A spectral projection method for transmission eigenvalues  

作　　者：ZENG Fang SUN JiGuang XU LiWei 

机构地区：[1]Institute of Computing and Data Sciences, College of Mathematics and Statistics,Chongqing University [2]Department of Mathematical Sciences, Michigan Technological University

出　　处：《Science China Mathematics》2016年第8期1613-1622,共10页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 11501063 and 11371385);National Science Foundation of USA (Grant No. DMS-1521555);the US Army Research Laboratory and the US Army Research Office (Grant No. W911NF-11-2-0046);the Start-up Fund of Youth 1000 Plan of China;that of Youth 100 plan of Chongqing University

摘　　要：We consider a nonlinear integral eigenvalue problem, which is a reformulation of the transmission eigenvalue problem arising in the inverse scattering theory. The boundary element method is employed for discretization, which leads to a generalized matrix eigenvalue problem. We propose a novel method based on the spectral projection. The method probes a given region on the complex plane using contour integrals and decides whether the region contains eigenvalue(s) or not. It is particularly suitable to test whether zero is an eigenvalue of the generalized eigenvalue problem, which in turn implies that the associated wavenumber is a transmission eigenvalue. Effectiveness and efficiency of the new method are demonstrated by numerical examples.We consider a nonlinear integral eigenvalue problem, which is a reformulation of the transmission eigenvalue problem arising in the inverse scattering theory. The boundary element method is employed for discretization, which leads to a generalized matrix eigenvalue problem. We propose a novel method based on the spectral projection. The method probes a given region on the complex plane using contour integrals and decides whether the region contains eigenvalue（s） or not. It is particularly suitable to test whether zero is an eigenvalue of the generalized eigenvalue problem, which in turn implies that the associated wavenumber is a transmission eigenvalue. Effectiveness and efficiency of the new method are demonstrated by numerical examples.

关 键 词：spectral projection boundary element method transmission eigenvalues 

分 类 号：O241.82[理学—计算数学]