The accurate modeling of electromagnetic devices, taking in to account the increasing complexity, e.g. non-linearity, high frequency effects (eddy current losses, proximity effects,..), movement etc. is a major concern from the early design stage. Numerical methods such as: the Finite Element (FE) method are widely used for modeling these phenomena. However, this method is extremely expensive, particularly when accounting for non-linearities (ferromagnetic materials), modern pulse width modulated supplies (PWM) working at ever increasing frequencies (fast switching), treatment of motion (re-meshing). The discretisation in space and time can thus yield a large system of equations with a prohibitive computational cost (time and storage). 


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KU Leuven
Aula van de Tweede Hoofdwet (T.I. 01.02), Thermotechnisch Instituut, Kasteelpark Arenberg 41
3001 Heverlee​
Belgium

In this dissertation, we aim at accurate and efficient FE based modeling of electromagnetic devices in reduced manner by means of Reduced Order Modeling (ROM) techniques to diminish the large computational cost. All the proposed developments have been applied to Proper Orthogonal Decomposition (POD) based RO models, combined with the Discrete Empirical Interpolation (DEIM) or the Gappy-POD (G-POD) in case of non-linearity. Furthermore, a linear matrix interpolation method has been implemented to account for parametric dependencies (parametric ROM, pROM) and movement in particular. As main achievements, it is worth mentioning: the original adaptive greedy algorithm used to model a microwave antenna; the stabilized Gappy-POD applied to a power transformer with eddy currents and the pROM proposed for handling an electromechanical levitation device. 

The applied ROM techniques are validated and investigated with the full order FE models. The construction of the RO models is done in a so-called offline stage that requires considerable computational resources, time and storage, for a prescribed accuracy. However, this computational cost can be dramatically reduced in the online stage by reusing the generated RO models for repetitive analysis. The parametric version (pROM) is particularly suited for such repetitive computational task, e.g., in design, optimisation and control. applications. Moreover, the proposed G-POD approach can help fixing the unstable RO models with high accuracy for a non-linear eddy current problem, whereas the DEIM fails.

Supervisors

Prof. dr. ir. R. Vazquez Sabariego (Supervisor)

Jury

Prof. dr. ir. J. Vandewalle (Chairman)
Prof. dr. ir. G. Deconinck
Prof. dr. ir. J. Driesen
Prof. dr. ir. J. Meyers
Prof. dr. ir. S. Clénet
Prof. dr. ir. C. Geuzaine
Prof. dr. ir. M. Clemens​