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Electrical 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.

The 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.

This 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.

The 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.

Globalisation is generally defined as the “denationalisation of clusters of political, economic, and social activities” that destabilize the ability of the sovereign State to control activities on its territory, due to the rising need to find solutions for universal problems, like the pollution of the environment, on an international level. Globalisation is a complex, forceful legal and social process that take place within an integrated whole with out regard to geographical boundaries. Globalisation thus differs from international activities, which arise between and among States, and it differs from multinational activities that occur in more than one nation‐State. This does not mean that countries are not involved in the sociolegal dynamics that those transboundary process trigger. In a sense, the movements triggered by global processes promote greater economic interdependence among countries. Globalisation can be traced back to the depression preceding World War II and globalisation at that time included spreading of the capitalist economic system as a means of getting access to extended markets. The first step was to create sufficient export surplus to maintain full employment in the capitalist world and secondly establishing a globalized economy where the planet would be united in peace and wealth. The idea of interdependence among quite separate and distinct countries is a very important part of talks on globalisation and a significant side of today’s global political economy.