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Convergence Acceleration of Infinite Series Involving the Product of Riccati-Bessel Function and Its Application for the Electromagnetic Field: Using the Continued Fraction Expansion Method
Fanghua, Zheng1,2,3; Qingyun, Di1,2,3; Zhe, Yun1,2,3; Ya, Gao1,2,3
2021-12-01
Source PublicationAPPLIED COMPUTATIONAL ELECTROMAGNETICS SOCIETY JOURNAL
ISSN1054-4887
Volume36Issue:12Pages:1518-1525
AbstractA summation technique has been developed based on the continuous fractional expansion to accelerate the convergence of infinite series involving the product of Riccati-Bessel functions, which are common to electromagnetic applications. The series is transformed into a new and faster convergent sequence with a continued fraction form, and then the continued fraction approximation is used to accelerate the calculation. The well-known addition theorem formula for spherical wave function is used to verify the correctness of the algorithm. Then, some fundamental aspects of the practical application of continuous fractional expansion for Mie scattering theory and electromagnetic exploration are considered. The results of different models show that this new technique can be applied reliably, especially in the electromagnetic field excited by the vertical electric dipole (VED) source in the "earth-ionospheric" cavity. The comparison among the new technology, the Watson transform, and the spherical harmonic series summation algorithm shows that this new technology only needs less than 120 series items which is already enough to obtain a small relative error, which greatly improves the convergence speed, and provides a new way to solve the problem.
Keywordinfinite series Riccati-Bessel function Mie scattering electromagnetic prospecting
DOI10.47037/2020.ACES.J.361202
Funding OrganizationScientific Instrument Developing Project of the Chinese Academy ; Scientific Instrument Developing Project of the Chinese Academy ; Scientific Instrument Developing Project of the Chinese Academy ; Scientific Instrument Developing Project of the Chinese Academy ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; Scientific Instrument Developing Project of the Chinese Academy ; Scientific Instrument Developing Project of the Chinese Academy ; Scientific Instrument Developing Project of the Chinese Academy ; Scientific Instrument Developing Project of the Chinese Academy ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; Scientific Instrument Developing Project of the Chinese Academy ; Scientific Instrument Developing Project of the Chinese Academy ; Scientific Instrument Developing Project of the Chinese Academy ; Scientific Instrument Developing Project of the Chinese Academy ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; Scientific Instrument Developing Project of the Chinese Academy ; Scientific Instrument Developing Project of the Chinese Academy ; Scientific Instrument Developing Project of the Chinese Academy ; Scientific Instrument Developing Project of the Chinese Academy ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China
WOS KeywordEARTH-IONOSPHERE CAVITY ; SCATTERING ; STRENGTHS
Language英语
Funding ProjectScientific Instrument Developing Project of the Chinese Academy[165587] ; Scientific Instrument Developing Project of the Chinese Academy[ZDZBGCH2018006] ; National Natural Science Foundation of China[41874088]
Funding OrganizationScientific Instrument Developing Project of the Chinese Academy ; Scientific Instrument Developing Project of the Chinese Academy ; Scientific Instrument Developing Project of the Chinese Academy ; Scientific Instrument Developing Project of the Chinese Academy ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; Scientific Instrument Developing Project of the Chinese Academy ; Scientific Instrument Developing Project of the Chinese Academy ; Scientific Instrument Developing Project of the Chinese Academy ; Scientific Instrument Developing Project of the Chinese Academy ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; Scientific Instrument Developing Project of the Chinese Academy ; Scientific Instrument Developing Project of the Chinese Academy ; Scientific Instrument Developing Project of the Chinese Academy ; Scientific Instrument Developing Project of the Chinese Academy ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; Scientific Instrument Developing Project of the Chinese Academy ; Scientific Instrument Developing Project of the Chinese Academy ; Scientific Instrument Developing Project of the Chinese Academy ; Scientific Instrument Developing Project of the Chinese Academy ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; National Natural Science Foundation of China
WOS Research AreaEngineering ; Telecommunications
WOS SubjectEngineering, Electrical & Electronic ; Telecommunications
WOS IDWOS:000769931100003
PublisherAPPLIED COMPUTATIONAL ELECTROMAGNETICS SOC
Citation statistics
Document Type期刊论文
Identifierhttp://ir.iggcas.ac.cn/handle/132A11/105005
Collection深部资源探测先导技术与装备研发中心
Corresponding AuthorFanghua, Zheng
Affiliation1.Chinese Acad Sci, Inst Geol & Geophys, CAS Engn Lab Deep Resources Equipment & Technol, Beijing 100029, Peoples R China
2.Chinese Acad Sci, Innovat Acad Earth Sci, Beijing 100029, Peoples R China
3.Univ Chinese Acad Sci, Beijing 100049, Peoples R China
First Author AffilicationInstitute of Geology and Geophysics, Chinese Academy of Sciences
Corresponding Author AffilicationInstitute of Geology and Geophysics, Chinese Academy of Sciences
Recommended Citation
GB/T 7714
Fanghua, Zheng,Qingyun, Di,Zhe, Yun,et al. Convergence Acceleration of Infinite Series Involving the Product of Riccati-Bessel Function and Its Application for the Electromagnetic Field: Using the Continued Fraction Expansion Method[J]. APPLIED COMPUTATIONAL ELECTROMAGNETICS SOCIETY JOURNAL,2021,36(12):1518-1525.
APA Fanghua, Zheng,Qingyun, Di,Zhe, Yun,&Ya, Gao.(2021).Convergence Acceleration of Infinite Series Involving the Product of Riccati-Bessel Function and Its Application for the Electromagnetic Field: Using the Continued Fraction Expansion Method.APPLIED COMPUTATIONAL ELECTROMAGNETICS SOCIETY JOURNAL,36(12),1518-1525.
MLA Fanghua, Zheng,et al."Convergence Acceleration of Infinite Series Involving the Product of Riccati-Bessel Function and Its Application for the Electromagnetic Field: Using the Continued Fraction Expansion Method".APPLIED COMPUTATIONAL ELECTROMAGNETICS SOCIETY JOURNAL 36.12(2021):1518-1525.
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