Evaluation of the generalized Fermi-Dirac integral and its derivatives for moderate/large values of the parameters. New version announcement

IF 7.2 2区物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computer Physics Communications Pub Date : 2025-04-02 DOI:10.1016/j.cpc.2025.109605

Amparo Gil , Andrzej Odrzywołek , Javier Segura , Nico M. Temme

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引用次数: 0

Abstract

A revised version of the Matlab implementations of the expansions for the Fermi-Dirac integral and its derivatives is presented. In the new version, our functions for computing the Kummer functions

M (a, b, x)

and

U (a, b, x)

are incorporated into the software. The algorithms for computing the Kummer functions are described in [1,2]. In this way, the implementations of the expansions for the Fermi-Dirac integral can be used in earlier Matlab versions and can be easily adapted to GNU Octave. The efficiency of the computations is also greatly improved.

New version program summary

Program Title: FermiDiracExpans

CPC Library link to program files: https://doi.org/10.17632/sk34wtcxhh.2

Licensing provisions: GPLv3

Programming language: Matlab

Journal reference of previous version: Comput. Phys. Commun. 283 (2023) 108563

Does the new version supersede the previous version?: Yes

Reasons for the new version: With the new version, the implementations of the expansions for the Fermi-Dirac integral can be used in earlier Matlab versions and can be easily adapted to GNU Octave. The efficiency of the computations is also greatly improved.

Summary of revisions: The built-in Matlab functions kummerU and hypergeom are replaced by our functions Uabx and Mabx, respectively. These functions improve both the accuracy and efficiency of the built-in Matlab functions for computing the Kummer functions. A few relations satisfied by the Kummer functions are used to adapt the expressions in the expansions involving Kummer functions with negative parameters into expressions with real positive parameters and arguments, as used in our algorithms for Kummer functions.

Nature of problem: The evaluation of the relativistic Fermi-Dirac function and its partial derivatives is needed in different problems in applied and theoretical physics, such as stellar astrophysics, plasma physics or electronics.

Solution method: Convergent and asymptotic expansions are provided to approximate the relativistic Fermi-Dirac function and its derivatives for moderate/large values of its parameters.

References

[1]
A. Gil, D. Ruiz-Antolin, J. Segura, N.M. Temme, Numer. Algorithms 94 (2023) 669–679.
[2]
A. Gil, D. Ruiz-Antolin, J. Segura, N.M. Temme, Lecture Notes in Computer Science, vol. 14477, Springer, Cham, 2025.

查看原文本刊更多论文

中/大参数值下广义费米-狄拉克积分及其导数的评定。新版本公告

本文给出了Fermi-Dirac积分及其导数的展开式的Matlab实现的修订版。在新版本中，我们用于计算Kummer函数M（a,b,x）和U（a,b,x）的函数被合并到软件中。计算Kummer函数的算法在[1,2]中有描述。通过这种方式，Fermi-Dirac积分展开的实现可以在早期的Matlab版本中使用，并且可以很容易地适应GNU Octave。计算效率也得到了很大的提高。新版本程序摘要程序标题：FermiDiracExpansCPC库链接到程序文件：https://doi.org/10.17632/sk34wtcxhh.2Licensing条款：gplv3编程语言：matlab上一版本的期刊参考：Comput。理论物理。common . 283(2023) 108563新版本是否取代旧版本？新版本的原因：在新版本中，Fermi-Dirac积分的展开实现可以在早期的Matlab版本中使用，并且可以很容易地适应GNU Octave。计算效率也得到了很大的提高。修订总结：内置的Matlab函数kummerU和hypergeom分别被我们的函数Uabx和Mabx所取代。这些函数提高了计算Kummer函数的内置Matlab函数的精度和效率。利用Kummer函数所满足的几个关系，将含负参数的Kummer函数展开式中的表达式转化为实正参数和实实实实实实实实实实实实实实实实实实实实实实。问题性质：相对论性费米-狄拉克函数及其偏导数的评价是应用物理和理论物理中的不同问题所需要的，例如恒星天体物理、等离子体物理或电子学。求解方法：对相对论性费米-狄拉克函数及其参数的中/大值导数，给出了近似的收敛展开式和渐近展开式。Gil， D. Ruiz-Antolin， J. Segura， N.M. Temme, number。算法94(2023)669-679。吉尔，D. Ruiz-Antolin， J. Segura， N.M. Temme，计算机科学讲义，vol. 14477, bbb, Cham, 2025。

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来源期刊

Computer Physics Communications 物理-计算机：跨学科应用

CiteScore

12.10

自引率

3.20%

发文量

287

审稿时长

5.3 months

期刊介绍： The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper. Computer Programs in Physics (CPiP) These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged. Computational Physics Papers (CP) These are research papers in, but are not limited to, the following themes across computational physics and related disciplines. mathematical and numerical methods and algorithms; computational models including those associated with the design, control and analysis of experiments; and algebraic computation. Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.