Analytical and numerical methods in shape optimization

摘要

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 well-posed and ill-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 (C) 2008 John Wiley & Sons, Ltd.