Abstract
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 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 aggressive
core-skipping. This is because the resonant DDMC runtime scales with the
spatial and frequency resolution rather than the number of scatterings - the
latter is typically $\tau_0$ for static media, or $(a
\tau_0)^2/3$ with core-skipping. We anticipate new frontiers in which
on-the-fly Ly$\alpha$ radiative transfer calculations are feasible in 3D RHD.
More generally, resonant DDMC is transferable to any computationally demanding
problem amenable to a Fokker-Planck approximation of frequency redistribution.
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