  The development and implementation of GEAR-RT, a radiative transfer solver
using the M1 closure in the open source code SWIFT, is presented, and validated
using standard tests for radiative transfer. GEAR-RT is modeled after RAMSES-RT
(Rosdahl et al. 2013) with some key differences. Firstly, while RAMSES-RT uses
Finite Volume methods and an Adaptive Mesh Refinement (AMR) strategy, GEAR-RT
employs particles as discretization elements and solves the equations using a
Finite Volume Particle Method (FVPM). Secondly, GEAR-RT makes use of the
task-based parallelization strategy of SWIFT, which allows for optimized load
balancing, increased cache efficiency, asynchronous communications, and a
domain decomposition based on work rather than on data. GEAR-RT is able to
perform sub-cycles of radiative transfer steps w.r.t. a single hydrodynamics
step. Radiation requires much smaller time step sizes than hydrodynamics, and
sub-cycling permits calculations which are not strictly necessary to be
skipped. Indeed, in a test case with gravity, hydrodynamics, and radiative
transfer, the sub-cycling is able to reduce the runtime of a simulation by over
90%. Allowing only a part of the involved physics to be sub-cycled is a
contrived matter when task-based parallelism is involved, and is an entirely
novel feature in SWIFT.
  Since GEAR-RT uses a FVPM, a detailed introduction into Finite Volume methods
and Finite Volume Particle Methods is presented. In astrophysical literature,
two FVPM methods are written about: Hopkins (2015) have implemented one in
their GIZMO code, while the one mentioned in Ivanova et al. (2013) isn't used
to date. In this work, I test an implementation of the Ivanova et al. (2013)
version, and conclude that in its current form, it is not suitable for use with
particles which are co-moving with the fluid, which in turn is an essential
feature for cosmological simulations.
