Polarized radiative transfer in complex media exposed to external irradiation

Abstract Polarized radiative transfer problems in two-dimensional complex media exposed to external irradiation are numerically investigated. The numerical algorithm used is a discontinuous finite element method (DFEM) where unstructured triangular meshes are applied to discretize the computational domain with irregular geometries. In the DFEM application, the discrete elements are assumed to be separated from each other, the shape functions are locally constructed on each element, and the computation domain is connected by simulating the numerical flux across the inner-element boundaries using the up-winding scheme. Thus the DFEM can eliminate the computation errors in the conventional finite element method (FEM) where the inner-elements are forced to be continuous. In this paper, the derivation of the DFEM discretization for vector radiative transfer equation (VRTE) is presented, the correctness of the DFEM for VRTE is validated, and polarized radiative transfer problems in several irregular media are carried out. The distributions of Stokes vector components and radiative flux are presented and analyzed.