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测地距离的基本解方法求解各向异性热传导方程 被引量：1

Method of fundamental solutions based on geodesic distance for anisotropic heat conduction problems
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摘要 基本解方法属于径向基函数类方法,它使用微分算子的基本解作为基于欧氏距离的径向基函数.借助测地距离,给出了求解各向异性材料中的热传导方程的基本解方法.该方法无需对时间进行离散或Laplace变换,也无需进行变量变换,而是直接在整个时间空间区域上进行求解.文中给出了数值例子,来验证基于测地距离的基本解方法在求解该各向异性问题时的稳定性和有效性. The method of fundamental solutions（MFS）, one of the radial basis function（RBF） methods, employs the fundamental solutions to the governing differential operator as the Euclidean distance based RBF. The Euclidean distance is replaced with the geodesic distance and a novel method of fundamental solutions to heat conduction equations in anisotropic media is proposed. The new approach is free from time discretization, Laplace transformation, or variables transformation. It solves the anisotropic problems in the whole spatial and time domains directly. Numerical results are presented, and the reliability and efficiency of the geodesic distance based MFS are examined.
作者 董超峰 李启会
机构地区 浙江大学数学系 嘉兴学院数学系
出处 《浙江大学学报（理学版）》 CAS CSCD 北大核心 2007年第4期390-395,399,共7页 Journal of Zhejiang University（Science Edition）
关键词 测地距离 基本解方法 径向基函数 热传导方程 各向异性 无网格方法 geodesic distance method of fundamental solutions radial basis function heat conduction anisotropy meshless method
分类号 O241.82 [理学—计算数学]
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参考文献13

  • 1YONG D L,TSAI C C,MURUGESAN K,et al.Time-dependent fundamental solutions for homogeneous diffusion problem[J].Engrg Anal Bound Elem,2004,28:1463-1473.
  • 2HON Y C,WEI T.A fundamental solution method for inverse heat conduction problem[J].Engrg Anal Bound Elem,2004,28:489-495.
  • 3HON Y C,WEI T.The method of fundamental solutions for solving multidimensional inverse heat conduction problems[J].CMES:Comput Model Engrg Sci,2005,7:119-132.
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同被引文献16

  • 1YONG D L, TSAI C C, MURUGESAN K, et al. Time-dependent fundamental solutions for homogeneous diffusion problem[J]. Engrg Anal Bound Elem, 2004,28(12) : 1463-1473.
  • 2HON Y C, WEI T. A fundamental solution method for inverse heat conduction problem[J]. Engrg Anal Bound Elem, 2004,28(5) :489-495.
  • 3HON Y C, WEI T. The method of fundamental solution for solving multidimensional inverse heat conduction problems [J]. CMES: Comput Model Engrg Sci, 2005,7(2) :119-132.
  • 4OZISIK M Necati. Heat Conduction[M]. New York: A Wiley-Interscience Publication, 1980.
  • 5DONG C F, SUN F Y, MENG B Q. A method of fundamental solution for inverse heat conduction problem in an anisotropic medium[J]. Engrg Anal Bound Elem, 2007,1(31) :75-82.
  • 6FERREIRA AIM, MARTINS PALS, ROQUE CMC. Solving time-dependent engineering problems with multiquadrics[J]. J of Sound and Vibration, 2005,280 (3-5) :595-610.
  • 7CHEN W. Distance function wavelets-Part Ⅲ: "Exotic" transform and series, Research report of Simula Research Laboratory[J/OL]. CoRR preprint[2002-07]. http:// arxiv.org/abs/cs. CE/0206016. June,2002.
  • 8FAIRWEATHER G, KARAGEORGHIS A. The method of fundamental solutions for elliptic boundary value problems[J]. Adv Comput Math, 1998,9 (1,2) : 69-95.
  • 9KANSA E J, HON Y C. Circumventing the ill-conditioning problem with multiquadratic radial basis functions: applications to elliptic partial differential equations[J]. Comput Math Appl, 2000, 39 (7, 8): 123-137.
  • 10HANSEN P C. Truncated SVD solutions to discrete ill-posed problems with ill-determined numerical rank [J]. SIAM J Sei Statist Comput, 1990,11(3) : 503- 518.

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浙江大学学报（理学版）
2007年 第4期

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