# Induced heating solver

Induction heating is the process of heating an electrically conducting object (usually a metal) by electromagnetic induction (usually with a moving or non-moving coil), where eddy currents are generated within the metal and resistance leads to Joule heating of the metal. Numerically, in order to solve an eddy current problem a EM time step compatible with the frequency (i.e. a time step such that there are at least a few dozens of steps in the quarter period of the current) is needed. For example, with a frequency of 1MHz, a time step around 1.e-8 seconds would be needed and thus 1.e8 time steps to solve a full problem lasting 1s. Therefore, an induction heating analysis would be time consuming using the classic Eddy-current solver.

The induction heating solver works the following way: it assumes a current which oscillates very rapidly compared to the total time of the process (typically, a current with a frequency ranging from kHz to Mhz and a total time for the process around a few seconds). The following assumption is done: a full eddy-current problem is solved on a half-period with a "micro" EM time step. An average of the EM fields during this half-period as well as the joule heating are computed. It is then assumed that the properties of the material (and mostly the electrical conductivity which drives the flow of the current and the joule heating) do not change for the next periods of the current. These properties depending mostly on the temperature, the assumption can therefore be considered accurate as long as the temperature doesn't change too much. During these periods, no EM computation is done, only the averaged joule heating is added to the thermal solver. But, as the temperature changes, and thus the electrical conductivity, the EM fields need to be updated accordingly, so another full eddy current resolution is computed for a half-period of the current giving new averaged EM fields. The solver can therefore efficiently solve problems involving inductive heating for a moving or non-moving coil.