Multilevel solvers for three-dimensional optimal shape design with an application to magneto-optics

This paper presents a new numerical technique for solving design shape optimization problems. The idea is to apply a standard optimization algorithm within a hierarchy of discretizations such that a coarse optimized design is used as the initial guess at the next finer discretized level. We give a comparison with the standard optimization approach which proceeds only on the finest discretization. The method is used for 3-dimensional optimal shape design of an electromagnet that arises in the research on magneto-optic effects.