Complex variable moving least-squares method: a meshless approximation technique

Based on the moving least‐squares (MLS) approximation, we propose a new approximation method—the complex variable moving least‐squares (CVMLS) approximation. With the CVMLS approximation, the trial function of a two‐dimensional problem is formed with a one‐dimensional basis function. The number of u...

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Bibliographic Details
Published in:International journal for numerical methods in engineering Vol. 70; no. 1; pp. 46 - 70
Main Authors: Liew, K. M., Feng, Cong, Cheng, Yumin, Kitipornchai, S.
Format: Journal Article
Language:English
Published: Chichester, UK John Wiley & Sons, Ltd 02.04.2007
Wiley
Subjects:
complex variable moving least-squares (CVMLS)
Computational techniques
elasticity
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Mathematical methods in physics
meshless method
Physics
Solid mechanics
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
Least squares method
Meshless method
elasticity
Node method
Function approximation
complex variable moving least-squares (CVMLS)
Trial function
Complex variable method
ISSN:0029-5981, 1097-0207
Online Access:Get full text
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Summary:Based on the moving least‐squares (MLS) approximation, we propose a new approximation method—the complex variable moving least‐squares (CVMLS) approximation. With the CVMLS approximation, the trial function of a two‐dimensional problem is formed with a one‐dimensional basis function. The number of unknown coefficients in the trial function of the CVMLS approximation is less than in the trial function of the MLS approximation, and we can thus select fewer nodes in the meshless method that is formed from the CVMLS approximation than are required in the meshless method of the MLS approximation with no loss of precision. The meshless method that is derived from the CVMLS approximation also has a greater computational efficiency. From the CVMLS approximation, we propose a new meshless method for two‐dimensional elasticity problems—the complex variable meshless method (CVMM)—and the formulae of the CVMM for two‐dimensional elasticity problems are obtained. Compared with the conventional meshless method, the CVMM has a greater precision and computational efficiency. For the purposes of demonstration, some selected numerical examples are solved using the CVMM. Copyright © 2006 John Wiley & Sons, Ltd.
Bibliography:istex:854072D63E3F6389CCCA9ED056A14C79828B3FBE
ark:/67375/WNG-LBN9HVVN-H
CityU SRG - No. 7001961
ArticleID:NME1870
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.1870