2022-12-04T19:47:16Zhttps://nagoya.repo.nii.ac.jp/oaioai:nagoya.repo.nii.ac.jp:000305452022-08-25T06:05:10ZA second-order shape optimization algorithm for solving the exterior Bernoulli free boundary problem using a new boundary cost functionalRabago, Julius Fergy T.Azegami, Hideyukiopen access“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”.Bernoulli problemDomain perturbationFree boundaryShape optimizationShape derivativeThe 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：2021/09/01Springer2020-09engjournal articleAMhttp://hdl.handle.net/2237/00032730https://nagoya.repo.nii.ac.jp/records/30545https://doi.org/10.1007/s10589-020-00199-70926-6003Computational Optimization and Applications771251305https://nagoya.repo.nii.ac.jp/record/30545/files/main.pdfapplication/pdf1.4 MB2021-09-01