2D Fourier finite element formulation for magnetostatics in curvilinear coordinates with a symmetry direction
Christopher G. Albert, Patrick Lainer, Oszkár Bíró
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.
BibTeX
@article{Albert_2022,
title={2D Fourier finite element formulation for magnetostatics in curvilinear coordinates with a symmetry direction},
volume={277},
ISSN={0010-4655},
url={http://dx.doi.org/10.1016/j.cpc.2022.108401},
DOI={10.1016/j.cpc.2022.108401},
journal={Computer Physics Communications},
publisher={Elsevier BV},
author={Albert, Christopher G. and Lainer, Patrick and Bíró, Oszkár},
year={2022},
month=aug,
pages={108401} }