Multiscale Petrov-Galerkin method for high-frequency heterogeneous Helmholtz equations
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 t...
| Main Authors: | , , |
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| Format: | Article |
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Springer
2017
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| Online Access: | https://eprints.nottingham.ac.uk/42391/ |
| _version_ | 1848796476584493056 |
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| author | Brown, Donald Gallistl, Dietmar Peterseim, Daniel |
| author_facet | Brown, Donald Gallistl, Dietmar Peterseim, Daniel |
| author_sort | Brown, Donald |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:48:35Z |
| format | Article |
| id | nottingham-42391 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:48:35Z |
| publishDate | 2017 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-423912020-05-04T18:41:12Z https://eprints.nottingham.ac.uk/42391/ Multiscale Petrov-Galerkin method for high-frequency heterogeneous Helmholtz equations Brown, Donald Gallistl, Dietmar Peterseim, Daniel 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. Springer 2017-04-08 Article PeerReviewed Brown, Donald, Gallistl, Dietmar and Peterseim, Daniel (2017) Multiscale Petrov-Galerkin method for high-frequency heterogeneous Helmholtz equations. Lecture Notes in Computational Science and Engineering, 115 . pp. 85-115. ISSN 1439-7358 https://link.springer.com/chapter/10.1007%2F978-3-319-51954-8_6 doi:10.1007/978-3-319-51954-8_6 doi:10.1007/978-3-319-51954-8_6 |
| spellingShingle | Brown, Donald Gallistl, Dietmar Peterseim, Daniel Multiscale Petrov-Galerkin method for high-frequency heterogeneous Helmholtz equations |
| title | Multiscale Petrov-Galerkin method for high-frequency heterogeneous Helmholtz equations |
| title_full | Multiscale Petrov-Galerkin method for high-frequency heterogeneous Helmholtz equations |
| title_fullStr | Multiscale Petrov-Galerkin method for high-frequency heterogeneous Helmholtz equations |
| title_full_unstemmed | Multiscale Petrov-Galerkin method for high-frequency heterogeneous Helmholtz equations |
| title_short | Multiscale Petrov-Galerkin method for high-frequency heterogeneous Helmholtz equations |
| title_sort | multiscale petrov-galerkin method for high-frequency heterogeneous helmholtz equations |
| url | https://eprints.nottingham.ac.uk/42391/ https://eprints.nottingham.ac.uk/42391/ https://eprints.nottingham.ac.uk/42391/ |