Convergence properties of the accelerated Λ-iteration method for the solution of radiative transfer problems

Abstract

We investigate the convergence properties and the computational speed of the accelerated Λ-iteration method for the solution of a wide variety of radiative transfer problems. The formal solution of the transfer equation is done using the short characteristics method. As the approximate Λ-operator we use bands of the discretized Λ-operator and derive the formulae for computing operators with arbitrary bandwidth. We define the optimum bandwidth of the approximate Λ-operator as the bandwidth for which the CPU time used for the solution of any particular radiative transfer problems is minimum. The radiative transfer equation is solved for a number of continuum and line transfer problems in spherical symmetry and for static to very rapidly expanding media. We find the optimum bandwidth is around 5–15 for workstation class computers whereas it is around 1–2 for supercomputers.