Three-dimensional polarized radiative transfer simulation using discontinuous finite element method

The polarized radiative transfer problem in three-dimensional scattering media is numerically solved by the discontinuous finite element method (DFEM). The discrete elements in the DFEM simulation are assumed to be discontinuous and the solution domain is connected by modeling the boundary numerical flux between adjacent elements, which makes the DFEM numerically stable for solving the radiative transfer equation. The shape functions are constructed on each element and the transformations between a general element and the standard element are presented. The accuracy of the DFEM for three-dimensional polarized radiative transfer is validated by comparing DFEM solutions with the published data in the literature. The DFEM is then applied to study the polarized radiative transfer problems in a cubic medium exposed to an external beam and in a cubic medium with an emitting surface. The distributions of the Stokes vector components are obtained and discussed.