A space-time finite element method for the eddy current approximation of rotating electric machines

TL;DR

This paper develops and analyzes a space-time finite element method for simulating rotating electric machines, enabling adaptive resolution and parallel computation in space and time.

Contribution

It introduces a novel space-time finite element formulation for eddy current problems in electric machines, with proven unique solvability and demonstrated numerical effectiveness.

Findings

Method accurately models eddy current phenomena in electric machines.

Adaptive space-time discretization improves solution resolution.

Parallel algorithms enable efficient computation for complex problems.

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 space-time domain. Based on the Babu\v{s}ka--Ne\v{c}as 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, efficiency and accuracy of the proposed approach.