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Applied Mathematics and Mechanics

, Volume 28, Issue 8, pp 1093–1099 | Cite as

Improved non-singular local boundary integral equation method

  • Fu Dong-jie  (付东杰)
  • Chen Hai-bo  (陈海波)Email author
  • Zhang Pei-qiang  (张培强)
Article

Abstract

When the source nodes are on the global boundary in the implementation of local boundary integral equation method (LBIEM), singularities in the local boundary integrals need to be treated specially. In the current paper, local integral equations are adopted for the nodes inside the domain and moving least square approximation (MLSA) for the nodes on the global boundary, thus singularities will not occur in the new algorithm. At the same time, approximation errors of boundary integrals are reduced significantly. As applications and numerical tests, Laplace equation and Helmholtz equation problems are considered and excellent numerical results are obtained. Furthermore, when solving the Helmholtz problems, the modified basis functions with wave solutions are adapted to replace the usually-used monomial basis functions. Numerical results show that this treatment is simple and effective and its application is promising in solutions for the wave propagation problem with high wave number.

Key words

meshless method local boundary integral equation method moving least square approximation singular integrals 

Chinese Library Classification

O302 

2000 Mathematics Subject Classification

70E05 

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Copyright information

© Editorial Committee of Appl. Math. Mech. 2007

Authors and Affiliations

  • Fu Dong-jie  (付东杰)
    • 1
    • 2
  • Chen Hai-bo  (陈海波)
    • 1
    • 2
    Email author
  • Zhang Pei-qiang  (张培强)
    • 1
    • 2
  1. 1.Department of Modern MechanicsUniversity of Science and Technology of ChinaHefeiP. R. China
  2. 2.CAS Key Laboratory of Mechanical Behavior and Design of MaterialsUniversity of Science and Technology of ChinaHefeiP. R. China

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