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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

A new energy-gap cost functional approach for the exterior Bernoulli free boundary problem

http://hdl.handle.net/2237/00030815
http://hdl.handle.net/2237/00030815
63103358-79ac-4f24-8531-0a11a06f52b3
名前 / ファイル ライセンス アクション
main.pdf main (939.3 kB)
Item type 学術雑誌論文 / Journal Article(1)
公開日 2019-10-16
タイトル
タイトル A new energy-gap cost functional approach for the exterior Bernoulli free boundary problem
言語 en
著者 Fergy T. Rabago, Julius

× Fergy T. Rabago, Julius

WEKO 93737

en Fergy T. Rabago, Julius

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Azegami, Hideyuki

× Azegami, Hideyuki

WEKO 93738

en 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 pre-copy-editing, author-produced PDF of an article accepted for publication in [Evolution Equations & Control Theory] following peer review. The definitive publisher-authenticated version [A new energy-gap cost functional approach for the exterior Bernoulli free boundary problem, Evolution Equations & Control Theory, 8, 4, 785-824, 2019-6-28, Julius Fergy T. Rabago, Hideyuki Azegami] is available online at: https://doi.org/10.3934/eect.2019038.
キーワード
主題Scheme Other
主題 Shape optimization
キーワード
主題Scheme Other
主題 shape derivative
キーワード
主題Scheme Other
主題 Bernoulli problem
キーワード
主題Scheme Other
主題 gradient method
キーワード
主題Scheme Other
主題 Newton method
抄録
内容記述 The solution to a free boundary problem of Bernoulli type, also known as Alt-Caffarelli problem, is studied via shape optimization techniques. In particular, a novel energy-gap cost functional approach with a state constraint consisting of a Robin condition is proposed as a shape optimization reformulation of the problem. Accordingly, the shape derivative of the cost is explicitly determined, and using the gradient information, a Lagrangian-like method is used to formulate an efficient boundary variation algorithm to numerically solve the minimization problem. The second order shape derivative of the cost is also computed, and through its characterization at the solution of the Bernoulli problem, the ill-posedness of the shape optimization formulation is proved. The analysis of the proposed formulation is completed by addressing the existence of optimal solution of the shape optimization problem and is accomplished by proving the continuity of the solution of the state problems with respect to the domain. The feasibility of the newly proposed method and its comparison with the classical energy-gap type cost functional approach is then presented through various numerical results. The numerical exploration issued in the study also includes results from a second-order optimization procedure based on a Newton-type method for resolving such minimization problem. This computational scheme put forward in the paper utilizes the Hessian information at the optimal solution and thus offers a state-of-the-art numerical approach for solving such free boundary problem via shape optimization setting.
言語 en
内容記述タイプ Abstract
内容記述
内容記述 Online Published: 2019-06-28 ファイル公開:2020-06-28
言語 ja
内容記述タイプ Other
出版者
言語 en
出版者 American Institute of Mathematical Sciences
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/10.3934/eect.2019038
ISSN(Online)
収録物識別子タイプ EISSN
収録物識別子 2163-2480
書誌情報 en : Evolution Equations & Control Theory

巻 8, 号 4, p. 785-824, 発行日 2019
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