The Second-Order Shape Derivative of Kohn–Vogelius-Type Cost Functional Using the Boundary Differentiation Approach

Mathematics

Jerico B. Bacani¹  Gunther Peichl² 

[1] Department of Mathematics and Computer Science, College of Science, University of the Philippines Baguio, Governor Pack Road, Baguio 2600, Philippines;Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, A-8010 Graz, Austria; E-Mail:

关键词: Bernoulli problem;    boundary value problems;    shape derivative;    boundary differentiation;   

DOI  :  10.3390/math2040196

来源: mdpi

【 摘 要 】

A shape optimization method is used to study the exterior Bernoulli free boundary problem. We minimize the Kohn–Vogelius-type cost functional over a class of admissible domains subject to two boundary value problems. The first-order shape derivative of the cost functional is recalled and its second-order shape derivative for general domains is computed via the boundary differentiation scheme. Additionally, the second-order shape derivative of J at the solution of the Bernoulli problem is computed using Tiihonen’s approach.

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland.