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A well-conditioned and efficient implementation of dual reciprocity method for Poisson equation
Khan, Suliman1; Khan, M. Riaz2,3; Alqahtani, Aisha M.4; Shah, Hasrat Hussain5; Issakhov, Alibek6,7; Shah, Qayyum8; EI-Shorbagy, M. A.9,10
2021
Source PublicationAIMS MATHEMATICS
Volume6Issue:11Pages:12560-12582
AbstractOne of the attractive and practical techniques to transform the domain integrals to equivalent boundary integrals is the dual reciprocity method (DRM). The success of DRM relies on the proper treatment of the non-homogeneous term in the governing differential equation. For this purpose, radial basis functions (RBFs) interpolations are performed to approximate the non-homogeneous term accurately. Moreover, when the interpolation points are large, the global RBFs produced dense and ill conditioned interpolation matrix, which poses severe stability and computational issues. Fortunately, there exist interpolation functions with local support known as compactly supported radial basis functions (CSRBFs). These functions produce a sparse and well-conditioned interpolation matrix, especially for large-scale problems. Therefore, this paper aims to apply DRM based on multiquadrics (MQ) RBFs and CSRBFs for evaluation of the Poisson equation, especially for large-scale problems. Furthermore, the convergence analysis of DRM with MQ and CSRBFs is performed, along with error estimate and stability analysis. Several experiments are performed to ensure the well-conditioned, efficient, and accurate behavior of the CSRBFs compared to the MQ-RBFs, especially for large-scale interpolation points.
Keyworddual reciprocity method multiquadrics compactly supported radial basis functions stability analysis condition number Poisson equation
DOI10.3934/math.2021724
Indexed BySCI
Language英语
Funding ProjectDeanship of Scientific Research at Princess Nourah bint Abdulrahman University through the Fast-track Research Funding Program
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000697908400044
PublisherAMER INST MATHEMATICAL SCIENCES-AIMS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/59372
Collection中国科学院数学与系统科学研究院
Corresponding AuthorKhan, Suliman; Alqahtani, Aisha M.
Affiliation1.Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Univ Chinese Acad Sci, LSEC, Beijing 100190, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Univ Chinese Acad Sci, ICMSEC, Beijing 100190, Peoples R China
4.Princess Nourah Bint Abdulrahman Univ, Coll Sci, Dept Math Sci, Riyadh, Saudi Arabia
5.Balochistan Univ Informat Technol Engn & Manageme, Dept Math Sci, Quetta, Pakistan
6.Al Farabi Kazakh Natl Univ, Dept Math & Comp Modeling, Alma Ata 050040, Kazakhstan
7.Kazakh British Tech Univ, Dept Math & Cybernet, Alma Ata 050000, Kazakhstan
8.Univ Engn & Technol, Dept Basic Sci, Peshawar, Pakistan
9.Prince Sattam Bin Abdulaziz Univ, Coll Sci & Humanities Al Kharj, Dept Math, Al Kharj 11942, Saudi Arabia
10.Menoufia Univ, Fac Engn, Dept Basic Engn Sci, Shibin Al Kawm 32511, Egypt
Recommended Citation
GB/T 7714
Khan, Suliman,Khan, M. Riaz,Alqahtani, Aisha M.,et al. A well-conditioned and efficient implementation of dual reciprocity method for Poisson equation[J]. AIMS MATHEMATICS,2021,6(11):12560-12582.
APA Khan, Suliman.,Khan, M. Riaz.,Alqahtani, Aisha M..,Shah, Hasrat Hussain.,Issakhov, Alibek.,...&EI-Shorbagy, M. A..(2021).A well-conditioned and efficient implementation of dual reciprocity method for Poisson equation.AIMS MATHEMATICS,6(11),12560-12582.
MLA Khan, Suliman,et al."A well-conditioned and efficient implementation of dual reciprocity method for Poisson equation".AIMS MATHEMATICS 6.11(2021):12560-12582.
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