  We present an improved version of the SimpleX method for radiative transfer
on an unstructured Delaunay grid. The grid samples the medium through which
photons are transported in an optimal way for fast radiative transfer
calculations. In this paper we study the detailed working of SimpleX in test
problems and show improvements over the previous version of the method. We have
applied a direction conserving transport scheme that correctly transports
photons in the optically thin regime, a regime where the original SimpleX
algorithm lost its accuracy. In addition, a scheme of dynamic grid updates is
employed to ensure correct photon transport when the optical depth changes
during a simulation. For the application to large data sets, the method is
parallellised for distributed memory machines using MPI. To test the new
method, we have performed standard tests for cosmological radiative transfer.
We show excellent correspondence with both the analytical solution (when
available) and to the results of other codes compared to the former version of
SimpleX, without sacrificing the benefits of the high computational speed of
the method.
