorbing boundary condition to reduce reflections from the artificial boundary. The scattering problem is solved iteratively by using a domain embedding method with an efficient separable preconditioner. With this approach, it is possible to realize the GMRES iterations in a low-dimensional subspace and use the partial solution method to solve the linear systems with the preconditioner. The accuracy and the efficiency of the proposed solution technique are studied with numerical experiments.