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Analytical and numerical methods in shape optimization

โœ Scribed by Helmut Harbrecht

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
257 KB
Volume
31
Category
Article
ISSN
0170-4214

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โœฆ Synopsis

Abstract

This paper is intended to overview on analytical and numerical methods in shape optimization. We compute and analyse the shape Hessian in order to distinguish wellโ€posed and illโ€posed shape optimization problems. We introduce different discretization techniques of the shape and present existence and convergence results of approximate solutions in case of well posedness. Finally, we survey on the efficient numerical solution of the state equation, including finite and boundary element methods as well as fictitious domain methods. Copyright ยฉ 2008 John Wiley & Sons, Ltd.

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