An efficient numerical algorithm for computing densely distributed positive interior transmission eigenvalues

Tiexiang Li Tsung-Ming Huang Wen-Wei Lin Jenn-Nan Wang

Numerical Analysis and Scientific Computing mathscidoc:1912.43738

Inverse Problems, 33, (3), 035009, 2017.2
We propose an efficient eigensolver for computing densely distributed spectra of the two-dimensional transmission eigenvalue problem (TEP), which is derived from Maxwell's equations with Tellegen media and the transverse magnetic mode. The governing equations, when discretized by the standard piecewise linear finite element method, give rise to a large-scale quadratic eigenvalue problem (QEP). Our numerical simulation shows that half of the positive eigenvalues of the QEP are densely distributed in some interval near the origin. The quadratic JacobiDavidson method with a so-called non-equivalence deflation technique is proposed to compute the dense spectrum of the QEP. Extensive numerical simulations show that our proposed method processes the convergence efficiently, even when it needs to compute more than 5000 desired eigenpairs. Numerical results also illustrate that the computed
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@inproceedings{tiexiang2017an,
  title={An efficient numerical algorithm for computing densely distributed positive interior transmission eigenvalues},
  author={Tiexiang Li, Tsung-Ming Huang, Wen-Wei Lin, and Jenn-Nan Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205419372979302},
  booktitle={Inverse Problems},
  volume={33},
  number={3},
  pages={035009},
  year={2017},
}
Tiexiang Li, Tsung-Ming Huang, Wen-Wei Lin, and Jenn-Nan Wang. An efficient numerical algorithm for computing densely distributed positive interior transmission eigenvalues. 2017. Vol. 33. In Inverse Problems. pp.035009. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205419372979302.
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