Shape Optimization of Homogeneous Electromagnets

Abstract

Magneto-optical effects are investigated among others for their application in storage media. Measurements of Kerr effect require magnetic field as homogeneous as possible. This is generated by so-called homogeneous electromagnets. The optimization aims at the optimal shape of the pole heads. The governing linear magnetostatic problem is approximated by the Finite Element Method (FEM) where quadratic triangular elements or edge elements are used in the 2-dimensional (2D) or 3-dimensional (3D) case, respectively. The solver is either a direct or multigrid Preconditioned Conjugate Gradient method (PCG), depending on the problem size. The Sequentional Quadratic Programming (SQP) method with the BFGS update of Hessian matrix was used for the optimization. We computed an optimized 2D coarse design which was produced afterwards. The measurements show significant improvements of the homogeneity. We also computed an optimized 2D fine design by a hierarchical strategy, which is an iterative process where a coarse optimized shape is used as an initial design for the optimization on a finer grid. This approach seems to suit our class of problems very well. Finally, a coarse approximation of the 3D optimal shape was calculated.