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

Barik, Nikunja Bihari; Ojha, Kanaka Lata; TVS, Sekhar; Mishra, Debasish

doi:10.22060/ajmc.2025.24615.1443

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

Articles in Press

Document Type : Original Article

Authors

Nikunja Bihari Barik ¹

Kanaka Lata Ojha ²

Sekhar TVS ³

Debasish Mishra ⁴

¹ PG Department of Mathematics, Government DAV College, Koraput-764021, India

² Department of Mathematics, Siksha ‘O’ Anusandhan University, Bhubaneswar, Odisha, India

³ School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar-752050, India

⁴ Centurion University of Technology and Management, Odisha, India

10.22060/ajmc.2025.24615.1443

Abstract

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.

Keywords

Multilevel v-cycle algorithm

meshfree method

Convection dominated problems

CPU time

convergence of the method

Subjects