中山大学学报自然科学版 ›› 2011, Vol. 50 ›› Issue (6): 1-6.

• 研究论文 •    下一篇

弱奇性积分方程的最优阶多尺度Petrov-Galerkin快速算法

程思睿1,詹杰民1,陈仲英2

  

  1. (1. 中山大学工学院应用力学与工程系,广东 广州 510275;2. 中山大学数学与计算科学学院, 广东 广州 510275)
  • 收稿日期:2011-01-04 修回日期:1900-01-01 出版日期:2011-11-25 发布日期:2011-11-25
  • 通讯作者: 詹杰民

Fast Multiscale Petrov-Galerkin Algorithms for Weakly Singular Integral Equations

CHENG Sirui1, ZHAN Jiemin1, CHEN Zhongying2   

  1. (1. Department of Applied Mechanics and Engineering, Sun Yatsen University, Guangzhou 510275, China;2. Department of Scientific Computing and Computer Applications, Sun Yatsen University, Guangzhou 510275, China)
  • Received:2011-01-04 Revised:1900-01-01 Online:2011-11-25 Published:2011-11-25

摘要: 考虑求解第二类Fredholm弱奇性积分方程的多尺度Petrov-Galerkin压缩格式,给出压缩策略中截断参数的选取范围,证明了相应的压缩格式在保持稳定性、计算复杂度和系数矩阵条件数一致有界的基础上,收敛阶达到最优。并以数值算例验证了理论结果的正确性和有效性。

关键词: 最优收敛阶, 多尺度Petrov-Galerkin算法, 弱奇性积分方程

Abstract: The compressed multiscale Petrov-Galerkin algorithm for solving the second kind weakly singular integral equations is considered. We give the range of the truncation parameters and prove that the corresponding compression algorithm can achieve the optimal convergent order while preserving the stability, computational complexity and the uniformly boundedness of the condition number of the coefficient matrix. The numerical results verify the validity of the theoretical analysis.

Key words: optimal convergent order, multiscale Petrov-Galerkin method, weakly singular integral equations

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