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Wind turbines organized in wind farms will be one of the main electric power sources of the future. Each wind turbine causes a wake with a reduced wind speed. This wake influences the power of downstream turbines. Therefore, there is a strong interaction between the individual wind turbines in a wind farm. This interaction is an opportunity for optimal control to maximize the total power and decrease the load (i.e., tower activity and pitch activity) of a wind farm. We use the already known axial-induction-based control but investigate its potential in the case of a wind gust using mathematical optimization. This case is particularly interesting because a wind gust requires a dynamic control reaction and the consideration of the time delay with which downstream turbines are affected. In particular, this enables to reduce the tower load of downstream wind turbines by dynamic axial-induction-based control of an upstream turbine.

This thesis challenges with the development of a computational framework facilitating the solution for the inverse medium problem in time-independent scattering in two- and three-dimensional setting. This includes three main application cases: the simulation of the scattered field for a given transmitter-receiver geometry; the generation of simulated data as well as the handling of real-world data; the reconstruction of the refractive index of a penetrable medium from several measured, scattered fields. We focus on an effective and efficient reconstruction algorithm. Therefore we set up a variational reconstruction scheme. The underlying paradigm is to minimize the discrepancy between the predicted data based on the reconstructed refractive index and the given data while taking into account various structural a priori information via suitable penalty terms, which are designed to promote information expected in real-world environments. Finally, the scheme relies on a primal-dual algorithm. In addition, information about the obstacle's shape and position obtained by the factorization method can be used as a priori information to increase the overall effectiveness of the scheme. An implementation is provided as MATLAB toolbox IPscatt. It is tailored to the needs of practitioners, e.g. a heuristic algorithm for an automatic, data-driven choice of the regularization parameters is available. The effectiveness and efficiency of the proposed approach are demonstrated for simulated as well as real-world data by comparisons with existing software packages.