Eliminating the pollution effect in Helmholtz problems by local subscale correction
Eliminating the pollution effect in Helmholtz problems by local subscale correction
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11.2014Verlag / herausgebende Einrichtung
Institut für Numerische Simulation (INS)Verlagsort
BonnMetadaten
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Zitierbarer Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11916
Inhalt
We introduce a new Petrov-Galerkin multiscale method for the numerical approximation of the Helmholtz equation with large wave number κ in bounded domains in ℝd. The discrete trial and test spaces are generated from standard mesh-based finite elements by local subscale correction in the spirit of numerical homogenization. The precomputation of the correction involves the solution of coercive cell problems on localized subdomains of size ℓH; H being the mesh size and ℓ being the oversampling parameter. If the mesh size and the oversampling parameter are such that Hκ and log(κ)/ℓ fall below some generic constants and if the cell problems are solved sufficiently accurate on some finer scale of discretization, then the method is stable and its error is proportional to H; pollution effects are eliminated in this regime.
Klassifikation (DDC)
510 Mathematik 518 Numerische AnalysisErstpublikation
https://ins.uni-bonn.de/publication/preprintsZugehörige Publikation(en)
https://doi.org/10.1090/mcom/3156Reihe, Nummer
INS Preprints ; 1411Peterseim, Daniel: Eliminating the pollution effect in Helmholtz problems by local subscale correction. In: INS Preprints, 1411.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11916
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11916
@unpublished{handle:20.500.11811/11916,
author = {{Daniel Peterseim}},
title = {Eliminating the pollution effect in Helmholtz problems by local subscale correction},
publisher = {Institut für Numerische Simulation (INS)},
year = 2014,
month = nov,
INS Preprints},
volume = 1411,
note = {We introduce a new Petrov-Galerkin multiscale method for the numerical approximation of the Helmholtz equation with large wave number κ in bounded domains in ℝd. The discrete trial and test spaces are generated from standard mesh-based finite elements by local subscale correction in the spirit of numerical homogenization. The precomputation of the correction involves the solution of coercive cell problems on localized subdomains of size ℓH; H being the mesh size and ℓ being the oversampling parameter. If the mesh size and the oversampling parameter are such that Hκ and log(κ)/ℓ fall below some generic constants and if the cell problems are solved sufficiently accurate on some finer scale of discretization, then the method is stable and its error is proportional to H; pollution effects are eliminated in this regime.},
url = {https://hdl.handle.net/20.500.11811/11916}
}
author = {{Daniel Peterseim}},
title = {Eliminating the pollution effect in Helmholtz problems by local subscale correction},
publisher = {Institut für Numerische Simulation (INS)},
year = 2014,
month = nov,
INS Preprints},
volume = 1411,
note = {We introduce a new Petrov-Galerkin multiscale method for the numerical approximation of the Helmholtz equation with large wave number κ in bounded domains in ℝd. The discrete trial and test spaces are generated from standard mesh-based finite elements by local subscale correction in the spirit of numerical homogenization. The precomputation of the correction involves the solution of coercive cell problems on localized subdomains of size ℓH; H being the mesh size and ℓ being the oversampling parameter. If the mesh size and the oversampling parameter are such that Hκ and log(κ)/ℓ fall below some generic constants and if the cell problems are solved sufficiently accurate on some finer scale of discretization, then the method is stable and its error is proportional to H; pollution effects are eliminated in this regime.},
url = {https://hdl.handle.net/20.500.11811/11916}
}
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