Discontinuous Finite Element Method for One-dimensional Polarized Radiative Transfer

The discontinuous finite element method (DFEM) is applied to solved the polarized radiative transfer in a one-dimensional scattering medium. The derivation in a discrete form of the polarized radiation governing equations is presented, in which the spatial domain is discretized into finite non-overlapped discontinuous elements, and the angular space is discretized by the Piecewise Constant Approximation (PCA) approach with a local refined modification to obtain the numerical results for key directions. Two steady cases are tested to verify the accuracy and computational efficiency of the developed DFEM. The DFEM is then extended to solve the transient polarized radiative transfer in a scattering medium, the comparisons of the time-resolved Stokes vector with the steady ones show that the developed DFEM can handle the transient polarized radiative transfer in a scattering medium accurately.