Multiple Level-Set Methods for Optimal Design of Nonlinear Magnetostatic System

This paper proposes an optimal design method using continuum sensitivity analysis and the multiple level-set methods for multi-material shape optimization in nonlinear magnetostatic systems. The general shape sensitivity formula for the nonlinear magnetostatic system is derived based on the material derivative concept of continuum mechanics and the adjoint variable method. In the multiple level-set methods, the sign combination of level-set functions is used to identify the different material regions and their interfaces. The multi-material shapes are simultaneously deformed by solving the multiple level-set equations coupled with the velocity fields in the sensitivity formula. Two numerical examples are employed to show the usefulness of the proposed design method.