Extrapolation methods to compute hypersingular integral in boundary element methods  

作　　者：LI Jin ZHANG XiaoPing YU DeHao 

机构地区：[1]School of Science,Shandong Jianzhu University [2]School of Mathematics and Statistics,Wuhan University [3]School of Mathematical Sciences,Xiamen University [4]LSEC,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing

出　　处：《Science China Mathematics》2013年第8期1647-1660,共14页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos. 11101247 and 11201209);Shandong Provincial Natural Science Foundation of China (Grant No.ZR2011AQ020);a project of Shandong Province Higher Educational Science and Technology Program (GrantNo. J11LE08);supported by National Natural Science Foundation of China (GrantNo. 11101317);supported by National Basic Research Program of China (Grant No.2005CB321701);the Reward Fund of CAS for National Prize

摘　　要：The composite trapezoidal rule for the computation of Hadamard finite-part integrals in boundary element methods with the hypersingular kernel I/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.The composite trapezoidal rule for the computation of Hadamard finite-part integrals in boundary element methods with the hypersingular kernel 1/sin 2(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.

关 键 词：hypersingular integrals trapezoidal rule asymptotic error expansion extrapolation algorithm 

分 类 号：O172.2[理学—数学]