We aim at finding an optimal design for an interior permanent magnet electric motor by means of a sensitivity-based topology optimization method. The gradient-based ON/OFF method, introduced by M. Ohtake, Y. Okamoto and N. Takahashi in [1], has been successfully applied to optimization problems of this form. We show that this method can be improved by considering the mathematical concept of topological derivatives. Topological derivatives for optimization problems constrained by linear partial differential equations (PDEs) are well-understood, whereas little is known about topological derivatives in combination with nonlinear PDE constraints. We derive the topological derivative for an optimization problem constrained by the equation of nonlinear two-dimensional magnetostatics and show how this information can be used to obtain optimal designs.
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