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A boundary-perturbation finite element approach for shape optimization. (English) Zbl 0962.76048

Summary: We propose a numerical method for shape optimization problems, which combines the boundary perturbation technique and finite element analysis. The method is computationally efficient in that it requires a number of finite element analyses with a fixed geometry, as opposed to standard shape optimization which requires re-analysis with varying geometry. We apply the method to general shape optimization. In addition, a special optimization scheme is devised for a class of problems governed by linear partial differential equations. The performance of the method is illustrated on acoustic wave scattering from an obstacle.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76Q05 Hydro- and aero-acoustics
65K10 Numerical optimization and variational techniques
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