Spectral‐element method for high‐speed rotating cylinders

Herbert De Gersem (Faculty of Sciences, Katholieke Universiteit Leuven, Kortrijk, Belgium)



The purpose of this paper is to offer a fast and reliable discretisation scheme for computing the electromagnetic fields inside a ferromagnetic cylinder, accounting for motional eddy currents under high velocities and accounting for the severe ferromagnetic saturation of the rotor surface.


A nonlinear spectral‐element (SE) formulation is developed and compared to existing analytical and finite‐element approaches.


The proposed SE method results in a higher accuracy, allows for smaller models, avoids upwinding and needs less computation time. Disadvantages are the dense system matrix and the bad condition number.

Research limitations/implications

The SE approach is only developed and tested for 2D models with a single cylindrical domain.

Practical implications

The results of the paper may improve the design and optimisation of solid‐rotor induction machines and magnetic bearings.


The paper offers an appropriate solution for a computational problem, which already has been encountered by a large community of researchers and engineers dealing with high‐speed rotating devices.



De Gersem, H. (2009), "Spectral‐element method for high‐speed rotating cylinders", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 28 No. 3, pp. 730-740. https://doi.org/10.1108/03321640910940981

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