A generalized mean intensity approach for the numerical solution of the radiative transfer equation

In [7] we proposed a general numerical approach to the (linear) radiative transfer equation which resulted in a high-dimensional linear system of equations. Using the concept of the generalized mean intensity, the dimension of the system can be drastically diminished, without losing any information. Additionally, the corresponding system matrices are positive definite under appropriate conditions on the choice of the discrete ordinates and, therefore, the classical conjugate gradient-iteration (CG) is converging. In connection with local preconditioners, we develop robust and efficient methods of conjugate gradient type which are superior to the classical approximate Λ-iteration, but with about the same numerical effort. For some numerical tests, which simulate the astrophysically interesting case of radiation of stars in dust clouds, we compare the methods derived and give some examples for their efficiency.