Discrete diffusion Lyman-alpha radiative transfer
  Due to its accuracy and generality, Monte Carlo radiative transfer (MCRT) has
emerged as the prevalent method for Ly$\alpha$ radiative transfer in arbitrary
geometries. The standard MCRT encounters a significant efficiency barrier in
the high optical depth, diffusion regime. Multiple acceleration schemes have
been developed to improve the efficiency of MCRT but the noise from photon
packet discretization remains a challenge. The discrete diffusion Monte Carlo
(DDMC) scheme has been successfully applied in state-of-the-art radiation
hydrodynamics (RHD) simulations. Still, the established framework is not
optimal for resonant line transfer. Inspired by the DDMC paradigm, we present a
novel extension to resonant DDMC (rDDMC) in which diffusion in space and
frequency are treated on equal footing. We explore the robustness of our new
method and demonstrate a level of performance that justifies incorporating the
method into existing Ly$\alpha$ codes. We present computational speedups of
$\sim 10^2$-$10^6$ relative to contemporary MCRT implementations with schemes
that skip scattering in the core of the line profile. This is because the rDDMC
runtime scales with the spatial and frequency resolution rather than the number
of scatterings - the latter is typically $\propto \tau_0$ for static media, or
$\propto (a \tau_0)^{2/3}$ with core-skipping. We anticipate new frontiers in
which on-the-fly Ly$\alpha$ radiative transfer calculations are feasible in 3D
RHD. More generally, rDDMC is transferable to any computationally demanding
problem amenable to a Fokker-Planck approximation of frequency redistribution.
