Algorithm 922

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.

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 13 articles )

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  1. An, Jing: A Legendre-Galerkin spectral approximation and estimation of the index of refraction for transmission eigenvalues (2016)
  2. Zeng, Fang; Sun, JiGuang; Xu, LiWei: A spectral projection method for transmission eigenvalues (2016)
  3. Huang, Tsung-Ming; Huang, Wei-Qiang; Lin, Wen-Wei: A robust numerical algorithm for computing Maxwell’s transmission eigenvalue problems (2015)
  4. Li, Tiexiang; Huang, Wei-Qiang; Lin, Wen-Wei; Liu, Jijun: On spectral analysis and a novel algorithm for transmission eigenvalue problems (2015)
  5. Zeng, Fang; Turner, Tiara; Sun, Jiguang: Some results on electromagnetic transmission eigenvalues (2015)
  6. Cakoni, Fioralba; Monk, Peter; Sun, Jiguang: Error analysis for the finite element approximation of transmission eigenvalues (2014)
  7. Ji, Xia; Sun, Jiguang; Xie, Hehu: A multigrid method for Helmholtz transmission eigenvalue problems (2014)
  8. An, Jing; Shen, Jie: A spectral-element method for transmission eigenvalue problems (2013)
  9. Gintides, Drossos; Pallikarakis, Nikolaos: A computational method for the inverse transmission eigenvalue problem (2013)
  10. Ji, Xia; Sun, Jiguang: A multi-level method for transmission eigenvalues of anisotropic media (2013)
  11. Wu, Xinming; Chen, Wenbin: Error estimates of the finite element method for interior transmission problems (2013)
  12. Monk, Peter; Sun, Jiguang: Finite element methods for Maxwell’s transmission eigenvalues (2012)
  13. Sun, Jiguang: An eigenvalue method using multiple frequency data for inverse scattering problems (2012)