Development of a new meshless — point weighted least-squares (PWLS) method for computational mechanics

Article

Wang, Q. X., Li, Hua and Lam, K. Y.. 2004. "Development of a new meshless — point weighted least-squares (PWLS) method for computational mechanics." Computational Mechanics. 35 (3), pp. 170-181. https://doi.org/10.1007/s00466-004-0611-z
Article Title

Development of a new meshless — point weighted least-squares (PWLS) method for computational mechanics

ERA Journal ID3732
Article CategoryArticle
AuthorsWang, Q. X. (Author), Li, Hua (Author) and Lam, K. Y. (Author)
Journal TitleComputational Mechanics
Journal Citation35 (3), pp. 170-181
Number of Pages12
Year2004
Place of PublicationGermany
ISSN0178-7675
1432-0924
Digital Object Identifier (DOI)https://doi.org/10.1007/s00466-004-0611-z
Web Address (URL)https://link.springer.com/article/10.1007/s00466-004-0611-z
Abstract

A truly meshless approach, point weighted least-squares (PWLS) method, is developed in this paper. In the present PWLS method, two sets of distributed points are adopted, i.e. fields node and collocation point. The field nodes are used to construct the trial functions. In the construction of the trial functions, the radial point interpolation based on local supported radial base function are employed. The collocation points are independent of the field nodes and adopted to form the total residuals of the problem. The weighted least-squares technique is used to obtain the solution of the problem by minimizing the functional of the summation of residuals. The present PWLS method possesses more advantages compared with the conventional collocation methods, e.g. it is very stable; the boundary conditions can be easily enforced; and the final coefficient matrix is symmetric. Several numerical examples of one- and two-dimensional ordinary and partial differential equations (ODEs and PDEs) are presented to illustrate the performance of the present PWLS method. They show that the developed PWLS method is accurate and efficient for the implementation.

KeywordsCollocation method; Least-squares technique; Meshless method; Numerical analysis; Radial point interpolation method
ANZSRC Field of Research 2020401706. Numerical modelling and mechanical characterisation
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Byline AffiliationsInstitute of High Performance Computing, Singapore
National University of Singapore
Institution of OriginUniversity of Southern Queensland
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