Multi-Scale Finite Element Methods for Eddy Current Problems MSFEM4ECP

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Fonds zur Förderung der wissenschaftlichen Forschung FWF
Grant number: P 31926
Funding periode: from November 1, 2018 to October 31, 2021


The iron core of electrical devices is laminated to reduce the eddy current (EC) losses. The geometric dimensions are extremely di�erent. The thickness of iron laminates is about 0.3mm and separated by quite small air gaps. On the other hand, the overall dimensions of the core are in the meter range consisting of up to several thousands of laminates. Finite element (FE) simulations are indispensable for the optimal design of the devices. However, modeling of each laminate by FEs leads to an extremely large nonlinear system of equations, well above hundreds of millions, which cannot reasonably be solved with present computer capacities. The development of multiscale �nite element methods (MSFEMs) for ECs in laminated iron has brought the simulation capabilities a major step forward. Nevertheless, MSFEMs su�er from various shortcomings and the computational costs are still too high. There is no error estimator for MSFEMs which is a big problem to trust in MSFEM solutions. MSFEMs in 3D are severely restricted to simple problems. These di�culties are major challenges in computational electromagnetics. Completely new methods will be developed to achieve the breakthrough of MSFEMs. Adaptive MSFEMs facilitating MSFEMs with di�erent potential formulations, higher order MSFEMs, harmonic balance MSFEMs etc. are absolutely unique and novel. E�cient and reliable equilibrated local error estimators with a computable constant and based on the theorem of Prager and Synge to allow both h- and p-re�nement will be developed. The simulation of one laminate often su�ces for electrical machines assuming common simpli �cations. To avoid expensive 3D FE simulations, completely new space splitting 2-D/1-D methods will be developed considering in particular the edge e�ect and Biot-Savart-�elds, leading to a major reduction of computational costs. The missing models for interfaces with large stray �elds are a very serious shortcoming of MSFEMs in 3D. Feasible solutions in 3D are of exceptional importance, because stray �elds are present in almost all electrical devices. Current MSFEM approaches vanish in air which represents a serious problem. Thus, radically new approaches have to be found. Novel nonlinear model order reduction (MOR) schemes have to be developed for di�erent MSFEMs to achieve tremendous savings in computational costs. MOR schemes exploiting the speci�c nature of MSFEMs of ECs will be provided to cope with large nonlinear systems of equations. The aims of the project are a strong reduction of the high computational costs of MSFEMs to run such simulations on personal computers without any di�culty. Unique adaptive MSFEMs will guarantee highly accurate and e�cient MSFEM solutions. Novel MSFEMs will solve the still existing shortcomings in 3D. The project will be carried out by the applicant and the doctoral candidate.


Finite element package ngsolve for electromagnetic problems.