# The Multiharmonic Finite Element Method for Simulation and Control of Eddy Current Problems

## Dipl.-Ing. Michael Kolmbauer

**March 15, 2011, 2:30 p.m. HS 14**

In this talk we discuss the application of the Multiharmonic Finite Element Method to the linear and non-linear time-harmonic eddy current problem. In particular, we provide existence and uniqueness results for the degenerated time-dependent eddy current problem in bounded and unbounded domains.

We apply a Multiharmonic approach in terms of a truncated Fourier series to switch from the time domain to the frequency domain. At least in the case of linear problems we can construct a parameter-robust preconditioned MinRes solver for the resulting systems of linear equations in the frequency domain. Furthermore, we discuss the application of this solver to linear eddy current problems with non-harmonic excitation and to non-linear problems.

Finally, we apply the Multiharmonic Finite Element Method to optimal control problems with distributed control leading to decoupled block systems for the Fourier coeffcients for which we can construct parameter-robust and optimal preconditioners by interpolation.