  We have developed a three-dimensional radiative transfer method designed
specifically for use with parallel adaptive mesh refinement hydrodynamics
codes. This new algorithm, which we call hybrid characteristics, introduces a
novel form of ray tracing that can neither be classified as long, nor as short
characteristics, but which applies the underlying principles, i.e. efficient
execution through interpolation and parallelizability, of both. Primary
applications of the hybrid characteristics method are radiation hydrodynamics
problems that take into account the effects of photoionization and heating due
to point sources of radiation. The method is implemented in the hydrodynamics
package FLASH. The ionization, heating, and cooling processes are modelled
using the DORIC ionization package. Upon comparison with the long
characteristics method, we find that our method calculates the column density
with a similarly high accuracy and produces sharp and well defined shadows. We
show the quality of the new algorithm in an application to the photoevaporation
of multiple over-dense clumps. We present several test problems demonstrating
the feasibility of our method for performing high resolution three-dimensional
radiation hydrodynamics calculations that span a large range of scales. Initial
performance tests show that the ray tracing part of our method takes less time
to execute than other parts of the calculation (e.g. hydrodynamics and adaptive
mesh refinement), and that a high degree of efficiency is obtained in parallel
execution. Although the hybrid characteristics method is developed for problems
involving photoionization due to point sources, the algorithm can be easily
adapted to the case of more general radiation fields.
