On the second-order shape derivative of the Kohn-Vogelius objective functional using the velocity method.(English)Zbl 1337.49073
Summary: The exterior Bernoulli free boundary problem is studied via the shape optimization technique. The problem is reformulated into the minimization of the so-called Kohn-Vogelius objective functional, where the involved two state variables separately satisfy two boundary value problems. The paper focuses on solving the second-order shape derivative of the objective functional using the velocity method with nonautonomous velocity fields. This work confirms the classical results of Delfour and Zolésio in relating shape derivatives of functionals using the velocity method and the perturbation of identity technique.
Keywords:
shape optimization;exterior Bernoulli free boundary problem;Kohn-Vogelius objective functional;shape derivativeCite
References:
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