  We present TREVR2 (Tree-based REVerse Ray Tracing 2), a fast, general
algorithm for computing the radiation field, suitable for both particle and
mesh codes. It is designed to self-consistently evolve chemistry for zoomed-in
astrophysical simulations, such as cosmological galaxies with both internal
sources and prescribed background radiation, rather than large periodic
volumes. Light is propagated until absorbed, with no imposed speed limit other
than those due to opacity changes (e.g. ionization fronts). TREVR2 searches
outward from receiving gas in discrete directions set by the HEALPIX algorithm
(unlike its slower predecessor TREVR), accumulating optical depth and adding
the flux due to sources combined into progressively larger tree cells with
distance. We demonstrate $N_\textrm{active}\log_2 N$ execution time with
absorption and many sources. This allows multi-band RT costs comparable to
tree-based gravity and hydrodynamics, and the usual speed-up when active
particles evolve on individual timesteps. Sources embedded in non-homogeneous
absorbing material introduce systematic errors. We introduce transmission
averaging instead of absorption averaging which dramatically reduces these
systematic effects. We outline other ways to address systematics including an
explicit complex source model. We demonstrate the overall performance of the
method via a set of astrophysical test problems.
