Low-rank approximation to heterogeneous elliptic problems
Low-rank approximation to heterogeneous elliptic problems
View/Date of Publication
03.2017Publisher
Institut für Numerische Simulation (INS)Publisher Location
BonnMetadata
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Citable Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11837
Abstract
In this work, we investigate the low-rank approximation of elliptic problems in heterogeneous media by means of Kolmogrov n-width and asymptotic expansion. This class of problems arises in practical applications involving high-contrast media, and their efficient approximation often relies crucially on certain low-rank structure of the solutions. We provide conditions on the permeability coefficient κ that ensure a favorable low-rank approximation. These conditions are expressed in terms of the distribution of the inclusions in the coefficient κ, e.g., the values, locations and diameters of the heterogeneous regions. Further, we provide a new asymptotic analysis for high-contrast elliptic problems based on the perfect conductivity problems and layer potential techniques. These results provide theoretical underpinnings for several multiscale model reduction algorithms.
Subjects
low-rank approximation, heterogeneous elliptic problems, eigenvalue decays, asymptotic expansion, layer potential techniques
Classification (DDC)
510 Mathematik 518 Numerische AnalysisFirst Publication
https://ins.uni-bonn.de/publication/preprintsRelated Publications
https://doi.org/10.1137/17M1120737Part of Series
INS Preprints ; 1704Li, Guanglian: Low-rank approximation to heterogeneous elliptic problems. In: INS Preprints, 1704.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11837
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11837
@unpublished{handle:20.500.11811/11837,
author = {{Guanglian Li}},
title = {Low-rank approximation to heterogeneous elliptic problems},
publisher = {Institut für Numerische Simulation (INS)},
year = 2017,
month = mar,
INS Preprints},
volume = 1704,
note = {In this work, we investigate the low-rank approximation of elliptic problems in heterogeneous media by means of Kolmogrov n-width and asymptotic expansion. This class of problems arises in practical applications involving high-contrast media, and their efficient approximation often relies crucially on certain low-rank structure of the solutions. We provide conditions on the permeability coefficient κ that ensure a favorable low-rank approximation. These conditions are expressed in terms of the distribution of the inclusions in the coefficient κ, e.g., the values, locations and diameters of the heterogeneous regions. Further, we provide a new asymptotic analysis for high-contrast elliptic problems based on the perfect conductivity problems and layer potential techniques. These results provide theoretical underpinnings for several multiscale model reduction algorithms.},
url = {https://hdl.handle.net/20.500.11811/11837}
}
author = {{Guanglian Li}},
title = {Low-rank approximation to heterogeneous elliptic problems},
publisher = {Institut für Numerische Simulation (INS)},
year = 2017,
month = mar,
INS Preprints},
volume = 1704,
note = {In this work, we investigate the low-rank approximation of elliptic problems in heterogeneous media by means of Kolmogrov n-width and asymptotic expansion. This class of problems arises in practical applications involving high-contrast media, and their efficient approximation often relies crucially on certain low-rank structure of the solutions. We provide conditions on the permeability coefficient κ that ensure a favorable low-rank approximation. These conditions are expressed in terms of the distribution of the inclusions in the coefficient κ, e.g., the values, locations and diameters of the heterogeneous regions. Further, we provide a new asymptotic analysis for high-contrast elliptic problems based on the perfect conductivity problems and layer potential techniques. These results provide theoretical underpinnings for several multiscale model reduction algorithms.},
url = {https://hdl.handle.net/20.500.11811/11837}
}
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