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This paper presents a multiscale Petrov-Galerkin finite element method fortime-harmonic acoustic scattering problems with heterogeneous coefficients inthe high-frequency regime. We show that the method is pollution- free also inthe case of heterogeneous media provided that the stability bound of thecontinuous problem grows at most polynomially with the wave number k. Bygeneralizing classical estimates of [Melenk, Ph.D. Thesis 1995] and [Hetmaniuk,Commun. Math. Sci. 5 (2007)] for homogeneous medium, we show that thisassumption of polynomially wave number growth holds true for a particular classof smooth heterogeneous material coefficients. Further, we present numericalexamples to verify our stability estimates and implement an example in thewider class of discontinuous coefficients to show computational applicabilitybeyond our limited class of coefficients.

Multiscale Petrov-Galerkin Method for High-Frequency Heterogeneous Helmholtz Equations