Near optimal angular quadratures for polarised radiative transfer

In three-dimensional (3D) radiative transfer (RT) problems, the tensor product quadratures are generally not optimal in terms of the number of discrete ray directions needed for a given accuracy of the angular integration of the radiation field. In this paper, we derive a new set of angular quadrature rules more suitable for solving 3D RT problems with the short- and long-characteristics formal solvers. These quadratures are more suitable than the currently used ones for numerical calculation of the radiation field tensors that are relevant in non-LTE radiative transfer problems with polarisation. We show that our new quadratures can save up to about 30 % of computing time with respect to the Gaussian-trapezoidal product quadratures with the same accuracy.