Extrapolation methods to compute hypersingular integral in boundary element methods

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• 作者：Jin Li (14593)
  XiaoPing Zhang (24593)
  DeHao Yu (34593) (44593)
  
• 关键词：hypersingular integrals ; trapezoidal rule ; asymptotic error expansion ; extrapolation algorithm ; 35S15 ; 65M38 ; 74S15 ; 30B50
• 刊名：SCIENCE CHINA Mathematics
• 出版年：2013
• 出版时间：August 2013
• 年：2013
• 卷：56
• 期：8
• 页码：1647-1660
• 全文大小：218KB
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• 作者单位：Jin Li (14593)
  XiaoPing Zhang (24593)
  DeHao Yu (34593) (44593)
  
  14593. School of Science, Shandong Jianzhu University, Jinan, 250101, China
  24593. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China
  34593. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China
  44593. LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China
  

文摘

The composite trapezoidal rule for the computation of Hadamard finite-part integrals in boundary element methods with the hypersingular kernel 1/sin2(x ?s) is discussed, and the main part of the asymptotic expansion of error function is obtained. Based on the main part of the asymptotic expansion, a series is constructed to approach the singular point. An extrapolation algorithm is presented and the convergence rate is proved. Some numerical results are also presented to confirm the theoretical results and show the efficiency of the algorithms.