## 摘要

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 Jacobi-Davidson 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 eigenvalue curves can be approximated by nonlinear functions, which can be applied to estimate the denseness of the eigenvalues for the TEP.

原文 | 英語 |
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文章編號 | 035009 |

期刊 | Inverse Problems |

卷 | 33 |

發行號 | 3 |

DOIs | |

出版狀態 | 已發佈 - 2017 二月 7 |

## ASJC Scopus subject areas

- 理論電腦科學
- 訊號處理
- 數學物理學
- 電腦科學應用
- 應用數學