Spectral Element Method for Vector Radiative Transfer Equation

TL;DR

This paper introduces a spectral element method (SEM) for solving the multidimensional polarized radiative transfer equation, demonstrating high accuracy, efficiency, and exponential convergence with p-refinement, validated through various test problems.

Contribution

The paper develops a novel SEM using Chebyshev polynomials for polarized radiative transfer, showing superior convergence and accuracy over traditional methods.

Findings

p-refinement exhibits exponential convergence

SEM achieves high accuracy in angular distribution predictions

Numerical results confirm SEM's effectiveness and efficiency

Abstract

A spectral element method (SEM) is developed to solve polarized radiative transfer in multidimensional participating medium. The angular discretization is based on the discrete-ordinates approach, and the spatial discretization is conducted by spectral element approach. Chebyshev polynomial is used to build basis function on each element. Four various test problems are taken as examples to verify the performance of the SEM. The effectiveness of the SEM is demonstrated. The h and the p convergence characteristics of the SEM are studied. The convergence rate of p-refinement follows the exponential decay trend and is superior to that of h-refinement. The accuracy and efficiency of the higher order approximation in the SEM is well demonstrated for the solution of the VRTE. The predicted angular distribution of brightness temperature and Stokes vector by the SEM agree very well with the benchmark solutions in references. Numerical results show that the SEM is accurate, flexible and effective to solve multidimensional polarized radiative transfer problems.