A FORTH-AND-BACK IMPLICIT LAMBDA-ITERATION

In many radiative transfer (RT) problems, the sources contain a scatte ring term that couples all the specific RT equations, one for each fre quency and direction, so that solving the problem means solving the sy stem formed by these equations. Each of them is a first-order linear d ifferential equation with its own initial condition assigned at a diff erent point of the medium, which makes the solution of the system extr aordinarily difficult. One simple way to achieve a solution is with th e so-called Lambda-iteration: sources and sinks given as a first appro ximation --> computation of the specific intensities from their own RT equations --> computation of the scattering terms --> recomputation o f the sources and sinks. This scheme is straightforward, but unfortuna tely in practice its convergence rate is too slow to be of value in th e case of optically thick systems. The aim of this paper is to show th at a forth-and-back approach (the natural approach to describing seque ntially the two intensities propagating along the two directions of a straight line), together with an implicit representation of the source function in the computation of the intensities within the above itera tive scheme, can dramatically accelerate the convergence of the iterat ive process while retaining the straightforwardness of ordinary Lambda -iteration.