Abstract
The discretization of the multidimensional radiative transfer equation results in a very large linear system of equations. The standard solution method used by astrophysicists is a simplified fixed-point iteration (called approximate Λ-iteration),which becomes slow for the 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 efficiency of these new solvers in combination with a finite-element upwind scheme on problem-adapted nonuniform grids is demonstrated by several test calculations for physically relevant data.
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