NUMERICAL SOLUTION OF THE SCATTERING PROBLEM FOR ACOUSTIC WAVES BY A TWO-SIDED CRACK IN 2-DIMENSIONAL SPACE  

作　　者：Jijun Liu P.A. Krutitskii M. Sini 

机构地区：[1]Department of Mathematics, Southeast University, Nanjing 210096, China [2]Keldysh Institute of Applied Mathematics, Moscow 125047, Russia [3]Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Linz A~40-40, Austria

出　　处：《Journal of Computational Mathematics》2011年第2期141-166,共26页计算数学（英文）

基　　金：The authors would like to thank the referees for their valuable comments and suggestions which lead to an improved version of this paper. The work of the first author is supported by NSFC（No.10771033）. The first and second authors thank RICAM （Austrian Academy of Sciences） for the hospitality during the special semester on computational biology in 2007 in Linz. The third author is supported by the Austrian science foundation FWF via the project SFB F013/1308. The authors also want to thank Prof. Valentina Kolybasova and H.F.Zhao for their contributions in constructing Example 3.

摘　　要：The wave scattering problem by a crack F in R2 with impedance type boundary is considered. This problem models the diffraction of waves by thin two-sided cylindrical screens. A numerical method for solving the problem is developed. The solution of the problem is represented in the form of the combined angular potential and single-layer potential. The linear integral equations satisfied by the density functions are derived for general parameterized arcs. The weakly singular integrals and the Cauchy singular integral arising in these equations are computed using a highly accurate scheme with a truncation error analysis. The advantage of the scheme proposed in this paper is, in one hand, the fact that we do not need the analyticity property of the crack and we allow different complex valued surface impedances in both sides of the crack. In the other hand, we avoid the hyper-singular integrals. Numerical implementations showing the validity of the scheme are presented.The wave scattering problem by a crack F in R2 with impedance type boundary is considered. This problem models the diffraction of waves by thin two-sided cylindrical screens. A numerical method for solving the problem is developed. The solution of the problem is represented in the form of the combined angular potential and single-layer potential. The linear integral equations satisfied by the density functions are derived for general parameterized arcs. The weakly singular integrals and the Cauchy singular integral arising in these equations are computed using a highly accurate scheme with a truncation error analysis. The advantage of the scheme proposed in this paper is, in one hand, the fact that we do not need the analyticity property of the crack and we allow different complex valued surface impedances in both sides of the crack. In the other hand, we avoid the hyper-singular integrals. Numerical implementations showing the validity of the scheme are presented.

关 键 词：Wave scattering Impedance boundary Integral equations Singularity analysis Numerics. 

分 类 号：O241.82[理学—计算数学] TN820[理学—数学]