# Simulation of electrical machines: a FEM-BEM coupling scheme

Simulation of electrical machines: a FEM-BEM coupling scheme PurposeElectrical machines commonly consist of moving and stationary parts. The field simulation of such devices can be demanding if the underlying numerical scheme is solely based on a domain discretization, such as in the case of the finite element method (FEM). This paper aims to present a coupling scheme based on FEM together with boundary element methods (BEMs) that neither hinges on re-meshing techniques nor deals with a special treatment of sliding interfaces. While the numerics are certainly more involved, the reward is obvious: the modeling costs decrease and the application engineer is provided with an easy-to-use, versatile and accurate simulation tool.Design/methodology/approachThe authors present the implementation of a FEM-BEM coupling scheme in which the unbounded air region is handled by the BEM, while only the solid parts are discretized by the FEM. The BEM is a convenient tool to tackle unbounded exterior domains, as it is based on the discretization of boundary integral equations (BIEs) that are defined only on the surface of the computational domain. Hence, no meshing is required for the air region. Further, the BIEs fulfill the decay and radiation conditions of the electromagnetic fields such that no additional modeling errors occur.FindingsThis work presents an implementation of a FEM-BEM coupling scheme for electromagnetic field simulations. The coupling eliminates problems that are inherent to a pure FEM approach. In detail, the benefits of the FEM-BEM scheme are: the decay conditions are fulfilled exactly, no meshing of parts of the exterior air region is necessary and, most importantly, the handling of moving parts is incorporated in an intriguingly simple manner. The FEM-BEM formulation in conjunction with a state-of-the-art preconditioner demonstrates its potency. The numerical tests not only reveal an accurate convergence behavior but also prove the algorithm to be suitable for industrial applications.Originality/valueThe presented FEM-BEM scheme is a mathematically sound and robust implementation of a theoretical work presented a decade ago. For the application within an industrial context, the original work has been extended by higher-order schemes, periodic boundary conditions and an efficient treatment of moving parts. While not intended to be used under all circumstances, it represents a powerful tool in case that high accuracies together with simple mesh-handling facilities are required. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering Emerald Publishing

# Simulation of electrical machines: a FEM-BEM coupling scheme

, Volume 36 (5): 12 – Sep 4, 2017
12 pages

/lp/emerald-publishing/simulation-of-electrical-machines-a-fem-bem-coupling-scheme-iEGLjkY5xd

# References (23)

Publisher
Emerald Publishing
ISSN
0332-1649
DOI
10.1108/COMPEL-02-2017-0061
Publisher site
See Article on Publisher Site

### Abstract

PurposeElectrical machines commonly consist of moving and stationary parts. The field simulation of such devices can be demanding if the underlying numerical scheme is solely based on a domain discretization, such as in the case of the finite element method (FEM). This paper aims to present a coupling scheme based on FEM together with boundary element methods (BEMs) that neither hinges on re-meshing techniques nor deals with a special treatment of sliding interfaces. While the numerics are certainly more involved, the reward is obvious: the modeling costs decrease and the application engineer is provided with an easy-to-use, versatile and accurate simulation tool.Design/methodology/approachThe authors present the implementation of a FEM-BEM coupling scheme in which the unbounded air region is handled by the BEM, while only the solid parts are discretized by the FEM. The BEM is a convenient tool to tackle unbounded exterior domains, as it is based on the discretization of boundary integral equations (BIEs) that are defined only on the surface of the computational domain. Hence, no meshing is required for the air region. Further, the BIEs fulfill the decay and radiation conditions of the electromagnetic fields such that no additional modeling errors occur.FindingsThis work presents an implementation of a FEM-BEM coupling scheme for electromagnetic field simulations. The coupling eliminates problems that are inherent to a pure FEM approach. In detail, the benefits of the FEM-BEM scheme are: the decay conditions are fulfilled exactly, no meshing of parts of the exterior air region is necessary and, most importantly, the handling of moving parts is incorporated in an intriguingly simple manner. The FEM-BEM formulation in conjunction with a state-of-the-art preconditioner demonstrates its potency. The numerical tests not only reveal an accurate convergence behavior but also prove the algorithm to be suitable for industrial applications.Originality/valueThe presented FEM-BEM scheme is a mathematically sound and robust implementation of a theoretical work presented a decade ago. For the application within an industrial context, the original work has been extended by higher-order schemes, periodic boundary conditions and an efficient treatment of moving parts. While not intended to be used under all circumstances, it represents a powerful tool in case that high accuracies together with simple mesh-handling facilities are required.

### Journal

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic EngineeringEmerald Publishing

Published: Sep 4, 2017