The Discontinuous Finite Element Method For Vector Radiative Transfer Equation

With the development of the technologies such as microwave remote sensing, biological tomography, laser cutting technology, the polarized factor in radiative transfer equation attracts more and more attention. Traditionally, the radiation intensity is the only factor concerned, the polarized information was neglected. While, a growing number of studies have showed that applying scalar radiative transfer equation in polarized radiation field calculation would induce significant errors. The radiation intensity in polarized field could be converted into polarized information. In this thesis, we use the discontinuous finite element method(DFEM) based on splited spatial unit for the numerical calculation of polarized radiative transfer equation and the comparisons between the calculation results respectively by the scalar radiative transfer equation and the vector radiative transfer equation are given in the end.The main contents of this thesis are:1. The information background of the polarized radiative transfer problem and the correlation coefficient of the polarized radiative transfer equation is reviewed.2. applying DFEM for the numerical calculation of polarized radiative transfer equation and compared with related papers to verify the accuracy and stability of the method.3. analyzing the nonphysical oscillations when angular discretion is not fine enough for the transient radiative transfer equation. Introduce the discontinuous petrove finite element method to deal with the problem and the computational stability is also validated.4. applying DFEM for the numerical calculation of transient polarized radiative transfer equation and analysis of the energy transfer is given.5. relative errors between the numerical results calculated respectively by SRTE and VRTE are given.