研究報告書 Shape Optimization Approach to a Free Boundary Problem

Maharani, Ahsani Ummi  ,  Kimura, Masato  ,  Azegami, Hideyuki  ,  Ohtsuka, Kohji  ,  Armanda, Ikhsan

6pp.42 - 55 , 2015-05-31 , Kanazawa e-Publishing
ISSN:2223-0785
内容記述
We take a shape optimization approach to solve a free boundary problem of the Poisson equation numerically. A numerical method called traction method invented by one of the authors are applied. We begin by changing the free boundary problem to a shape optimization problem and define a least square functional as a cost function. Then shape derivative of the cost function is derived by using Lagrange multiplier method. Detail structures and profiles of exact solutions to a concrete free boundary problem due to A. Henrot are also illustrated with proofs. They are used to check the efficiency of the traction method.
Selected Papers from the International Symposium on Computational Science - International Symposium on Computational Science Kanazawa University, Japan
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