Algorithm 922 swMATH ID: 12858 Software Authors: X. Ji, T. Turner; J. Sun Description: Algorithm 922: A mixed finite element method for Helmholtz transmission eigenvalues. Transmission eigenvalue problem has important applications in inverse scattering. Since the problem is non-self-adjoint, the computation of transmission eigenvalues needs special treatment. Based on a fourth-order reformulation of the transmission eigenvalue problem, a mixed finite element method is applied. The method has two major advantages: 1) the formulation leads to a generalized eigenvalue problem naturally without the need to invert a related linear system, and 2) the nonphysical zero transmission eigenvalue, which has an infinitely dimensional eigenspace, is eliminated. To solve the resulting non-Hermitian eigenvalue problem, an iterative algorithm using restarted Arnoldi method is proposed. To make the computation efficient, the search interval is decided using a Faber-Krahn type inequality for transmission eignevalues and the interval is updated at each iteration. The algorithm is implemented using Matlab. The code can be easily used in the qualitative methods in inverse scattering and modified to compute transmission eigenvalues for other models such as elasticity problem. Homepage: http://dl.acm.org/citation.cfm?id=2331137 Dependencies: Matlab Related Software: iFEM; JDQZ; FEAST; Matlab; DLMF; lobpcg.m; DistMesh; JDQR Cited in: 40 Publications all top 5 Cited by 42 Authors 10 Ji, Xia 10 Sun, Jiguang 8 Yang, Yidu 6 Bi, Hai 6 Han, Jiayu 6 Xi, Yingxia 5 An, Jing 4 Lin, Wen-Wei 3 Huang, Tsungming 3 Li, Hao 3 Li, Tiexiang 3 Wang, Jenn-Nan 3 Xie, Hehu 3 Zhang, Yu 2 Huang, Weiqiang 2 Monk, Peter B. 2 Shen, Jie 2 Tan, Ting 2 Turner, Tiara 2 Wu, Xinming 2 Zeng, Fang 2 Zhang, Shuo 1 Boujlida, H. 1 Cakoni, Fioralba 1 Cao, Waixiang 1 Chang, Wei-Chen 1 Chen, Wenbin 1 Geng, Hongrui 1 Gintides, Drossos 1 Huang, Ruihao 1 Khenissi, Moez 1 Li, Peijun 1 Liu, Jijun 1 Mei, Liquan 1 Meng, Jian 1 Pallikarakis, Nikolaos 1 Ren, Shanjing 1 Struthers, Allan A. 1 Wang, Gang 1 Wang, Shixi 1 Xu, Liwei 1 Zhang, Ruming all top 5 Cited in 21 Serials 7 Journal of Scientific Computing 4 Computers & Mathematics with Applications 4 Journal of Computational Physics 3 Inverse Problems 3 Communications in Computational Physics 2 Computer Methods in Applied Mechanics and Engineering 2 SIAM Journal on Scientific Computing 2 Science China. Mathematics 1 Mathematical Methods in the Applied Sciences 1 ACM Transactions on Mathematical Software 1 Applied Mathematics and Computation 1 Calcolo 1 Journal of Computational and Applied Mathematics 1 Applied Numerical Mathematics 1 SIAM Journal on Applied Mathematics 1 Discrete and Continuous Dynamical Systems. Series B 1 Computational Methods in Applied Mathematics 1 Inverse Problems and Imaging 1 Numerical Mathematics: Theory, Methods and Applications 1 Advances in Applied Mathematics and Mechanics 1 Results in Applied Mathematics all top 5 Cited in 8 Fields 35 Numerical analysis (65-XX) 22 Partial differential equations (35-XX) 10 Optics, electromagnetic theory (78-XX) 4 Operator theory (47-XX) 4 Mechanics of deformable solids (74-XX) 2 Fluid mechanics (76-XX) 1 Potential theory (31-XX) 1 Ordinary differential equations (34-XX) Citations by Year