Multiscale Finite Element Formulations for 2D/1D Problems

• Published in: IEEE transactions on energy conversion Vol. 39; no. 2; pp. 953 - 962
• Main Authors: Hollaus, Karl, Schobinger, Markus
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: 2D/1D multiscale finite element method MSFEM; Biot-Savart-field; Boundary conditions; direct solver; Eddy currents; Edge effect; Finite element analysis; Finite element method; Insulation; Iron; iterative solver; Magnetic vector potentials; Mathematical models; thin iron sheets; Three-dimensional displays
• ISSN: 0885-8969; 1558-0059; 1558-0059
• DOI: 10.1109/TEC.2023.3333530

Multiscale finite element methods for 2D/1D problems have been studied in this work to demonstrate their excellent ability to solve the eddy current problem in a single iron sheet of electrical machines. We believe that these methods are much more efficient than conventional 3D finite element methods and just as accurate. The 2D/1D multiscale finite element methods are based on a magnetic vector potential or a current vector potential. Known currents for excitation can be replaced by the Biot-Savart-field. Boundary conditions allow to integrate planes of symmetry. All approaches consider eddy currents, an insulation layer and preserve the edge effect. A segment of a fictitious electrical machine has been studied to demonstrate all above options, the accuracy and the low computational costs of the 2D/1D multiscale finite element methods. Numerous simulations are presented. Direct and iterative solvers were investigated to reliably solve the system of equations from 2D/1D MSFEMs.