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) radiat ive transfer equation which resulted in a high-dimensional linear syst em of equations. Using the concept of the generalized mean intensity, the dimension of the system can be drastically diminished, without los ing any information. Additionally, the corresponding system matrices a re positive definite under appropriate conditions on the choice of the discrete ordinates and, therefore, the classical conjugate gradient-i teration (CG) is converging. In connection with local preconditioners, we develop robust and efficient methods of conjugate gradient type wh ich are superior to the classical approximate LAMBDA-iteration, but wi th about the same numerical effort. For some numerical tests, which si mulate the astrophysically interesting case of radiation of stars in d ust clouds, we compare the methods derived and give some examples for their efficiency.