An efficient numerical algorithm for computing the positive dense spectrum of the transmission eigenvalue problem with complex media

Tiexiang Li Department of Mathematics, Southeast University Tsung-Ming Huang Department of Mathematics, National Taiwan Normal University Wen-Wei Lin Department of Applied Mathematics, National Chiao Tung University Jenn-Nan Wang Institute of Applied Mathematics, National Taiwan University

Mathematical Physics mathscidoc:1607.22001

Inverse Problems, 33, 035009, 2017
We study a robust and efficient eigensolver for computing the positive dense spectrum of the two-dimensional transmission eigenvalue problem (TEP) which is derived from the Maxwell’s equation with complex media in pseudo-chiral model and the transverse magnetic mode. The discretized governing equations by the N ́ed ́elec edge element result in a large-scale quadratic eigenvalue problem (QEP). We estimate half of the positive eigenvalues of the QEP are on some interval which forms a dense spectrum of the QEP. The quadratic Jacobi-Davidson method with a so-called non-equivalence deflation technique is proposed to compute the dense spectrum of the QEP. Intensive numerical experiments show that our proposed method makes the convergence efficiently and robustly even it needs to compute more than 5000 desired eigenpairs. Numerical results also illustrate that the computed eigenvalue curves can be approximated by the non- linear functions which can be applied to estimate the density of the eigenvalues for the TEP.
Two-dimensional transmission eigenvalue problem, pseudo-chiral model, transverse magnetic mode, dense spectrum, quadratic Jacobi-Davidson method, non-equivalence deflation
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@inproceedings{tiexiang2017an,
  title={An efficient numerical algorithm for computing the positive dense spectrum of the transmission eigenvalue problem with complex media},
  author={Tiexiang Li, Tsung-Ming Huang, Wen-Wei Lin, and Jenn-Nan Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160707121605664630046},
  booktitle={Inverse Problems},
  volume={33},
  pages={035009},
  year={2017},
}
Tiexiang Li, Tsung-Ming Huang, Wen-Wei Lin, and Jenn-Nan Wang. An efficient numerical algorithm for computing the positive dense spectrum of the transmission eigenvalue problem with complex media. 2017. Vol. 33. In Inverse Problems. pp.035009. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160707121605664630046.
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