Model Order Reduction Methods for Parameterized Systems in Electromagnetic Field Simulations

The topic of this thesis falls in the field of system approximation. The original large-scale and parameter-dependent model is reduced to a smaller model which approximates the transfer function of the original model while the parameter dependence is retained in the reduced model. The simplified model is then succesfully used instead of the original model in a large variety of applications. The models stem from the Maxwell grid equations, which are obtained from the continuous Maxwell equations with the help of the Finite Integration Theory (FIT). In general, a variety of parameters is possible for electromagnetic field problems. In this work though, the focus has been set to material and geometry parameters with particular emphasis on the latter. To this purpose, two main strategies are followed. The first strategy is based on already existing work on parametric order reduction which are not applicable in the form naturally obtained by the Maxwell grid equations. Therefore, a linearization step is shown that appropriately adapts the FIT systems to the desired form. An alternative approach is based on using the system in the form directly obtained from the Maxwell grid equations, and defines the projection matrix of the parametric systems as the composition of local projection matrices. This method provides more flexibility in the geometry variation than the approach described above. The methods developed in this thesis have been applied to several numerical examples.

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