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Barik, Nikunja, Ojha, Kanaka, TVS, Sekhar, Mishra, Debasish. (1405). Accurate and efficient multilevel v-cycle algorithm for meshfree RBF method. نشریه مهندسی عمران امیرکبیر, (), -. doi: 10.22060/ajmc.2025.24615.1443
Nikunja Bihari Barik; Kanaka Lata Ojha; Sekhar TVS; Debasish Mishra. "Accurate and efficient multilevel v-cycle algorithm for meshfree RBF method". نشریه مهندسی عمران امیرکبیر, , , 1405, -. doi: 10.22060/ajmc.2025.24615.1443
Barik, Nikunja, Ojha, Kanaka, TVS, Sekhar, Mishra, Debasish. (1405). 'Accurate and efficient multilevel v-cycle algorithm for meshfree RBF method', نشریه مهندسی عمران امیرکبیر, (), pp. -. doi: 10.22060/ajmc.2025.24615.1443
Barik, Nikunja, Ojha, Kanaka, TVS, Sekhar, Mishra, Debasish. Accurate and efficient multilevel v-cycle algorithm for meshfree RBF method. نشریه مهندسی عمران امیرکبیر, 1405; (): -. doi: 10.22060/ajmc.2025.24615.1443

Accurate and efficient multilevel v-cycle algorithm for meshfree RBF method

AUT Journal of Mathematics and Computing
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 28 فروردین 1405
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22060/ajmc.2025.24615.1443
نویسندگان
Nikunja Bihari Barik* 1؛ Kanaka Lata Ojha2؛ Sekhar TVS3؛ Debasish Mishra4
1PG Department of Mathematics, Government DAV College, Koraput-764021, India
2Department of Mathematics, Siksha ‘O’ Anusandhan University, Bhubaneswar, Odisha, India
3School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar-752050, India
4Centurion University of Technology and Management, Odisha, India
چکیده
An accurate and efficient multilevel v-cycle algorithm for radial basis function-based finite difference (RBF-FD) method is presented in this paper. The primary goal of the algorithm is level-by-level calculation from finest level to coarsest level and then level-by-level correction from coarsest level to finest level. The algorithm produces an accurate solution by solving corresponding error equations of the discretized equations from coarsest level to coarser level and then finer level to desired finest level. Convection-dominated problems are taken to demonstrate the validity of the algorithm. The computing time of the proposed algorithm is calculated, and it saves at least 51% of computation time than the general RBF-FD method. The necessary and sufficient convergence conditions of the iteration matrix of the proposed method were verified numerically. The tests show that the developed algorithm is accurate, which accelerates to a significant reduction in computational cost compared with the general RBF-FD method.
کلیدواژه‌ها
Multilevel v-cycle algorithm؛ meshfree method؛ Convection dominated problems؛ CPU time؛ convergence of the method
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