A Discrete 2-D Formulation for 3-D Field Problems With Continuous Symmetry

In this paper, we describe a general formalism that allows to reduce the spatial dimension of a field problem from 3-D to (2$+$1)-D. Subsequently, we identify conditions under which the third dimension can be eliminated. We see that the resulting 2-D field problems only decouple if an orthogonality criterion is fulfilled. The approach is based solely on differential-form calculus and can therefore be easily transferred into a discrete setting. As a numerical example, we compute the field of twisted wires.