Space-time Finite Element Methods for the Eddy Current Problem and Applications
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Beschreibung
We investigate space-time finite element methods for simulating the eddy current problem, potentially incorporating hysteretic effects in electric motors. By treating time as an additional spatial dimension, our approach enables efficient parallelization of computations across space and time simultaneously.
We formulate and analyze space-time finite element methods for the numerical simulation of the eddy current approximation in Bochner spaces. First, we examine the resulting elliptic-parabolic interface problem posed on electrically conducting and non-conducting stationary regions, providing the analysis of the unique solvability for the linear and nonlinear case. Furthermore, we address hysteresis effects in ferromagnetic materials by proposing a space-time finite element method tailored to a specific hysteretic material law. The investigation extends to moving bodies, analyzing the corresponding elliptic-parabolic interface problem. The Petrov-Galerkin space-time finite element discretization is formulated on completely unstructured decompositions of the space-time cylinder into simplicial elements, which allows for an adaptive resolution of the solution both in space and time. However, it requires the solution of the overall system of algebraic equations. While the use of parallel solution algorithms seems to be mandatory, this method also allows for a parallelization in space and time simultaneously. The numerical experiments confirm related a priori error estimates and demonstrate the applicability and accuracy of the proposed approach applied to realistic problems.
Autor*in
Mario Gobrial
Themen in »Space-time Finite Element Methods for the Eddy Current Problem and Applications«
Space-time finite element methods Eddy current problem Hysteresis Electric motors Parallel computing