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A meshless algorithm with moving least square approximations for elliptic Signorini problems 被引量：1

A meshless algorithm with moving least square approximations for elliptic Signorini problems
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摘要 Based on the moving least square （MLS） approximations and the boundary integral equations （BIEs）, a meshless algorithm is presented in this paper for elliptic Signorini problems. In the algorithm, a projection operator is used to tackle the nonlinear boundary inequality conditions. The Signorini problem is then reformulated as BIEs and the unknown boundary variables are approximated by the MLS approximations. Accordingly, only a nodal data structure on the boundary of a domain is required. The convergence of the algorithm is proven. Numerical examples are given to show the high convergence rate and high computational efficiency of the presented algorithm. Based on the moving least square （MLS） approximations and the boundary integral equations （BIEs）, a meshless algorithm is presented in this paper for elliptic Signorini problems. In the algorithm, a projection operator is used to tackle the nonlinear boundary inequality conditions. The Signorini problem is then reformulated as BIEs and the unknown boundary variables are approximated by the MLS approximations. Accordingly, only a nodal data structure on the boundary of a domain is required. The convergence of the algorithm is proven. Numerical examples are given to show the high convergence rate and high computational efficiency of the presented algorithm.
作者 王延冲 李小林
机构地区 College of Mathematics Science
出处 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第9期35-42,共8页 中国物理B（英文版）
基金 supported by the National Natural Science Foundation of China(Grant No.11101454) the Natural Science Foundation of Chongqing CSTC,China(Grant No.cstc2014jcyjA00005) the Program of Innovation Team Project in University of Chongqing City,China(Grant No.KJTD201308)
关键词 meshless method Signorini problem moving least square approximations CONVERGENCE meshless method, Signorini problem, moving least square approximations, convergence
分类号 O241.82 [理学—计算数学]
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参考文献33

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同被引文献15

  • 1Ito K, Kunisch K. Semi-smooth Newton methods for the Signorini problem[J]. Applications of Mathematics, 2008, 53:445-468.
  • 2Coorevits P, Hild P, Lhalouani K. Mixed finite element methods for unilateral problems:convergence analysis and numerical studies [J ]. Mathematics of Computation, 2002, 71 : 1-25.
  • 3Zhang S, Zhu J. The boundary element-linear complementa- ry method for the Signorini problem[J]. Engineering Anal- ysis with Boundary Elements, 2012,36 : 112-117.
  • 4Zhang S, Zhu J. A projection iterative algorithm boundary element method for the Signorini problem[J]. Engineering Analysis with Boundary Elements, 2013,37 : 176-181.
  • 5Zhang S. A projection iterative algorithm for the Signorini problem using the boundary element method[J].Engineer- ing Analysis with Boundary Elements, 2015,50 : 313-319.
  • 6Li F, Li X. The interpolating boundary element-free method for unilateral problems arising in variational inequalities [J]. Mathematical Problems in Engineering, 2014 (5) : 1-11.
  • 7Ren Y L,Li X L. The boundary meshless radial point inter polation method for Signorini problems[J].Journal of Chongqing Normal University: Natural Science, 2015, 32 (3) :77-82.
  • 8Ren Y L, Li X L. A meshfree method for Signorini prob- lems using boundary integral equations[J]. Mathematical Problems in Engineering,2014(1):1-12.
  • 9Zheng H, Li X. Application of the method of fundamental solutions to 2D and 3D Signorini problems[J]. Engineering Analysis with Boundary Elements, 2015,58 : 48-57.
  • 10Li X. An interpolating boundary element-free method for three-dimensional potential problems[J].Applied Mathe- matical Modelling, 2015,39 : 3116-3134.

引证文献1

Chinese Physics B
2014年 第9期

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