论文标题
依赖速度的VOIGT和RAUTIAN概况的计算方面
Computational Aspects of Speed-Dependent Voigt and Rautian Profiles
论文作者
论文摘要
为了使分子横截面的准确逐线建模必须考虑几个物理过程“超越voigt”。对于速度依赖性的Voigt和Rautian配置文件（SDV，SDR）和Hartmann-Tran配置文件，两个复杂错误函数（本质上是voigt函数）的差异$ W（i z _+）$必须评估在函数$ z_ pm $ z_ \ z_ pm $的位置，由两个函数$ z_ \ pm $通过两个sum and n sul of两个square and nower。描述$ z_ \ pm $的这两个术语可能是巨大的，差异的默认实现可能会导致较大的取消错误。首先，我们证明可以通过简单的$ z _- $重新重新重新重新重新重新进行这些问题来避免这些问题。此外，我们表明，复杂误差函数在整个复杂平面中有效的单个合理近似（例如，Humlicek，1979或Weideman，1994）可以计算SDV和SDR，具有四个有效的数字或更高的数字。我们的基准表明，与VOIGT函数相比，SDV和SDR函数的速度要慢2.2慢，但是对于分子横截面的评估，这段时间滞后并不能显着延长整个程序执行，因为仅速度依赖性参数仅适用于强的强线。
For accurate line-by-line modeling of molecular cross sections several physical processes "beyond Voigt" have to be considered. For the speed-dependent Voigt and Rautian profiles (SDV, SDR) and the Hartmann-Tran profile the difference $w(i z_-)-w(i z_+)$ of two complex error functions (essentially Voigt functions) has to be evaluated where the function arguments $z_\pm$ are given by the sum and difference of two square roots. These two terms describing $z_\pm$ can be huge and the default implementation of the difference can lead to large cancellation errors. First we demonstrate that these problems can be avoided by a simple reformulation of $z_-$. Furthermore we show that a single rational approximation of the complex error function valid in the whole complex plane (e.g. by Humlicek, 1979 or Weideman, 1994) enables computation of the SDV and SDR with four significant digits or better. Our benchmarks indicate that the SDV and SDR functions are about a factor 2.2 slower compared to the Voigt function, but for evaluation of molecular cross sections this time lag does not significantly prolong the overall program execution because speed-dependent parameters are available only for a fraction of strong lines.
