  We present TRAPHIC, a novel radiative transfer scheme for Smoothed Particle
Hydrodynamics (SPH) simulations. TRAPHIC is designed for use in simulations
exhibiting a wide dynamic range in physical length scales and containing a
large number of light sources. It is adaptive both in space and in angle and
can be employed for application on distributed memory machines. The commonly
encountered computationally expensive scaling with the number of light sources
in the simulation is avoided by introducing a source merging procedure. The
(time-dependent) radiative transfer equation is solved by tracing individual
photon packets in an explicitly photon-conserving manner directly on the
unstructured grid traced out by the set of SPH particles. To accomplish
directed transport of radiation despite the irregular spatial distribution of
the SPH particles, photons are guided inside cones. We present and test a
parallel numerical implementation of TRAPHIC in the SPH code GADGET-2,
specified for the transport of mono-chromatic hydrogen-ionizing radiation. The
results of the tests are in excellent agreement with both analytic solutions
and results obtained with other state-of-the-art radiative transfer codes.
