部分频率重分布下辐射转移的Gauss-Seidel和逐次超松弛方法
Gauss-Seidel and Successive Overrelaxation Methods for Radiative Transfer with Partial Frequency Redistribution
摘要：
由散射过程产生的线偏振太阳临边光谱包含了大量关于太阳外层大气的物理条件和磁场的信息，但对其许多最强谱线的建模需要解决一个涉及部分再分布（PRD）效应的非LTE辐射转移问题。快速辐射转移方法的PRD问题的数值解也需要一个适当的处理氢线时，针对现实的时间依赖的磁流体动力学模拟的太阳色球。在这里，我们展示了如何通过应用基于高斯-赛德尔（GS）和连续超松弛（SOR）辐射转移方法的高度收敛的迭代方案，可以准确和有效地解决两个能级原子的PRD问题，并没有偏振完全重新分布（CRD）的情况下。特别感兴趣的是对称SOR方法，它使我们能够达到完全收敛的解决方案的数量级的改善，在总的计算时间相对于Jacobi为基础的本地ALI（加速λ迭代）方法。
英文摘要：
The linearly-polarized solar limb spectrum that is produced by scattering processes contains a wealth of information on the physical conditions and magnetic fields of the solar outer atmosphere, but the modeling of many of its strongest spectral lines requires solving an involved non-LTE radiative transfer problem accounting for partial redistribution (PRD) effects. Fast radiative transfer methods for the numerical solution of PRD problems are also needed for a proper treatment of hydrogen lines when aiming at realistic time-dependent magnetohydrodynamic simulations of the solar chromosphere. Here we show how the two-level atom PRD problem with and without polarization can be solved accurately and efficiently via the application of highly convergent iterative schemes based on the Gauss-Seidel (GS) and Successive Overrelaxation (SOR) radiative transfer methods that had been previously developed for the complete redistribution (CRD) case. Of particular interest is the Symmetric SOR method, which allows us to reach the fully converged solution with an order of magnitude of improvement in the total computational time with respect to the Jacobi-based local ALI (Accelerated Lambda Iteration) method.
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