Efficient algorithmic implementation of the Voigt/complex error function based on exponential series approximation

被引:66
作者
Abrarov, S. M. [1 ]
Quine, B. M. [1 ,2 ]
机构
[1] York Univ, Dept Earth & Space Sci & Engn, Toronto, ON M3J 1P3, Canada
[2] York Univ, Dept Phys & Astron, Toronto, ON M3J 1P3, Canada
关键词
Complex error function; Voigt function; Faddeeva function; Weideman's algorithm; Complex probability function; Plasma dispersion function; Spectral line broadening; VOIGT PROFILE FUNCTION; HUMLICEK ALGORITHM; COMPUTATION;
D O I
10.1016/j.amc.2011.06.072
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We show that a Fourier expansion of the exponential multiplier yields an exponential series that can compute high-accuracy values of the complex error function in a rapid algorithm. Numerical error analysis and computational test reveal that with essentially higher accuracy it is as fast as FFT-based Weideman's algorithm at a regular size of the input array and considerably faster at an extended size of the input array. As this exponential series approximation is based only on elementary functions, the algorithm can be implemented utilizing freely available functions from the standard libraries of most programming languages. Due to its simplicity, rapidness, high-accuracy and coverage of the entire complex plane, the algorithm is efficient and practically convenient in numerical methods related to the spectral line broadening and other applications requiring error-function evaluation over extended input arrays. (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码:1894 / 1902
页数:9
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