کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5429508 | 1397356 | 2011 | 16 صفحه PDF | دانلود رایگان |
Rational functions are frequently used as efficient yet accurate numerical approximations for real and complex valued functions. For the complex error function w(x+iy), whose real part is the Voigt function K(x,y), code optimizations of rational approximations are investigated. An assessment of requirements for atmospheric radiative transfer modeling indicates a y range over many orders of magnitude and accuracy better than 10â4. Following a brief survey of complex error function algorithms in general and rational function approximations in particular the problems associated with subdivisions of the x, y plane (i.e., conditional branches in the code) are discussed and practical aspects of Fortran and Python implementations are considered. Benchmark tests of a variety of algorithms demonstrate that programming language, compiler choice, and implementation details influence computational speed and there is no unique ranking of algorithms. A new implementation, based on subdivision of the upper half-plane in only two regions, combining Weideman's rational approximation for small |x|+y<15 and Humlicek's rational approximation otherwise is shown to be efficient and accurate for all x, y.
Research highlights⺠Function arguments spanning many orders of magnitude. ⺠No approximation good for all arguments, but two subregions sufficient. ⺠Line center: just a few evaluations, accuracy more important than speed. ⺠Combination of two rational approximations: Weideman and asymptotic Humlicek. ⺠Code performance is system dependent, no unique ranking of algorithms.
Journal: Journal of Quantitative Spectroscopy and Radiative Transfer - Volume 112, Issue 6, April 2011, Pages 1010-1025