改进的无奇异局部边界积分方程方法

付东杰; 陈海波; 张培强

改进的无奇异局部边界积分方程方法

中国科学技术大学力学和机械工程系;中科院材料力学行为和设计重点实验室,合肥 230026

详细信息

作者简介:
付东杰(1977- ),河北人,博士生(E-mail:djfu@mail.uste.edu.cn);陈海波(1968- ),教授,博士生导师(联系人.Tel:+86-551-3603724;Fax:+86-551-3606459;E-mail:hbchen@ustc.edu.cn).

中图分类号: O302
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出版历程
- 收稿日期: 2006-12-06
- 修回日期: 2007-03-06
- 刊出日期: 2007-08-15

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

摘要

摘要: 在局部边界积分方程方法中，当源节点位于分析域的整体边界上时，局部边界积分将出现奇异积分问题，这些奇异积分需要做特别的处理．为此，提出了对域内节点采用局部积分方程，而对边界节点直接采用移动最小二乘近似函数引入边界条件来解决奇异积分问题，这同时也解决了对积分边界进行插值引入近似误差的问题．作为应用和数值实验，对Laplace方程和Helmholtz方程问题进行了分析，取得了很好的数值结果．进而，在Helmholtz方程求解中，采用了含波解信息的修正基函数来代替单项式基函数进行近似．数值结果显示，这样处理是简单高效的，在高波数声传播问题的求解中非常具有前景．
- 无网格方法 /
- 移动最小二乘近似 /
- 局部边界积分方程方法 /
- 奇异积分
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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参考文献(13)

[1]	Fries Thomas-Peter,Matthies Hermann G.Classication and overview of mesh- free methods[R]. Institute of Scientic Computing, Technical University Braunschweig Brunswick,Germany, 2003.
[2]	张雄,刘岩.无网格法.北京：清华大学出版社，2004.
[3]	Zhu T,Zhang J D, Atluri S N.A local boundary integral equation (LBIE) method in computational mechanics, and a meshless discretization approach[J].Computational Mechanics,1998,21(3):223-235. doi: 10.1007/s004660050297
[4]	Sladek J,Sladek V, Atluri S N.Application of the local boundary integral equation method to boundary-value problems[J].International Applied Mechanics,2002,38(9):1025-1047. doi: 10.1023/A:1021785329593
[5]	龙述尧，熊渊博. 关于薄板的无网格局部边界积分方程方法中的友解[J].应用数学和力学,2004,25(4)：379-384.
[6]	LONG Shu-yao, ZHANG Qin.Analysis of thin plates by the local boundary integral equation (LBIE) method[J].Engineering Analysis With Boundary Elements,2002,26(8):707-718. doi: 10.1016/S0955-7997(02)00025-5
[7]	Sladek J, Sladek V, Atluri S N.Local boundary integral equation (LBIE) method for solving problems of elasticity with nonhomogeneous material properties[J].Computational Mechanics,2000,24(6):456-462. doi: 10.1007/s004660050005
[8]	Zhu T, Zhang J, Atluri S N.A meshless local boundary integral equation (LBIE) method for solving nonlinear problems[J].Computational Mechanics,1998,22(2):174-186. doi: 10.1007/s004660050351
[9]	Chen H B, Lu P, Huang M G,et al.An effective method for finding values on and near boundaries in the elastic BEM[J].Computers and Structures,1998,69(4):421-431. doi: 10.1016/S0045-7949(98)00122-9
[10]	Chen H B,Lu P,Schnack E.Regularized algorithms for the calculation on and near boundary in 2D elastic BEM[J].Engineering Analysis with Boundary Elements,2001,25(10):851-876. doi: 10.1016/S0955-7997(01)00069-8
[11]	Sladek V, Sladek J,Atluri S N,et al.Numerical integration of singularities in meshless implementation of local boundary integral equations[J].Computational Mechanics,2000,25(4):394-403. doi: 10.1007/s004660050486
[12]	郭晓峰，陈海波，王宁宇，等. 二维位势问题中正则局部边界积分方法[J].中国科学技术大学学报，2006,36(6):636-640.
[13]	Chen H B, Fu D J,Zhang P Q.An investigation of Helmholtz problems with high wave numbers via the meshless LBIEM[A].In:S.M. Sivakumar, A. Meher Prasad, B. Dattaguru,et al Eds.Advances in Computational & Experimental Engineering and Sciences (Proceeding of ICCES'05, 1-10 December 2005, India),Tech Science Press, 2005, 114-119.

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改进的无奇异局部边界积分方程方法

作者简介:
付东杰(1977- ),河北人,博士生(E-mail:djfu@mail.uste.edu.cn);陈海波(1968- ),教授,博士生导师(联系人.Tel:+86-551-3603724;Fax:+86-551-3606459;E-mail:hbchen@ustc.edu.cn).

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Improved Non-Singular Local Boundary Integral Equation Method

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留言板

改进的无奇异局部边界积分方程方法

作者简介: 付东杰(1977- ),河北人,博士生(E-mail:djfu@mail.uste.edu.cn);陈海波(1968- ),教授,博士生导师(联系人.Tel:+86-551-3603724;Fax:+86-551-3606459;E-mail:hbchen@ustc.edu.cn).

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出版历程

Improved Non-Singular Local Boundary Integral Equation Method

计量

出版历程

目录

作者简介:
付东杰(1977- ),河北人,博士生(E-mail:djfu@mail.uste.edu.cn);陈海波(1968- ),教授,博士生导师(联系人.Tel:+86-551-3603724;Fax:+86-551-3606459;E-mail:hbchen@ustc.edu.cn).