Optimal trajectory planning for multiphysics problems governed by electromagnetic and thermal phenomena

In this thesis, the optimal trajectory planning of electromagnetic heating systems is tackled by formulating and numerically solving a PDE constrained optimization problem. The optimization of the electrical excitation and spatial configuration of the actuator relies on the formal Lagrangian technique and the adjoint-based sensitivity analysis. The corresponding optimality conditions are derived in the function space of the original problem formulation following a FOTD approach to ensure that not only the system dynamics but rather the whole optimality system can be numerically solved by FEM-based simulation software. The solution approach is characterized by its generality to deal with typical problems of electromagnetic heating. This means that different excitation strategies for the actuator, geometrical setups with arbitrary complexity, and various application examples can be handled with relative ease. In order to account for state constraints, an outer penalty function approach and augmented Lagrangian method are presented. The three main components of this thesis, i. e., the optimal excitation of the actuator, its optimal spatial configuration, and the incorporation of state constraints for the trajectory planning, are tackled by an optimization framework that closely couples FEM software and optimization algorithms. The state-of-the-art FEM software Comsol Multiphysics and the software package Matlab are combined to cope with the trajectory planning problem. The algorithmic level of the optimization framework in Matlab consists of a gradient method, respectively an augmented Lagrangian method, to solve the optimality conditions. The numerical effort that is associated with the trajectory planning, however, is outsourced to Comsol Multiphysics.