Element diffusion in the atmospheres of magnetic, chemically peculiar upper main sequence (CP) stars is expected to produce complex surface abundance distributions. In view of modelling the buildup of these abundance inhomogeneities, we have developed a new numerical tool based on accurate polarised radiative transfer: the object-oriented diffusion code CARAT. Its novel approach to thread-parallel high-performance computing is discussed in some detail. Our first results show that radiative accelerations experienced by chemical elements in a stellar atmosphere can be strongly affected by Zeeman splitting due to magnetic fields of moderate strength (a few Teslas). Amplifications of the accelerations - relative to the zero-field case - are found to be strongly dependent on field strength and direction, reaching a maximum near the inclination of 60° between field vector and the vertical. They are also very sensitive to the Zeeman patterns of the spectral lines and to magneto-optical effects which can by no means be neglected as has often been done in the past.