Analysis of Meshfree Galerkin Methods Based on Moving Least Squares and Local Maximum-Entropy Approximation Schemes

Hongtao Yang, Hao Wang and Bo Li ()
Additional contact information
Hongtao Yang: College of Engineering, Peking University, Beijing 100187, China
Hao Wang: School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN 47907, USA
Bo Li: College of Engineering, Peking University, Beijing 100187, China

Mathematics, 2024, vol. 12, issue 3, 1-20

Abstract: Over the last two decades, meshfree Galerkin methods have become increasingly popular in solid and fluid mechanics applications. A variety of these methods have been developed, each incorporating unique meshfree approximation schemes to enhance their performance. In this study, we examine the application of the Moving Least Squares and Local Maximum-Entropy (LME) approximations within the framework of Optimal Transportation Meshfree for solving Galerkin boundary-value problems. We focus on how the choice of basis order and the non-negativity, as well as the weak Kronecker-delta properties of shape functions, influence the performance of numerical solutions. Through comparative numerical experiments, we evaluate the efficiency, accuracy, and capabilities of these two approximation schemes. The decision to use one method over the other often hinges on factors like computational efficiency and resource management, underscoring the importance of carefully considering the specific attributes of the data and the intrinsic nature of the problem being addressed.

Keywords: meshfree methods; local maximum entropy; moving least squares; boundary value problems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/3/494/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/3/494/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:3:p:494-:d:1333164

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().