AbstractThe particle‐in‐cell method is coupled with boundary‐fitted co‐ordinates in order to model the stationary Maxwell–Lorentz problem in technical devices. New numerical algorithms describing the transition between the grid model and the mesh‐free model are developed and the existing techniques of finite difference schemes for equidistant grids are extended to non‐equidistant, arbitrarily shaped, convex four‐point meshes. The modelling process is described, and both the numerical approximation and the algorithms are discussed. Applications in different technical devices show the flexibilit