A well-conditioned and efficient implementation of dual reciprocity method for Poisson equation

doi:10.3934/math.2021724

	A well-conditioned and efficient implementation of dual reciprocity method for Poisson equation
	Khan, Suliman 3; Khan, M. Riaz 2,10; Alqahtani, Aisha M.1; Shah, Hasrat Hussain 9; Issakhov, Alibek 7,8; Shah, Qayyum 6; EI-Shorbagy, M. A.4,5
刊名	AIMS MATHEMATICS
	2021
卷号	6 期号:11 页码:12560-12582
关键词	dual reciprocity method multiquadrics compactly supported radial basis functions stability analysis condition number Poisson equation
DOI	10.3934/math.2021724
英文摘要	One 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.
资助项目	Deanship of Scientific Research at Princess Nourah bint Abdulrahman University through the Fast-track Research Funding Program
WOS研究方向	Mathematics
语种	英语
出版者	AMER INST MATHEMATICAL SCIENCES-AIMS
WOS记录号	WOS:000697908400044
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/59371]
专题	中国科学院数学与系统科学研究院
通讯作者	Khan, Suliman; Alqahtani, Aisha M.
作者单位	1.Princess Nourah Bint Abdulrahman Univ, Coll Sci, Dept Math Sci, Riyadh, Saudi Arabia 2.Chinese Acad Sci, Acad Math & Syst Sci, Univ Chinese Acad Sci, LSEC, Beijing 100190, Peoples R China 3.Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China 4.Menoufia Univ, Fac Engn, Dept Basic Engn Sci, Shibin Al Kawm 32511, Egypt 5.Prince Sattam Bin Abdulaziz Univ, Coll Sci & Humanities Al Kharj, Dept Math, Al Kharj 11942, Saudi Arabia 6.Univ Engn & Technol, Dept Basic Sci, Peshawar, Pakistan 7.Kazakh British Tech Univ, Dept Math & Cybernet, Alma Ata 050000, Kazakhstan 8.Al Farabi Kazakh Natl Univ, Dept Math & Comp Modeling, Alma Ata 050040, Kazakhstan 9.Balochistan Univ Informat Technol Engn & Manageme, Dept Math Sci, Quetta, Pakistan 10.Chinese Acad Sci, Acad Math & Syst Sci, Univ Chinese Acad Sci, ICMSEC, Beijing 100190, Peoples R China
推荐引用方式 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.