A boundary-perturbation finite element approach for shape optimization

A numerical method is proposed for the efficient solution of 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. The application of the method to general shape optimization is considered. 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 scattering from an obstacle. Copyright (C) 2000 John Wiley & Sons, Ltd.