A 3D radiative transfer framework: III. periodic boundary conditions
  We present a general method to solve radiative transfer problems including scattering in the continuum as well as in lines in 3D configurations with periodic boundary conditions. he scattering problem for line transfer is solved via means of an operator splitting (OS) technique. The formal solution is based on a full characteristics method. The approximate $\Lambda$ operator is constructed considering nearest neighbors exactly. The code is parallelized over both wavelength and solid angle using the MPI library. We present the results of several test cases with different values of the thermalization parameter and two choices for the temperature structure. The results are directly compared to 1D plane parallel tests. The 3D results agree very well with the well-tested 1D calculations. 
Peter H. Hauschildt, E. Baron