Reconstruction of three-dimensional eddy-current effects from two-dimensional simulations

Develop a reliable reconstruction of genuinely three-dimensional eddy-current effects from two-dimensional simulations, and rigorously justify hybrid reconstruction strategies through error estimation and asymptotic analysis.

Background

The paper develops a global linear correction strategy for estimating eddy-current reaction fields from two-dimensional nonlinear magnetostatic simulations and demonstrates its accuracy for a two-dimensional permanent-magnet synchronous motor model. Although the splitting strategy is stated to be applicable in two and three space dimensions, the paper does not resolve how genuinely three-dimensional effects can be recovered from two-dimensional computations.

Existing hybrid approaches cited by the paper require substantial additional modelling and computational effort, and their benefits have not been demonstrated conclusively. The authors identify both the reconstruction problem and the need for rigorous error estimates and asymptotic analysis as unresolved research directions.

References

Recovering genuinely three-dimensional effects from two-dimensional simulations, however, remains an open challenge. Existing hybrid approaches require substantial additional modelling and computational effort, while their benefits have not yet been demonstrated conclusively. A rigorous justification of such reconstruction strategies by error estimation and asymptotic analysis therefore remains an important topic for future research.

— Efficient computation of eddy-currents for nonlinear magnetic field problems  (2608.17860 - Egger et al., 18 Aug 2026) in Section 5, Discussion