  Context. Three-dimensional non-local thermodynamical equilibrium (NLTE)
radiative transfer calculations are a fundamental tool for a detailed spectral
analysis in stellar atmospheres, but require vast amounts of computer power.
This prevents their broader application. Aims. We undertake a first exploration
of the use of 3D irregular grids in stellar atmospheres. In particular, we aim
to test whether irregular grids can be used to speed up the 3D NLTE problem, in
the same way as depth optimisation can lead to faster running times in 1D.
Methods. We created irregular grids based on 3D Voronoi diagrams, sampling
different distributions from a 3D radiation-magnetohydrodynamic Bifrost
simulation. We developed a method for solving radiation on the 3D irregular
grid and implemented a simple NLTE solver using $\Lambda$-iteration and
statistical equilibrium. We applied this to a simplified hydrogen-like atom and
studied the convergence properties and accuracy of the irregular grid methods.
For reference, we compared them to a standard short-characteristics solver on a
regular grid. Results. We find that our method for radiation in irregular grids
gives similar results to those from regular grids, and that it is possible to
obtain nearly the same results with about ten times fewer points in the
irregular grid for the continuum intensity in local thermodynamical
equilibrium. We find that the irregular grid can give good results for the NLTE
problem, but it takes four times longer per iteration than the regular grid,
and it converges in about the same number of iterations. This makes it
particularly inefficient. Our formulation therefore does not lead to an
improvement. We also find that the design of the irregular grid is crucial for
accurate results, and find it non-trivial to design an irregular grid that can
work well across a wide range of heights.
