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A sliding mesh-mortar method for a two dimensional eddy currents model of electric engines. (English) Zbl 0986.35111
Summary: The paper deals with the application of a non-conforming domain decomposition method to the problem of the computation of induced currents in electric engines with moving conductors. The eddy currents model is considered as a quasi-static approximation of Maxwell equations and we study its two-dimensional formulation with either the modified magnetic vector potential or the magnetic field as primary variable. Two discretizations are proposed, the first one based on curved finite elements and the second one based on iso-parametric finite elements in both the static and moving parts. The coupling is obtained by means of the mortar element method [cf. C. Bernardi, Y. Maday and A. T. Patera, A new nonconforming approach to domain decomposition: The mortar element method, Paris, 13-51 (1964; Zbl 0797.65094)] and the approximation on the whole domain turns out to be nonconforming. In both cases optimal error estimates are provided. Numerical tests are then proposed in the case of standard first-order finite elements to test the reliability and precision of the method. An application of the method to study the influence of the free part movement on the currents distribution is also provided.

MSC:
35Q60 PDEs in connection with optics and electromagnetic theory
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
68U20 Simulation (MSC2010)
78A30 Electro- and magnetostatics
65N15 Error bounds for boundary value problems involving PDEs
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