CONVERGENCE PROPERTIES OF THE ACCELERATED LAMBDA-ITERATION METHOD FOR THE SOLUTION OF RADIATIVE-TRANSFER PROBLEMS

We investigate the convergence properties and the computational speed of the accelerated LAMBDA-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 LAMBDA-operator we use bands or the discretized LAMBDA-operator and derive the formulae for computing operators with arbitrary bandwidth. We define the optimum bandwidth of the approximate LAMBDA-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.