Improved Non-Singular Local Boundary Integral Equation Method

FU Dong-jie; CHEN Hai-bo; ZHANG Pei-qiang

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Article Navigation > Applied Mathematics and Mechanics > 2007 > 28(8): 976-982

FU Dong-jie, CHEN Hai-bo, ZHANG Pei-qiang. Improved Non-Singular Local Boundary Integral Equation Method[J]. Applied Mathematics and Mechanics, 2007, 28(8): 976-982.

Citation:

FU Dong-jie, CHEN Hai-bo, ZHANG Pei-qiang. Improved Non-Singular Local Boundary Integral Equation Method[J]. Applied Mathematics and Mechanics, 2007, 28(8): 976-982.

Citation:

FU Dong-jie, CHEN Hai-bo, ZHANG Pei-qiang. Improved Non-Singular Local Boundary Integral Equation Method[J]. Applied Mathematics and Mechanics, 2007, 28(8): 976-982.

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Improved Non-Singular Local Boundary Integral Equation Method

Department of Modern Mechanics, University of Science and Technology of China; CAS Key Laboratory of Mechanical Behavior and Design of Materials, Hefei 230026, P. R. China

Received Date: 2006-12-06
Rev Recd Date: 2007-03-06
Publish Date: 2007-08-15

Abstract

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.Local integral equations were 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 reduce significantly.As applications and numerical tests,Laplace equation and Helmholtz equation problems were considered and excellent numerical results were obtained.Furthermore,when solving the Helmholtz problems, the modified basis functions with wave solutions were adopted 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.
- meshless method,
- moving least square approximation,
- local boundary integral equation method,
- singular integral

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References(13)

References

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