2D Fourier finite element formulation for magnetostatics in curvilinear coordinates with a symmetry direction

Christopher G. Albert; Oszkár Bíró; Patrick Lainer

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arXiv · 2008.13681

2D Fourier finite element formulation for magnetostatics in curvilinear coordinates with a symmetry direction

Christopher G. Albert·Oszkár Bíró·Patrick Lainer

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Abstract

We present a numerical method for the solution of linear magnetostatic problems in domains with a symmetry direction, including axial and translational symmetry. The approach uses a Fourier series decomposition of the vector potential formulation along the symmetry direction and covers both, zeroth (non-oscillatory) and non-zero (oscillatory) harmonics. For the latter it is possible to eliminate one component of the vector potential resulting in a fully transverse vector potential orthogonal to the transverse magnetic field. In addition to the Poisson-like equation for the longitudinal component of the non-oscillatory problem, a general curl-curl Helmholtz equation results for the transverse problem covering both, non-oscillatory and oscillatory case. The derivation is performed in the covariant formalism for curvilinear coordinates with a tensorial permeability and symmetry restrictions on metric and permeability tensor. The resulting variational forms are treated by the usual nodal finite element method for the longitudinal problem and by a two-dimensional edge element method for the transverse problem. The numerical solution can be computed independently for each harmonic which is favourable with regard to memory usage and parallelisation.

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Christopher G. Albert, Oszkár Bíró, Patrick Lainer. 2020-08-31. 2D Fourier finite element formulation for magnetostatics in curvilinear coordinates with a symmetry direction. https://arxiv.org/abs/2008.13681

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