Multiscale partition of unity
Multiscale partition of unity
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12.2013Verlag / herausgebende Einrichtung
Institut für Numerische Simulation (INS)Verlagsort
BonnMetadaten
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Zitierbarer Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11931
Inhalt
We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatz space or the existence of a finite element mesh. The method modifies a given partition of unity such that optimal convergence is achieved independent of oscillation or discontinuities of the diffusion coefficient. The modification is based on an orthogonal decomposition of the solution space while preserving the partition of unity property. This precomputation involves the solution of independent problems on local subdomains of selectable size. We deduce quantitative error estimates for the method that account for the chosen amount of localization. Numerical experiments illustrate the high approximation properties even for ‘cheap’ parameter choices.
Schlagwörter
partition of unity method, multiscale method, LOD, upscaling, homogenization
Klassifikation (DDC)
510 Mathematik 518 Numerische AnalysisErstpublikation
https://ins.uni-bonn.de/publication/preprintsZugehörige Publikation(en)
https://doi.org/10.1007/978-3-319-06898-5_10Reihe, Nummer
INS Preprints ; 1315Henning, Patrick; Morgenstern, Philipp; Peterseim, Daniel: Multiscale partition of unity. In: INS Preprints, 1315.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11931
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11931
@unpublished{handle:20.500.11811/11931,
author = {{Patrick Henning} and {Philipp Morgenstern} and {Daniel Peterseim}},
title = {Multiscale partition of unity},
publisher = {Institut für Numerische Simulation (INS)},
year = 2013,
month = dec,
INS Preprints},
volume = 1315,
note = {We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatz space or the existence of a finite element mesh. The method modifies a given partition of unity such that optimal convergence is achieved independent of oscillation or discontinuities of the diffusion coefficient. The modification is based on an orthogonal decomposition of the solution space while preserving the partition of unity property. This precomputation involves the solution of independent problems on local subdomains of selectable size. We deduce quantitative error estimates for the method that account for the chosen amount of localization. Numerical experiments illustrate the high approximation properties even for ‘cheap’ parameter choices.},
url = {https://hdl.handle.net/20.500.11811/11931}
}
author = {{Patrick Henning} and {Philipp Morgenstern} and {Daniel Peterseim}},
title = {Multiscale partition of unity},
publisher = {Institut für Numerische Simulation (INS)},
year = 2013,
month = dec,
INS Preprints},
volume = 1315,
note = {We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatz space or the existence of a finite element mesh. The method modifies a given partition of unity such that optimal convergence is achieved independent of oscillation or discontinuities of the diffusion coefficient. The modification is based on an orthogonal decomposition of the solution space while preserving the partition of unity property. This precomputation involves the solution of independent problems on local subdomains of selectable size. We deduce quantitative error estimates for the method that account for the chosen amount of localization. Numerical experiments illustrate the high approximation properties even for ‘cheap’ parameter choices.},
url = {https://hdl.handle.net/20.500.11811/11931}
}
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