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用测地距离的基本解方法求解非齐次各向异性热传导方程 被引量：1

Method of fundamental solutions based on geodesic distance for inhomogeneous heat conduction equations in anisotropic medium
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摘要 近年来,径向基函数类方法数值求解偏微分方程问题越来越受欢迎.借此提出了一种求解非齐次各向异性热传导方程的基于测地距离的基本解方法,该方法属于径向基函数类方法,它无需进行变量变换,也无需计算奇异积分.用截断奇异值分解(TSVD)求解病态线性方程组.后面的数值例子将验证这种方法的稳定性和有效性. The radial basis function （RBF） collocation techniques for the numerical solution of partial differential equation problems are increasingly popular in recent years. A new method of fundamental solutions based on geodesic distance for inhomogeneous heat conduction equations in anisotropic medium is proposed. The new approach, one of the RBF methods, is free from variables transform or singular integral. Numerical results are presented, and the reliability and efficiency of the method are examined.
作者 王金玉 孙方裕
机构地区 广西师范大学数学科学学院 浙江大学数学系
出处 《浙江大学学报（理学版）》 CAS CSCD 北大核心 2008年第2期138-144,149,共8页 Journal of Zhejiang University（Science Edition）
基金 863探索基金资助项目
关键词 测地距离 基本解方法 Multiquadrie(MQ) 非齐次 截断奇异值分解(TSVD) geodesic distance method of fundamental solutions Multiquadric （MQ） inhomogeneous truncated singular value decomposition（TSVD）
分类号 O241.82 [理学—计算数学]
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参考文献17

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二级参考文献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.
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  • 10KANSA E J,HON Y C.Circumventing the ill-conditioningproblem with multiquadratic radial basis functions:applications to elliptic partial differential equations[J].Comput Math Appl,2000,39(7,8):123-137.

同被引文献31

  • 1董超峰,孙方裕.基本解方法求解各向异性材料中热传导方程的时间反向问题[J].浙江大学学报（理学版）,2007,34(1):33-39. 被引量：5
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  • 3HANSEN P C. Analysis of the discrete ill-posed problems by means of the L-curve[J].SIAM Rev, 1992,34 (4) : 561-580.
  • 4HANSEN P C, O'LEARY D P. The use of L-curve in the regularization of discrete ill-posed problems [J].SIAM J Sel Comput,1993,14(6) :1487-1503.
  • 5JONAS P, LOUIS A K. Approximate inverse for a one-dimensional inverse heat conduction problem[J]. Inverse Problems, 2000,16 : 17 5- 8 5.
  • 6LESNIC D, ELLIOTT L. The decomposition approach to inverse heat conduction[J]. J Math Anal Appl, 1999, 232:82-98.
  • 7LIU J. A stability analysis on Beck's procedure for inverse heat conduction problem[J].J Comput Phys, 1996,123:65-73.
  • 8SHEN S Y. A numerical study of inverse heat conduction problem[J]. Comput Math Appl, 1999,38 : 173- 88.
  • 9KUPRADZE V D, ALEKSIDZE M A. The method of functional equations for the approximate solution of certain boundary value problems [J]. Comput Math Math Phys, 1964,4 : 82-126.
  • 10FAIR WEATHER G, KARAGEORGHIS A. The method of fundamental solutions for elliptic boundary value problems[J]. Adv Comput Math, 1998,9 (1,2) 69-95.

引证文献1

浙江大学学报（理学版）
2008年 第2期

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