A Dimension Splitting-Interpolating Moving Least Squares (DS-IMLS) Method with Nonsingular Weight Functions

Jufeng Wang, Fengxin Sun and Rongjun Cheng
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Jufeng Wang: College of Finance & Information, Ningbo University of Finance & Economics, Ningbo 315175, China
Fengxin Sun: Faculty of Science, Ningbo University of Technology, Ningbo 315016, China
Rongjun Cheng: Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China

Mathematics, 2021, vol. 9, issue 19, 1-22

Abstract: By introducing the dimension splitting method (DSM) into the improved interpolating moving least-squares (IMLS) method with nonsingular weight function, a dimension splitting–interpolating moving least squares (DS-IMLS) method is first proposed. Since the DSM can decompose the problem into a series of lower-dimensional problems, the DS-IMLS method can reduce the matrix dimension in calculating the shape function and reduce the computational complexity of the derivatives of the approximation function. The approximation function of the DS-IMLS method and its derivatives have high approximation accuracy. Then an improved interpolating element-free Galerkin (IEFG) method for the two-dimensional potential problems is established based on the DS-IMLS method. In the improved IEFG method, the DS-IMLS method and Galerkin weak form are used to obtain the discrete equations of the problem. Numerical examples show that the DS-IMLS and the improved IEFG methods have high accuracy.

Keywords: meshless method; dimension splitting–interpolating moving least squares (DS-IMLS) method; improved interpolating element-free Galerkin (IEFG) method; potential problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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