Numerical analysis for optimal shape design in elliptic boundary value problems. (English) Zbl 0662.65062

Author’s summary: Shape optimization problems are optimal design problems in which the shape of the boundary plays the role of a design, i.e. the unknown part of the problem. Such problems arise in structural mechanics, acoustics, electrostatics, fluid flow and other areas of engineering and applied science. The mathematical theory of such kind of problems has been developed during the last twelve years. Recently the theory has been extended to cover also situations in which the behaviour of the system is governed by partial differential equations with unilateral boundary conditions. In the paper an efficient method of nonlinear programming for solving optimal shape design problems is presented. Effectiveness of the technique proposed is demonstrated by numerical examples.
Reviewer: I.Dvořák


65K10 Numerical optimization and variational techniques
49M37 Numerical methods based on nonlinear programming
49J20 Existence theories for optimal control problems involving partial differential equations
49J40 Variational inequalities


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