Schreier, Franz (2011) Optimized implementations of rational approximations for the Voigt and complex error function. Journal of Quantitative Spectroscopy and Radiative Transfer, 112 (6), pp. 1010-1025. Elsevier. DOI: 10.1016/j.jqsrt.2010.12.010.
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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 10−4. 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.
|Title:||Optimized implementations of rational approximations for the Voigt and complex error function|
|Journal or Publication Title:||Journal of Quantitative Spectroscopy and Radiative Transfer|
|In ISI Web of Science:||Yes|
|Page Range:||pp. 1010-1025|
|Keywords:||Plasma dispersion function; Complex probability function; Python; Fortran; Atmospheric radiative transfer|
|HGF - Research field:||Aeronautics, Space and Transport (old)|
|HGF - Program:||Space (old)|
|HGF - Program Themes:||W EO - Erdbeobachtung|
|DLR - Research area:||Space|
|DLR - Program:||W EO - Erdbeobachtung|
|DLR - Research theme (Project):||W - Vorhaben Entwicklung von Atmosphärenprozessoren (old)|
|Institutes and Institutions:||Remote Sensing Technology Institute > Atmospheric Processors|
|Deposited By:||Dr.rer.nat. Franz Schreier|
|Deposited On:||02 Mar 2011 06:28|
|Last Modified:||26 Mar 2013 12:27|
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