Multiscale Petrov-Galerkin method for high-frequency heterogeneous Helmholtz equations
Multiscale Petrov-Galerkin method for high-frequency heterogeneous Helmholtz equations
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12.2015Verlag / herausgebende Einrichtung
Institut für Numerische Simulation (INS)Verlagsort
BonnMetadaten
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Zitierbarer Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11904
Inhalt
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.
Klassifikation (DDC)
510 Mathematik 518 Numerische AnalysisErstpublikation
https://ins.uni-bonn.de/publication/preprintsZugehörige Publikation(en)
https://doi.org/10.1007/978-3-319-51954-8_6Reihe, Nummer
INS Preprints ; 1526Brown, Donald L.; Gallistl, Dietmar; Peterseim, Daniel: Multiscale Petrov-Galerkin method for high-frequency heterogeneous Helmholtz equations. In: INS Preprints, 1526.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11904
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11904
@unpublished{handle:20.500.11811/11904,
author = {{Donald L. Brown} and {Dietmar Gallistl} and {Daniel Peterseim}},
title = {Multiscale Petrov-Galerkin method for high-frequency heterogeneous Helmholtz equations},
publisher = {Institut für Numerische Simulation (INS)},
year = 2015,
month = dec,
INS Preprints},
volume = 1526,
note = {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.},
url = {https://hdl.handle.net/20.500.11811/11904}
}
author = {{Donald L. Brown} and {Dietmar Gallistl} and {Daniel Peterseim}},
title = {Multiscale Petrov-Galerkin method for high-frequency heterogeneous Helmholtz equations},
publisher = {Institut für Numerische Simulation (INS)},
year = 2015,
month = dec,
INS Preprints},
volume = 1526,
note = {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.},
url = {https://hdl.handle.net/20.500.11811/11904}
}
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