Control fictitious domain method for solving optimal shape design problems. (English) Zbl 0772.65043

In the numerical implementation of optimal shape design, the problem is solved many times on the domain, changing during the computation. Very often, this requires the use of mesh generator, and the structural data which define the finite dimensional approximation have to be computed again and again.
In order to circumvent this difficulty, a so-called control/fictious domain technique is proposed, the main features of which are the following: one can select a simple form for the domain, the triangulation is elementary, and all the computations involve the same stiffness matrix. The present paper deals with the mathematical analysis of the method for the Dirichlet problem. The topic is functional analysis.


65K10 Numerical optimization and variational techniques
49M15 Newton-type methods
49J15 Existence theories for optimal control problems involving ordinary differential equations
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