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Laros, M. --- Laros, Matthias

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This thesis deals with topology and shape optimization methods for finding optimal geometries of devices from electrical engineering. As a model problem, we consider the design optimization of an electric motor. Here, the performance of the motor depends on the electromagnetic fields in its interior, which, among other factors, also depend on the geometry of the motor via the solution to Maxwell's equations. In our model, we use a special regime of Maxwell's equations, namely the partial differential equation (PDE) of nonlinear magnetostatics, and consider a two-dimensional setting of the electric motor. Thus, we are facing a PDE-constrained optimization problem where the unknown is the geometry of a given part of the motor. An important tool for solving shape optimization problems is the shape derivative, i.e., the sensitivity of the domain-dependent objective function with respect to a smooth variation of a boundary or material interface.