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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/2237/00030413b9ca07cc-871d-41b9-91b4-0a8aab696a23
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
main (1.3 MB)
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| Item type | 学術雑誌論文 / Journal Article(1) | |||||
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| 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× Azegami, Hideyuki |
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| 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 | ||||||
| 内容記述タイプ | Abstract | |||||
| 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 | ||||||
| 内容記述タイプ | Other | |||||
| 内容記述 | ファイル公開：2020/01/01 | |||||
| 言語 | ja | |||||
| 出版者 | ||||||
| 出版者 | Springer | |||||
| 言語 | en | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| 資源タイプ | ||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
| 資源タイプ | 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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| 著者版フラグ | ||||||
| 値 | author | |||||
