Hypersingular Integral Equations and Related Numerical Methods
In many scientific and engineering problems, such as acoustics, electromagnetic scattering and fracture mechanics, one encounters integral equations with hypersingular kernels. The hypersingular integrals have some quite different properties from regular and weak singular integrals. The standard numerical integration is not effective for hypersingular integrals, and some special numerical integration should be developed.One of the major problems arising from the numerical methods, such as the boundary element method, for solving such integral equations, is how to evaluate the hypersingular integrals on the interval and on the circle efficiently, which should be understand in the Hadamard sense.In 1983 the method using series expansion of the integral kernel was first suggested by D.H. Yu. He solved the harmonic and biharmonic natural boundary integral equations on circle successfully. Then numerous works have been devoted to this area. The method of subtracting the singularity, the method of regularization, the approximate integration formulas for finite-part integrals, and the indirect method are also developed.In this talk we will mainly discuss the Newton-Cotes methods on the interval and on the circle. The related superconvergence results and the generalized extrapolation for computation of hypersingular integrals have also been presented. Some numerical examples are given to illustrate the theoretical analysis and the validity of the method.
Xiaoping Zhang Jin Li Dehao Yu
LSEC,Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science,Chinese Academy of Sciences P.O.Box 2719,Beijing 100190,China
国际会议
南京
英文
1
2009-10-18（万方平台首次上网日期，不代表论文的发表时间）