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

IF 1 4区 数学 Q3 MATHEMATICS, APPLIED Computational Methods in Applied Mathematics Pub Date : 2024-09-02 DOI:10.1515/cmam-2024-0033
Peter Gangl, Mario Gobrial, Olaf Steinbach
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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.
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用于旋转电机涡流近似的时空有限元方法
在本文中,我们提出并分析了一种用于旋转电机数值模拟的时空有限元方法,其中有限元网格固定在时空域中。基于 Babuška-Nečas 理论,我们证明了连续变量公式和标准 Galerkin 有限元离散时空域的唯一可解性。这种方法可以在空间和时间上自适应地求解,但需要求解整个代数方程系统。虽然似乎必须使用并行求解算法,但这也允许在空间和时间上同时进行并行化。这种方法用于麦克斯韦方程的涡流近似,其结果是椭圆-抛物线界面问题。线性和非线性材料构成关系的数值结果证实了所提方法的适用性和准确性。
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来源期刊
CiteScore
2.40
自引率
7.70%
发文量
54
期刊介绍: The highly selective international mathematical journal Computational Methods in Applied Mathematics (CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics. The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.
期刊最新文献
Variational Approximation for a Non-Isothermal Coupled Phase-Field System: Structure-Preservation & Nonlinear Stability A Space-Time Finite Element Method for the Eddy Current Approximation of Rotating Electric Machines An Inverse Matrix Eigenvalue Problem for Constructing a Vibrating Rod On Error Estimates of a discontinuous Galerkin Method of the Boussinesq System of Equations Computational Methods in Applied Mathematics (CMAM 2022 Conference, Part 2)
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