A second-order shape optimization algorithm for solving the exterior Bernoulli free boundary problem using a new boundary cost functional

Autor:	Julius Fergy T. Rabago, Hideyuki Azegami
Jazyk:	angličtina
Rok vydání:	2020
Předmět:	Hessian matrix Control and Optimization 0211 other engineering and technologies Boundary (topology) 010103 numerical & computational mathematics 02 engineering and technology Derivative 01 natural sciences Free boundary Bernoulli's principle symbols.namesake Shape optimization Shape derivative Free boundary problem Applied mathematics 0101 mathematics Bernoulli problem Mathematics 021103 operations research Applied Mathematics Function (mathematics) Chain rule Computational Mathematics Domain perturbation symbols
Zdroj:	Computational Optimization and Applications. 77(1):251-305
ISSN:	0926-6003
Popis:	The exterior Bernoulli problem is rephrased into a shape optimization problem using a new type of objective function called the Dirichlet-data-gap cost function which measures the L^2-distance between the Dirichlet data of two state functions. The first-order shape derivative of the cost function is explicitly determined via the chain rule approach. Using the same technique, the second-order shape derivative of the cost function at the solution of the free boundary problem is also computed. The gradient and Hessian informations are then used to formulate an efficient second-order gradient-based descent algorithm to numerically solve the minimization problem. The feasibility of the proposed method is illustrated through various numerical examples. ファイル公開：2021/09/01
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bc2761cd3b03d87a1b16e560c037b60b https://nagoya.repo.nii.ac.jp/records/30545 Zobrazit plný text záznamu Plný text ve formátu PDF Plný text ve formátu HTML
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