Multiscale Petrov-Galerkin method for high-frequency heterogeneous Helmholtz equations

Brown, Donald; Gallistl, Dietmar; Peterseim, Daniel

Abstract

This paper presents a multiscale Petrov-Galerkin finite element method for time-harmonic acoustic scattering problems with heterogeneous coefficients in the high-frequency regime. We show that the method is pollution free also in the case of heterogeneous media provided that the stability bound of the continuous problem grows at most polynomially with the wave number k. By generalizing classical estimates of Melenk (Ph.D. Thesis 1995) and Hetmaniuk (Commun. Math. Sci. 5, 2007) for homogeneous medium, we show that this assumption of polynomially wave number growth holds true for a particular class of smooth heterogeneous material coefficients. Further, we present numerical examples to verify our stability estimates and implement an example in the wider class of discontinuous coefficients to show computational applicability beyond our limited class of coefficients.

Citation

Brown, D., Gallistl, D., & Peterseim, D. (in press). Multiscale Petrov-Galerkin method for high-frequency heterogeneous Helmholtz equations. Lecture Notes in Computational Science and Engineering, 115, https://doi.org/10.1007/978-3-319-51954-8_6

• Journal Article Type: Article
• Acceptance Date: Apr 1, 2017
• Online Publication Date: Apr 8, 2017
• Deposit Date: May 8, 2017
• Publicly Available Date: May 8, 2017
• Journal: Lecture Notes in Computational Science and Engineering
• Electronic ISSN: 1439-7358
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 115
• DOI: https://doi.org/10.1007/978-3-319-51954-8_6
• Public URL: https://nottingham-repository.worktribe.com/output/854983
• Publisher URL: https://link.springer.com/chapter/10.1007%2F978-3-319-51954-8_6
• Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-51954-8