Novel Regularized Boundary Integral Equations for Potential Plane Problems
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摘要: 广泛实践集中在直接变量边界积分方程的规则化研究，其本质是利用简单解消除边界积分的奇异性．然而，至今关于平面位势问题的第一类边界积分方程的规则化研究尚未涉足．致力于间接变量边界积分方程的规则化方法研究，基于一种新的思想和观点，确立平面位势问题的间接变量规则边界积分方程，它不包含CPV强奇异积分和HFP超奇异积分．数值算例表明现在的方法可取得很好的精度和效率，特别是边界量的计算．
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关键词:
- 位势平面问题 /
- 边界积分方程（BIEs） /
- 间接变量BIEs /
- 规则化BIEs
Abstract: The universal practices have been centralizing on the research of regularization to the DBIE. The character is elimination of singularities by using the simple solutions. However, up to now the research of regularization to the first kind integral equations for plane potential problems has never been found in previous literatures. The presentation was mainly devoted to the research on the regularization of the singular boundary integral equations with indirect unknowns. A novel view and idea was presented herein, in which the regularized boundary integral equations with indirect unknowns excluding the CPV and HFP integrals were established for the plane potential problems. With some numerical results, it is shown that the better accuracy and higher efficiency, especially on the boundary, can be achieved by the present system. -
[1] Brebbia C A,Tells J C F,Wrobel L C.Boundary Elements Techniques Theory and Application in Engineering[M].Berlin,Heidelberg,New York,Tokyo：Springer-Verlag,1984. [2] 孙焕纯.无奇异边界元法[M].大连：大连理工大学出版社,1999. [3] 张耀明，孙焕纯.直接边界元法中边界积分的解析处理[J].应用数学和力学，2001,22(6):593—601. [4] Wang John,Tsay Ting-Kuei.Analytical evaluation and application of the singularities in boundary element method[J].Engrg Anal Boundary Elements,2005,29(3):241—256. doi: 10.1016/j.enganabound.2004.12.008 [5] Lifeng M A,Alexander M Korsunsky.A note on the Gauss-Jacobi quadrature formulae for singular integral equations of the second kind[J].International Journal of Fracture,2004,126(4):339—405. [6] Davydov A G,Zakharov E V. Some computational aspects of the hypersingular integral equation method in electrodynamics[J].Computational Mechanics,2004,15(2):105—109. [7] Liu Y J.On the simple-solution method and non-singular nature of the BIE/BEM-a review and some new results[J].Engrg Anal Boundary Elements,2000,24(10):789—795. doi: 10.1016/S0955-7997(00)00061-8 [8] Jorge A B,Ribeiro G O,Cruse T A.Self-regularized boundary integral equation formulations for Laplace's equation in 2-D[J].Internat J Numer Methods Engrg,2001,51(1):1—29. doi: 10.1002/nme.138 [9] Krutitskii P A.Hypersingular integral equations not needed in the impedance problem in scattering theory[J].Computers and Mathematics With Applications,2003,45(1/3):391—399. doi: 10.1016/S0898-1221(03)80025-1 [10] 张耀明，温卫东，王利民，等.弹性力学平面问题中一类新的无奇异边界积分方程[J].力学学报，2004,36(3):311—321. -
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