论文标题
偏光辐射的角度平均重新分布函数的快速准确近似
Fast and accurate approximation of the angle-averaged redistribution function for polarized radiation
论文作者
论文摘要
从计算的角度来看，众所周知，将光谱线曲线考虑到频率重新分布效应是一个挑战性的问题，尤其是当考虑到极化现象（原子极化和极化辐射）时。通过重新分布函数形式主义来方便地描述了频率重新分布效应，并且经常引入角度平均近似值以简化问题。即使在这种情况下，对极化辐射的发射系数的评估仍在计算上仍然是昂贵的，尤其是在存在磁场或复杂的原子模型时。我们旨在开发一种有效的算法来数字评估偏光辐射的角度平均重新分布函数。我们提出的方法是基于通过Trivariate多项式的低级别近似值，其单变量成分以Chebyshev表示。对于10^-6和10^-2之间的任何目标准确性，所得算法明显比基于标准的正交方案的速度明显快。
Modeling spectral line profiles taking frequency redistribution effects into account is a notoriously challenging problem from the computational point of view, especially when polarization phenomena (atomic polarization and polarized radiation) are taken into account. Frequency redistribution effects are conveniently described through the redistribution function formalism, and the angle-averaged approximation is often introduced to simplify the problem. Even in this case, the evaluation of the emission coefficient for polarized radiation remains computationally costly, especially when magnetic fields are present or complex atomic models are considered. We aim to develop an efficient algorithm to numerically evaluate the angle-averaged redistribution function for polarized radiation. Our proposed approach is based on a low-rank approximation via trivariate polynomials whose univariate components are represented in the Chebyshev basis. The resulting algorithm is significantly faster than standard quadrature-based schemes for any target accuracy in the range between 10^-6 and 10^-2.
