Meshless Galerkin algorithms for boundary integral equations with moving least square approximations

2011 ◽  
Vol 61 (12) ◽  
pp. 1237-1256 ◽  
Author(s):  
Xiaolin Li
Keyword(s):  
Integral Equations ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Least Square ◽  
Moving Least Square

scholarly journals The Interpolating Boundary Element-Free Method for Unilateral Problems Arising in Variational Inequalities

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Fen Li ◽  
Xiaolin Li
Keyword(s):  
Variational Inequalities ◽  
Boundary Element ◽  
Meshless Method ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Least Square ◽  
Moving Least Square ◽  
Unilateral Problems ◽  
Element Free Method ◽  
Element Free

The interpolating boundary element-free method (IBEFM) is developed in this paper for boundary-only analysis of unilateral problems which appear in variational inequalities. The IBEFM is a direct boundary only meshless method that combines an improved interpolating moving least-square scheme for constructing interpolation functions with boundary integral equations (BIEs) for representing governing equations. A projection operator is used to formulate the BIEs and then the formulae of the IBEFM are obtained for unilateral problems. The convergence of the developed meshless method is derived mathematically. The capability of the method is also illustrated and assessed through some numerical experiments.

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