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Spatially tuning core permeability of an electromagnetic device enables superior performance. A permeability profile can be heuristically selected to improve the flux distribution in a device with a given geometry, but in order to fully leverage the capacity of spatial dependent permeability engineering, the geometry and the permeability should be optimized simultaneously. The work herein presented sets forth a multi-physics design optimization paradigm that includes the permeability profile tuning in the context of both inductor and converter design. This approach enables the determination of Pareto optimal fronts consisting of a set of optimal solutions against competing objectives (e.g. mass and loss) under imposed constraints. To this end, computationally efficient analytical solutions of the heat transfer and electromagnetic formulations are derived for toroidal inductors, which are validated with Finite Element Analysis based simulations. The software implemented in Matlab 2018b is available online as an attachment to this paper.

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