Two-step MPS-MFS ghost point method for solving partial differential equations
Journal
Computers and Mathematics with Applications
Journal Volume
94
Pages
38-46
Date Issued
2021
Author(s)
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. ? 2021
Subjects
Functions; Numerical methods; Partial differential equations; Base function; Fictitious point method; Method of fundamental solutions; Method of particular solution; Multiquadrics; Particular solution method; Point methods; Radial basis; Shape parameters; Two step method; Radial basis function networks
Type
journal article