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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Abstract
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.
Item URL in elib: | https://elib.dlr.de/69057/ | ||||||
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Document Type: | Article | ||||||
Title: | Optimized implementations of rational approximations for the Voigt and complex error function | ||||||
Authors: |
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Date: | 2011 | ||||||
Journal or Publication Title: | Journal of Quantitative Spectroscopy and Radiative Transfer | ||||||
Refereed publication: | Yes | ||||||
Open Access: | No | ||||||
Gold Open Access: | No | ||||||
In SCOPUS: | Yes | ||||||
In ISI Web of Science: | Yes | ||||||
Volume: | 112 | ||||||
DOI : | 10.1016/j.jqsrt.2010.12.010 | ||||||
Page Range: | pp. 1010-1025 | ||||||
Publisher: | Elsevier | ||||||
Status: | Published | ||||||
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) | ||||||
Location: | Oberpfaffenhofen | ||||||
Institutes and Institutions: | Remote Sensing Technology Institute > Atmospheric Processors | ||||||
Deposited By: | Schreier, Dr.rer.nat. Franz | ||||||
Deposited On: | 02 Mar 2011 07:28 | ||||||
Last Modified: | 06 Sep 2019 15:28 |
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