Coupled electromagnetic-heat problems have been studied for induction or inductive heating, for dielectric heating, for testing of corrosion, for detection of cracks, for hardening of steel, and more recently for inductive charging of electric vehicles. In nearly all cases a simple co-simulation is made where the electromagnetic problem is solved in the frequency domain (and which thus is assumed to be linear) and the heat equation in the time domain. One exchanges data after each time step (or after some change in the heat pro¿le). However, the coupled problem is non-linear in the heat variable.
In this paper we propose to split the time domain in windows in which we solve the electromagnetics problem in frequency domain. We strengthen the coupling by iterations, for which we prove convergence. By this we obtain a higher accuracy, which will allow for larger time steps and also for higher order time integration. This fully exploits the multirate behavior of the coupled system. An industrial example illustrates the analysis.