2020-10-26T07:51:07Zhttps://nagoya.repo.nii.ac.jp/?action=repository_oaipmhoai:nagoya.repo.nii.ac.jp:000305452020-10-15T00:32:47Z00312:00313:00314
A second-order shape optimization algorithm for solving the exterior Bernoulli free boundary problem using a new boundary cost functionalengBernoulli problemDomain perturbationFree boundaryShape optimizationShape derivativehttp://hdl.handle.net/2237/00032730Journal ArticleRabago, Julius Fergy T.Azegami, HideyukiThe 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：2021/09/01Computational Optimization and Applications7712513052020-090926-6003https://doi.org/10.1007/s10589-020-00199-7“This is a post-peer-review, pre-copyedit version of an article published in [Computational Optimization and Applications]. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10589-020-00199-7”.authorhttps://nagoya.repo.nii.ac.jp/?action=repository_action_common_download&item_id=30545&item_no=1&attribute_id=17&file_no=1Springer2020-10-15