Shape calculus for the efficient solution of shape optimization problems with elliptic and parabolic state equation

点击翻译按钮获取中文摘要

Throughout the last 25-30 years, optimal shape design has become more and more important in engineering applications. Many problems that arise in structural mechanics, fluid dynamics and electromagnetics lead to the minimization of functionals defined over a class of admissible domains, governed by the solutions of boundary value problems or initial boundary value problems.The methodology of the present application is based on a mathematical shape sensitivity analysis and exploits the analytic computation of the shape gradient and, if available, even higher derivatives. Afterwords, the shape (and thus, the shape gradient) as well as the underlying state equation are discretized, which is in contrast to fully discrete shape optimization methods. The scope of the present project is the realization of an efficient solver in spirit of this policy, based on finite element techniques, in particular for three dimensional applications.