Level-set-based Shape Optimization on Soft Magnetic Composites with Isotropy Constraint

Soft Magnetic Composites (SMCs) demonstrate excellent potentials for electromagnetic applications. The isotropy is one critical feature in designing the composite. This work presents a shape optimization algorithm for SMCs subject to isotropy and volume constraints. The maximal isotropic effective permeability is the design target for a fixed volume fraction of the SMCs inclusion. Augmented Lagrange is applied to satisfy the volume requirement. In addition, an adaptive weighted sum approach is employed to deal with the isotropy constraint. A level-set function is defined on the whole design domain and propagates the shape of the inclusion. Shape derivative is deduced to determine the descent direction. A numerical application is implemented for SMCs in magnetostatics in 2D for various initial shapes. The local minimum is located at a rapid convergence rate.