A discrete 2-D Formulation for 3-D Field Problems with Continuous Symmetry

摘要

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.