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  1. A500 情報学部/情報学研究科・情報文化学部・情報科学研究科
  2. A500a 雑誌掲載論文
  3. 学術雑誌

Shape optimization approach to defect-shape identification with convective boundary condition via partial boundary measurement

http://hdl.handle.net/2237/00030413
http://hdl.handle.net/2237/00030413
b9ca07cc-871d-41b9-91b4-0a8aab696a23
名前 / ファイル ライセンス アクション
main.pdf main (1.3 MB)
Item type 学術雑誌論文 / Journal Article(1)
公開日 2019-06-11
タイトル
タイトル Shape optimization approach to defect-shape identification with convective boundary condition via partial boundary measurement
言語 en
著者 T. Rabago, Julius Fergy

× T. Rabago, Julius Fergy

WEKO 91861

en T. Rabago, Julius Fergy

Search repository
Azegami, Hideyuki

× Azegami, Hideyuki

WEKO 91862

en Azegami, Hideyuki

Search repository
アクセス権
アクセス権 open access
アクセス権URI http://purl.org/coar/access_right/c_abf2
権利
言語 en
権利情報 “This is a post-peer-review, pre-copyedit version of an article published in [Japan Journal of Industrial and Applied Mathematics]. The final authenticated version is available online at: http://dx.doi.org/10.1007/s13160-018-0337-5”.
キーワード
主題Scheme Other
主題 Shape identification
キーワード
主題Scheme Other
主題 Shape optimization
キーワード
主題Scheme Other
主題 Geometric inverse problem
キーワード
主題Scheme Other
主題 Lagrange multiplier method
キーワード
主題Scheme Other
主題 Minimax formulation
抄録
内容記述 We aim to identify the geometry (i.e., the shape and location) of a cavity inside an object through the concept of thermal imaging. More precisely, we present an identification procedure to determine the geometric shape of a cavity with convective boundary condition in a heat-conducting medium using the measured temperature on a part of the surface of the object. The inverse problem of identifying the cavity is resolved by shape optimization techniques, specifically by minimizing a least-squares type cost functional over a set of admissible geometries. The computation of the first-order shape derivative or shape gradient of the cost is carried out through minimax formulation, which is then justified by the Correa–Seeger theorem coupled with function space parametrization technique. We further characterize its boundary integral form using some identities from tangential calculus. Then, we utilize the computed expression for the shape gradient to implement an effective boundary variation algorithm for the numerical resolution of the shape optimization problem. To avoid boundary oscillations or irregular shapes in our approximations, we execute the gradient-based scheme using the H^1 gradient method with perimeter regularization. Also, we propose a novel application of the said method in computing the mean curvature of the free boundary appearing in the shape gradient of the cost functional. We illustrate the feasibility of the proposed method by testing the numerical scheme to several cavity identification problems. Additionally, we also give some numerical examples for the case of corrosion detection since its inverse problem interpreted in the framework of electrostatic imaging is closely related to the focused problem.
言語 en
内容記述タイプ Abstract
内容記述
内容記述 ファイル公開:2020/01/01
言語 ja
内容記述タイプ Other
出版者
言語 en
出版者 Springer
言語
言語 eng
資源タイプ
資源タイプresource http://purl.org/coar/resource_type/c_6501
タイプ journal article
出版タイプ
出版タイプ AM
出版タイプResource http://purl.org/coar/version/c_ab4af688f83e57aa
DOI
関連タイプ isVersionOf
識別子タイプ DOI
関連識別子 https://doi.org/10.1007/s13160-018-0337-5
ISSN(print)
収録物識別子タイプ PISSN
収録物識別子 0916-7005
ISSN(Online)
収録物識別子タイプ EISSN
収録物識別子 1868-937X
書誌情報 en : Japan Journal of Industrial and Applied Mathematics

巻 36, 号 1, p. 131-176, 発行日 2019-01
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