Localized Meshless Methods Based On Polynomial Basis Functions for Solving Axisymmetric Equations
Document Type
Article
Publication Date
11-1-2020
Department
Mathematics
School
Mathematics and Natural Sciences
Abstract
© 2020 International Association for Mathematics and Computers in Simulation (IMACS) In this paper, two localized meshless methods based on polynomial basis functions are utilized to solve axisymmetric problems. In the first approach, we applied the localized method of particular solutions (LMPS) and the closed-form particular solution to simplify the two-stage approach using Chebyshev polynomial as the basis functions for solving axisymmetric problems. We also propose the modified local Pascal polynomial method (MLPM) to compare the results with LMPS. Since only the low order polynomial basis functions are used, no preconditioning treatment is required and the solution is quite stable. Four numerical examples are given to demonstrate the effectiveness of the proposed methods.
Publication Title
Mathematics and Computers in Simulation
Volume
177
First Page
487
Last Page
499
Recommended Citation
Chang, W.,
Chen, C.,
Liu, X.,
Li, J.
(2020). Localized Meshless Methods Based On Polynomial Basis Functions for Solving Axisymmetric Equations. Mathematics and Computers in Simulation, 177, 487-499.
Available at: https://aquila.usm.edu/fac_pubs/17843