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New concepts in meshless methods
Author(s) -
Atluri S. N.,
Zhu Tulong
Publication year - 2000
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(20000110/30)47:1/3<537::aid-nme783>3.0.co;2-e
Subject(s) - regularized meshless method , singular boundary method , meshfree methods , moving least squares , interpolation (computer graphics) , mathematics , petrov–galerkin method , boundary (topology) , boundary value problem , finite element method , method of fundamental solutions , boundary element method , computer science , mathematical optimization , mathematical analysis , physics , artificial intelligence , motion (physics) , thermodynamics
Meshless methods have been extensively popularized in literature in recent years, due to their flexibility in solving boundary value problems. Two kinds of truly meshless methods, the meshless local boundary integral equation (MLBIE) method and the meshless local Petrov–Galerkin (MLPG) approach, are presented and discussed. Both methods use the moving least‐squares approximation to interpolate the solution variables, while the MLBIE method uses a local boundary integral equation formulation, and the MLPG employs a local symmetric weak form. The two methods are truly meshless ones as both of them do not need a ‘finite element or boundary element mesh’, either for purposes of interpolation of the solution variables, or for the integration of the ‘energy’. All integrals can be easily evaluated over regularly shaped domains (in general, spheres in three‐dimensional problems) and their boundaries. Numerical examples presented in the paper show that high rates of convergence with mesh refinement are achievable. In essence, the present meshless method based on the LSWF is found to be a simple, efficient and attractive method with a great potential in engineering applications. Copyright © 2000 John Wiley & Sons, Ltd.