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A Space-Time Finite Element Method for the Eddy Current Approximation of Rotating Electric Machines

  • Peter Gangl ORCID logo EMAIL logo , Mario Gobrial and Olaf Steinbach ORCID logo
Published/Copyright: September 3, 2024

Abstract

In this paper we formulate and analyze a space-time finite element method for the numerical simulation of rotating electric machines where the finite element mesh is fixed in a space-time domain. Based on the Babuška–Nečas theory we prove unique solvability both for the continuous variational formulation and for a standard Galerkin finite element discretization in the space-time domain. This approach allows for an adaptive resolution of the solution both in space and time, but it requires the solution of the overall system of algebraic equations. While the use of parallel solution algorithms seems to be mandatory, this also allows for a parallelization simultaneously in space and time. This approach is used for the eddy current approximation of the Maxwell equations which results in an elliptic-parabolic interface problem. Numerical results for linear and nonlinear constitutive material relations confirm the applicability and accuracy of the proposed approach.

Funding source: Austrian Science Fund

Award Identifier / Grant number: TRR361/F90

Award Identifier / Grant number: P 32911

Funding statement: This work has been supported by the Austrian Science Fund (FWF) under the Grant Collaborative Research Center TRR361/F90: CREATOR Computational Electric Machine Laboratory. Peter Gangl is partially supported by the State of Upper Austria and also acknowledges the support of the FWF project P 32911.

Acknowledgements

We would like to thank U. Iben, J. Fridrich, I. Kulchytska-Ruchka, O. Rain, D. Scharfenstein, and A. Sichau (Robert Bosch GmbH, Renningen, Germany) for the cooperation and fruitful discussions during this work.

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Received: 2024-03-09
Revised: 2024-06-09
Accepted: 2024-08-02
Published Online: 2024-09-03
Published in Print: 2025-04-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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