TY - JOUR
T1 - New concepts in meshless methods
AU - Atluri, S. N.
AU - Zhu, Tulong
N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2000/1/10
Y1 - 2000/1/10
N2 - 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.
AB - 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.
KW - Local Petrov-Galerkin formulation
KW - Local boundary integral equation
KW - Local symmetric weak form
KW - Meshless methods
KW - Moving least-squares approximation
UR - http://www.scopus.com/inward/record.url?scp=0033908369&partnerID=8YFLogxK
U2 - 10.1002/(SICI)1097-0207(20000110/30)47:1/3<537::AID-NME783>3.0.CO;2-E
DO - 10.1002/(SICI)1097-0207(20000110/30)47:1/3<537::AID-NME783>3.0.CO;2-E
M3 - Article
AN - SCOPUS:0033908369
VL - 47
SP - 537
EP - 556
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
SN - 0029-5981
IS - 1-3
ER -