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The last decade has seen applications of Adaptive Mesh Refinement (AMR)methods for a wide range of problems from space physics to cosmology. With theadvent of these methods, in which space is discretized into a mesh of manyindividual cubic elements, the contemporary analog of the extensively studiedline radiative transfer (RT) in a semi-infinite slab is that of RT in a cube.In this study we provide an approximate solution of the RT equation, as well asanalytic expressions for the probability distribution functions (pdfs) of theproperties of photons emerging from a cube, and compare them with thecorresponding slab problem. These pdfs can be used to perform fastresonant-line RT in optically thick AMR cells where, otherwise, it could takeunrealistically long times to transfer even a handful of photons.Comment: 5 two-column pages, 2 figures; matches accepted version, to appear on  Ap

On the Transfer of Resonant‐Line Radiation in Mesh Simulations