Two-Step MPS-MFS Ghost Point Method for Solving Partial Differential Equations
Document Type
Article
Publication Date
7-15-2021
Department
Mathematics
School
Mathematics and Natural Sciences
Abstract
The fictitious boundary surrounding the domain is required in the implementation of the method of fundamental solutions (MFS). A similar approach of taking a portion of the centres of radial basis functions (RBFs) outside the domain in the context of the method of particular solutions (MPS) is proposed to further improve the performance of a two-step MPS-MFS method. Since the shape parameter of RBFs is problem dependent, several known procedures on how to determine a good shape parameter are introduced for solving various types of problems. The proposed method is not only highly accurate but also fairly stable due to the use of the particular solutions and fundamental solutions. To demonstrate the effectiveness of the proposed method, five numerical examples in highly complicate and irregular domains, which include second and fourth order elliptic partial differential equations in 2D and 3D, are presented.
Publication Title
Computers and Mathematics with Applications
Volume
94
First Page
38
Last Page
46
Recommended Citation
Young, D.,
Lin, S.,
Chen, C.,
Chen, C.
(2021). Two-Step MPS-MFS Ghost Point Method for Solving Partial Differential Equations. Computers and Mathematics with Applications, 94, 38-46.
Available at: https://aquila.usm.edu/fac_pubs/18822