A boundary-perturbation finite element approach for shape optimization

A numerical method is proposed for the e cient solution of shape optimization problems, which combines the boundary perturbation technique and nite element analysis. The method is computationally e cient in that it requires a number of nite element analyses with a xed 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 di erential equations. The performance of the method is illustrated via an example which involves acoustic wave scattering from an obstacle