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A separating oscillation method of recovering the G-limit in standard and non-standard homogenization problems
Örebro University, School of Science and Technology.ORCID iD: 0000-0003-0332-2315
Department of Engineering and Sustainable Development, Mid-Sweden University, Östersund, Sweden.
Department of Engineering and Sustainable Development, Mid-Sweden University, Östersund, Sweden.
Örebro University, School of Science and Technology. (Mathematics)ORCID iD: 0000-0003-4023-6352
2016 (English)In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 32, no 2, article id 025005Article in journal (Refereed) Published
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 -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
Bristol, United Kingdom: Institute of Physics (IOP), 2016. Vol. 32, no 2, article id 025005
Keywords [en]
homogenization; inverse problems; regularization; G-limit
National Category
Computational Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:oru:diva-47918DOI: 10.1088/0266-5611/32/2/025005ISI: 000372370900005Scopus ID: 2-s2.0-84962255423OAI: oai:DiVA.org:oru-47918DiVA, id: diva2:900400
Available from: 2016-02-04 Created: 2016-02-04 Last updated: 2017-11-30Bibliographically approved

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Gulliksson, MårtenZhang, Ye

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CiteExportLink to record
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