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Finite element differential-algebraic systems for eddy current problems. (English) Zbl 1012.78015

Summary: Finite element discretization of some time-dependent eddy current problems yields ordinary differential-algebraic systems with large sparse matrices. Properties and stability of these systems are analyzed for two classes of eddy current problems: (i) two-dimensional coupled field-circuit problems with arbitrary external circuit connections between conductors; (ii) “2.5-dimensional” problems characterized by axisymmetric geometry and non-axisymmetric excitation. Extension of the analysis to many other formulations of eddy current problems in 2D and 3D is straightforward.

MSC:

78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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