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...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.展开更多
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)+3 种基金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
文摘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.
