求解辐射转移问题的隐式积分法的改进
An improved version of the Implicit Integral Method to solving radiative transfer problems
摘要：
源函数中含有类散射积分的辐射转移（RT）问题是典型的两点边值问题。它们通过微分方程的解意味着对解本身，即辐射场的比强度I（τ;n）做出假设。相反，积分方法需要对源函数S（tau）做出假设。当然，对后者做假设看起来更合理，因为可以预期S（tau）随深度的运行比I（tau;n）的运行更平滑。在以前的工作中，我们假设一个分段抛物近似的源函数，这保证了连续的S（tau）和它的一阶导数在每个深度点。在这里，我们强加了二阶导数S”（τ）的连续性。换句话说，我们采用三次样条表示的源函数，这高度稳定的数值过程。
英文摘要：
Radiative transfer (RT) problems in which the source function includes a scattering-like integral are typical two-points boundary problems. Their solution via differential equations implies to make hypotheses on the solution itself, namely the specific intensity I(tau;n) of the radiation field. On the contrary, integral methods require to make hypotheses on the source function S(tau). It looks of course more reasonable to make hypotheses on the latter because one can expect that the run of S(tau) with depth be smoother than that of I(tau;n). In previous works we assumed a piece-wise parabolic approximation for the source function, which warrants the continuity of S(tau) and its first derivative at each depth point. Here we impose the continuity of the second derivative S"(tau). In other words, we adopt a cubic spline representation to the source function, which highly stabilize the numerical processes.
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