Accelerating NLTE radiative transfer by means of the Forth-and-Back Implicit Lambda Iteration: A two-level atom line formation in 2D Cartesian coordinates

摘要

State-of-the-art methods in multidimensional NLTE radiative transfer arebased on the use of local approximate lambda operator within either Jacobi orGauss-Seidel iterative schemes. Here we propose another approach to thesolution of 2D NLTE RT problems, Forth-and-Back Implicit Lambda Iteration(FBILI), developed earlier for 1D geometry. In order to present the method andexamine its convergence properties we use the well-known instance of thetwo-level atom line formation with complete frequency redistribution. In theformal solution of the RT equation we employ short characteristics withtwo-point algorithm. Using an implicit representation of the source function inthe computation of specific intensities, we compute and store the coefficientsof the linear relations J = a + bS between the mean intensity J and thecorresponding source function S. The use of iteration factors in the 'local'coefficients of these implicit relations in two 'inward' directions, along withthe update of the source function in other two, 'outward', directions leads tofour times faster solution than the Jacobi's one. Moreover, the update made inall four consecutive sweeps of the grid leads to an acceleration by a factor of6-7 compared to the Jacobi iterative scheme.