• Univ.Prof. Dr. Joachim Schöberl

Fonds zur Förderung der wissenschaftlichen Forschung FWF, opens an external URL in a new window
Grant number: P 31926
Funding periode: from November 1, 2018 to October 31, 2022

The iron core of electrical devices is laminated to reduce the eddy current (EC) losses. The geometric dimensions are extremely different, the thickness of iron laminates is about 0.3mm separated by quite small air gaps and, on the other, the overall dimensions of the core are in the meter range and it consists of up to several thousands of laminates.

Finite element (FE) simulations are indispensable for an optimal design of these devices. However, modeling of each laminate by FEs requires a very high number of elements leading to an extremely large nonlinear system of equations, well above hundreds of millions, whose solution cannot reasonably be considered with present computer capacities.

The development of multiscale finite element methods (MSFEMs) for ECs in laminated iron has brought the simulation capabilities a major step forward. Nevertheless, the memory requirement and the computation time are still too high. There is also no possibility except reference solutions to estimate or to control the error of MSFEM solutions representing a serious problem which has not yet been addressed in this context. That is why this subject is one of the major challenges in computational electromagnetics.
Adaptive MSFEMs will be realized with local a posteriori equilibrium error estimators based on the theorem of Prager and Synge and exploiting both h- and p-refinement to estimate and to minimize the MSFEM approximation error. Adaptive MSFEMs are absolutely new and shall cope with MSFEM using different potential formulations, higher order MSFEM, harmonic balance MSFEM etc.

MSFEM solutions exhibit boundary layers which are expensive to model. Hierarchical singular functions will be introduced to enrich the corresponding standard FE basis.

The simulation of one laminate instead of the whole core usually suffices for electrical machines assuming common simplifications. To avoid brute force FE simulations, 2-D/1-D methods are attractive. MSFEM approaches shall improve the computational costs and the accuracy of 2-D/1-D-methods significantly.

The missing models for interfaces with large stray fields are a very serious shortcoming of MSFEMs in 3D. Feasible solutions in 3D are of exceptional importance, because large stray fields are unavoidably present in almost all electrical devices. Current MSFEM approaches vanish in air. Thus, radically new approaches have to be found. There is no systematic way to develop them, representing serious difficulties.

Model order reduction (MOR) methods exploiting the specific nature of the nonlinear systems arising from MSFEMs of ECs in laminated iron haven't been developed so far. The new MOR methods for different MSFEMs to be developed shall also contribute to the reduction of the computational costs essentially.

Finite element package ngsolve, opens an external URL in a new window for electromagnetic problems.