In this talk, we present a novel ellipsoidal formulation and massively parallel implementation of a perfectly matched layer (PML) for acoustics and structural acoustics. Perfectly matched layers and infinite elements are commonly used for finite element simulations of acoustic waves on unbounded domains. PML is a more recent technology that is gaining popularity due to ease of implementation and effectiveness as an absorbing boundary condition. In this study, we extend well-known curvilinear formulations for PML to ellipsoidal domains, thus allowing for a minimal volume encapsulation of the structure of interest. We discuss the issues involved in parallelization and compare the performance of PML against infinite elements on a set of representative acoustic problems on exterior domains. We examine the conditioning of the linear systems generated by the two techniques by examining the number of Krylov-iterations needed for convergence to a fixed solver tolerance. We also examine the scalability of the methods in terms of the number of Helmholtz solver iterations as the number of PML layers and infinite element order are increased. [Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL850000.]