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A separating oscillation method of recovering the G-limit in standard and non-standard homogenization problems
Univ Orebro, Sch Sci & Technol, Dept Math, SE-70182 Örebro, Sweden.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.ORCID iD: 0000-0001-6742-5781
Mid Sweden University, Faculty of Science, Technology and Media, Department of Quality Technology and Management, Mechanical Engineering and Mathematics.ORCID iD: 0000-0001-9984-2424
Univ Orebro, Sch Sci & Technol, Dept Math, SE-70182 Orebro, Sweden.
2016 (English)In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 32, no 2, article id 025005Article in journal (Refereed) Published
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Abstract [en]

Reconstructing the homogenized coefficient, which is also called the G-limit, in elliptic equations involving heterogeneous media is a typical nonlinear ill-posed inverse problem. In this work, we develop a numerical technique to determine G-limit that does not rely on any periodicity assumption. The approach is a technique that separates the computation of the deviation of the G-limit from the weak L-2-limit of the sequence of coefficients from the latter. Moreover, to tackle the ill-posedness, based on the classical Tikhonov regularization scheme we develop several strategies to regularize the introduced method. Various numerical tests for both standard and non-standard homogenization problems are given to show the efficiency and feasibility of the proposed method.

Place, publisher, year, edition, pages
2016. Vol. 32, no 2, article id 025005
Keywords [en]
homogenization, inverse problems, regularization, G-limit
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-27817DOI: 10.1088/0266-5611/32/2/025005ISI: 000372370900005Scopus ID: 2-s2.0-84962255423OAI: oai:DiVA.org:miun-27817DiVA, id: diva2:934275
Available from: 2016-06-08 Created: 2016-06-07 Last updated: 2017-11-30Bibliographically approved

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Holmbom, AndersPersson, Jens

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