Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (3): 611-619.

Previous Articles     Next Articles

Efficient Numerical Methods for Integral Equations with Oscillatory Hankel Kernels

Qinghua Wu1,2()   

  1. 1 School of Mathematics and Computational Science, Xiangtan University, Hunan Xiangtan 411105
    2 College of Science, Hunan University of Science and Engineering, Hunan Yongzhou 425199
  • Received:2017-03-16 Online:2019-06-26 Published:2019-06-27
  • Supported by:
    the NSFC(11701170);the NSF of Hunan Province(2017JJ3029);the Young Core Teacher Foundation of Hunan Province


In this paper, we consider the numerical solution of boundary integral equations (BIE) arise in the study of the 2D scattering of a time-harmonic acoustic incident plane wave. Fast multipole method (FMM) is a very efficient and popular algorithm for the rapid solution of boundary value problems. However, when the FMM method is used for high frequency acoustic wave problems, it will give rise to the computation of oscillatory integrals. The standard quadrature methods are exceedingly difficult to calculate these oscillatory integrals and the computation cost steeply increases with the frequency. We apply the boundary element method (BEM) to discretize the BIE and use the FMM to accelerate the solutions of BEM. Oscillatory integrals are calculated by using efficient Clenshaw-Curtis Filon (CCF) methods. The effectiveness and accuracy of the proposed method are tested by numerical examples.

Key words: Oscillatory hankel kernels, Highly oscillatory integral equations, Fast multipole method

CLC Number: 

  • O241.83