Dietmar Hömberg
In the first part of my talk, a model for multifrequency induction hardening of steel parts is presented. It consists of a system of partial differential equations including Maxwell’s equations and the heat equation. We show that the coupled system admits a unique weak solution. In the second part of the talk I will discuss the numerical approximation of the problem. It turns out to be quite intricate since one has to cope with different time scales for heat diffusion and the Maxwell system. Moreover, owing to the skin effect only the boundary layers of the component are heated by induced eddy currents, hence we also have to consider different spatial scales. We present a numerical algorithm based on adaptive edge-finite elements for the Maxwell system which allows to treat these difficulties. We show some 3D simulations and conclude with results of an experimental validation in an industrial setting.