An Efficient Solution Technique for the Radiative Transfer Equation

The discretization of the multi{dimensional radiative transfer equation results in a very large linear system of equations. The standard solution method used by astrophysicists is a simpliied xed point iteration (called approximate {iteration) which becomes slow for problems most interesting in astrophysics. As an alternative, a class of (block) conjugate gradient{like methods is proposed, together with special preconditioners for coping with the nonsymmetry and the bad condition number. The eeciency of these new solvers in combination with a nite element upwind scheme on problem adapted nonuniform grids is demonstrated by several test calculations for physically relevant data.