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高精度特征解方法和外推解位势方程

程攀 黄晋 曾光

程攀, 黄晋, 曾光. 高精度特征解方法和外推解位势方程[J]. 应用数学和力学, 2010, 31(12): 1445-1453. doi: 10.3879/j.issn.1000-0887.2010.12.005
引用本文: 程攀, 黄晋, 曾光. 高精度特征解方法和外推解位势方程[J]. 应用数学和力学, 2010, 31(12): 1445-1453. doi: 10.3879/j.issn.1000-0887.2010.12.005
CHENG Pan, HUANG Jin, ZENG Guang. High Accuracy Eigensolution and Its Extrapolation for Potential Equations[J]. Applied Mathematics and Mechanics, 2010, 31(12): 1445-1453. doi: 10.3879/j.issn.1000-0887.2010.12.005
Citation: CHENG Pan, HUANG Jin, ZENG Guang. High Accuracy Eigensolution and Its Extrapolation for Potential Equations[J]. Applied Mathematics and Mechanics, 2010, 31(12): 1445-1453. doi: 10.3879/j.issn.1000-0887.2010.12.005

高精度特征解方法和外推解位势方程

doi: 10.3879/j.issn.1000-0887.2010.12.005
基金项目: 国家自然科学基金资助项目(10871034)
详细信息
    作者简介:

    程攀(1976- ),男,重庆人,讲师,博士(联系人.E-mail:cheng_pass@sina.com).

  • 中图分类号: O24;O39

High Accuracy Eigensolution and Its Extrapolation for Potential Equations

  • 摘要: 根据位势理论,基本边界特征值问题可转化为具有对数奇性的边界积分方程.利用机械求积方法求解特征值和特征向量λ(l),u(l),以及利用这些特征解求解Laplace方程.特征解和Laplace方程的解具有高精度O(h3)和低的计算复杂度O(h-1).利用Anselone聚紧和渐近紧理论,证明了方法的收敛性和稳定性.此外,还给出了误差的奇数阶渐近展开.利用h3-Richardson外推,不仅误差近似的精度阶大为提高O(h5),而且,得到的后验误差估计可以构造自适应算法.具体的数值例子说明了算法的有效性.
  • [1] Courant R, Hilbert D. Methods of Mathematical Physics[M]. New York: John Wiley and Sons, 1953.
    [2] Lanczos C. Discourse on Fourier Series[M]. Edinburgh: Oliver and Boyd, 1966.
    [3] Hadjesfandiari A R, Dargush G F. Theory of boundary eigensolutions in engineering mechanics[J]. J Appl Mech, 2001,68(1): 101-108. doi: 10.1115/1.1331059
    [4] Banerjee P K. The Boundary Element Methods in Engineering[M]. London: McGraw-Hill, 1994.
    [5] Li Z C. Combinations of method of fundamental solutions for Laplace’s equation with singularities[J]. Engineering Analysis With Boundary Elements, 2008, 32(10): 856-869. doi: 10.1016/j.enganabound.2008.01.002
    [6] Amini S. Nixon S P. Preconditioned multiwavelet Galerkin boundary element solution of Laplace’s equation[J]. Engineering Analysis With Boundary Elements, 2006, 30(7): 523-530. doi: 10.1016/j.enganabound.2006.02.003
    [7] 吕涛, 黄晋. 第二类弱奇异积分方程的高精度Nystrm方法与外推[J].计算物理,1997, 14(3): 349-355.
    [8] Liu C S. A modified collocation Trefftz method for the inverse Cauchy problem of Laplace equation[J]. Engineering Analysis With Boundary Elements, 2008, 32(9): 778-785. doi: 10.1016/j.enganabound.2007.12.002
    [9] Sidi A, Israrli M. Quadrature methods for periodic singular and weakly singular Fredholm integral equations[J]. J Sci Comput, 1988, 3(2): 201-231. doi: 10.1007/BF01061258
    [10] Huang J, Wang Z. Extrapolation algorithm for solving mixed boundary integral equations of the Helmholtz equation by mechanical quadrature methods[J]. SIAM J Sci Comput, 2009, 31(6): 4115-4129.
    [11] Sloan I H, Spence A. The Galerkin method for integral equations of the first kind with logarithmic kernel: theorm[J].IMA J Numer Anal,1988, 8(1):105-122. doi: 10.1093/imanum/8.1.105
    [12] Anselone P M. Collectively Compact Operator Approximation Theory[M]. New Jersey: Prentice-Hall, Englewood Cliffs, 1971.
    [13] Chatelin F. Spectral Approximation of Linear Operator[M]. Academic Press, 1983.
    [14] Lin C B, Lü T, Shih T M. The Splitting Extrapolation Method[M]. Singapore: World Scientific, 1995.
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出版历程
  • 收稿日期:  1900-01-01
  • 修回日期:  2010-11-05
  • 刊出日期:  2010-12-15

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