A boundary-perturbation finite element approach for shape optimization

A numerical method is proposed for the efficient solution of shape optimiza tion problems, which combines the boundary perturbation technique and finit e element analysis. The method is computationally efficient in that it requ ires a number of finite element analyses with a fixed geometry, as opposed to standard shape optimization which requires re-analysis with varying geom etry. The application of the method to general shape optimization is consid ered. 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 via an example which involves acoustic wave s cattering from an obstacle. Copyright (C) 2000 John Wiley & Sons, Ltd.