  Numerical models for the atmospheres of magnetic ApBp stars have in the past
dealt only with centred dipole magnetic field geometries. These models include
atomic diffusion that stratifies the abundances of metals according to the
local magnetic field strength and the direction with respect to the surface
normal. The magnetic variations with rotational phase of most well observed
stars however reveal that this assumption is far too simplistic. In this work
we establish for the first time a three-dimensional (3D) model with abundance
stratifications arising from atomic diffusion of 16 metals, adopting a
non-axisymmetric magnetic field geometry inspired by the configuration derived
for a real ApBp star. We find that the chemical elements are distributed in
complex patterns in all three dimensions, far from the simple rings that have
been proposed as the dominant abundance structures from calculations that
assume a perfectly centred dipolar magnetic geometry
