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

## Dipl.-Ing. Michael Kolmbauer

Oct. 19, 2012, 4:30 p.m. HS 3

This thesis deals with the simulation and control of time-dependent, but
time-periodic eddy current problems in unbounded domains in
$\mathbb{R}^3$. In order to discretize such problems in the full
space-time cylinder, we use a non-standard space-time discretization
method, namely, the \emph{multiharmonic finite element and boundary
element method}. This discretization technique yields large systems of
linear algebraic equations, whereas the fast solution of these systems
determines the efficiency of this method. Here, suitable preconditioners
are needed in order to ensure \emph{efficient} and
\emph{parameter-robust} convergence rates of the applied iterative
method. Therefore, the main focus of this thesis lies on the
construction and analysis of robust and efficient preconditioning
strategies for the resulting systems of linear equations.