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The Voigt and complex error function: Humlicek's rational approximation generalized

Schreier, Franz (2018) The Voigt and complex error function: Humlicek's rational approximation generalized. Monthly Notices of the Royal Astronomical Society, 479, pp. 3068-3075. Oxford University Press. doi: 10.1093/mnras/sty1680. ISSN 0035-8711.

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Official URL: https://doi.org/10.1093/mnras/sty1680


Accurate yet efficient computation of the Voigt and complex error function is a challenge since decades in astrophysics and other areas of physics. Rational approximations have attracted considerable attention and are used in many codes, often in combination with other techniques. The 12-term code "cpf12" of Humlicek achieves an accuracy of five to six significant digits throughout the entire complex plane. Here we generalize this algorithm to a larger (even) number of terms. The n = 16 approximation has a relative accuracy better than 10-5 for almost the entire complex plane except for very small imaginary values of the argument even without the correction term required for the cpf12 algorithm. With 20 terms the accuracy is better than 10-6. In addition to the accuracy assessment we discuss methods for optimization and propose a combination of the 16-term approximation with the asymptotic approximation of the w4 code of Humlicek for high efficiency.

Item URL in elib:https://elib.dlr.de/120657/
Document Type:Article
Title:The Voigt and complex error function: Humlicek's rational approximation generalized
AuthorsInstitution or Email of AuthorsAuthor's ORCID iD
Schreier, Franzfranz.schreier (at) dlr.dehttps://orcid.org/0000-0001-7196-6599
Date:June 2018
Journal or Publication Title:Monthly Notices of the Royal Astronomical Society
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In ISI Web of Science:Yes
DOI :10.1093/mnras/sty1680
Page Range:pp. 3068-3075
Publisher:Oxford University Press
Keywords:Complex error function; Complex probability function; Plasma dispersion function; Fadde(y)eva function
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Earth Observation
DLR - Research area:Raumfahrt
DLR - Program:R EO - Earth Observation
DLR - Research theme (Project):Vorhaben Spectroscopic Methods in Remote Sensing (old)
Location: Oberpfaffenhofen
Institutes and Institutions:Remote Sensing Technology Institute > Atmospheric Processors
Deposited By: Schreier, Dr.rer.nat. Franz
Deposited On:02 Jul 2018 11:48
Last Modified:06 Sep 2019 15:17

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