### 摘要

We study a robust and efficient eigensolver for computing a few smallest positive eigenvalues of the three-dimensional Maxwell's transmission eigenvalue problem. The discretized governing equations by the Nédélec edge element result in a large-scale quadratic eigenvalue problem (QEP) for which the spectrum contains many zero eigenvalues and the coefficient matrices consist of patterns in the matrix form XY^{-1}Z, both of which prevent existing eigenvalue solvers from being efficient. To remedy these difficulties, we rewrite the QEP as a particular nonlinear eigenvalue problem and develop a secant-type iteration, together with an indefinite locally optimal block preconditioned conjugate gradient (LOBPCG) method, to sequentially compute the desired positive eigenvalues. Furthermore, we propose a novel method to solve the linear systems in each iteration of LOBPCG. Intensive numerical experiments show that our proposed method is robust, although the desired real eigenvalues are surrounded by complex eigenvalues.

原文 | 英語 |
---|---|

頁（從 - 到） | A2403-A2423 |

期刊 | SIAM Journal on Scientific Computing |

卷 | 37 |

發行號 | 5 |

DOIs | |

出版狀態 | 已發佈 - 2015 一月 1 |

### 指紋

### ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics

### 引用此文

*SIAM Journal on Scientific Computing*,

*37*(5), A2403-A2423. https://doi.org/10.1137/15M1018927

**A robust numerical algorithm for computing Maxwell's transmission eigenvalue problems.** / Hwang, Tsung-Min; Huang, Wei Qiang; Lin, Wen Wei.

研究成果: 雜誌貢獻 › 文章

*SIAM Journal on Scientific Computing*, 卷 37, 編號 5, 頁 A2403-A2423. https://doi.org/10.1137/15M1018927

}

TY - JOUR

T1 - A robust numerical algorithm for computing Maxwell's transmission eigenvalue problems

AU - Hwang, Tsung-Min

AU - Huang, Wei Qiang

AU - Lin, Wen Wei

PY - 2015/1/1

Y1 - 2015/1/1

N2 - We study a robust and efficient eigensolver for computing a few smallest positive eigenvalues of the three-dimensional Maxwell's transmission eigenvalue problem. The discretized governing equations by the Nédélec edge element result in a large-scale quadratic eigenvalue problem (QEP) for which the spectrum contains many zero eigenvalues and the coefficient matrices consist of patterns in the matrix form XY-1Z, both of which prevent existing eigenvalue solvers from being efficient. To remedy these difficulties, we rewrite the QEP as a particular nonlinear eigenvalue problem and develop a secant-type iteration, together with an indefinite locally optimal block preconditioned conjugate gradient (LOBPCG) method, to sequentially compute the desired positive eigenvalues. Furthermore, we propose a novel method to solve the linear systems in each iteration of LOBPCG. Intensive numerical experiments show that our proposed method is robust, although the desired real eigenvalues are surrounded by complex eigenvalues.

AB - We study a robust and efficient eigensolver for computing a few smallest positive eigenvalues of the three-dimensional Maxwell's transmission eigenvalue problem. The discretized governing equations by the Nédélec edge element result in a large-scale quadratic eigenvalue problem (QEP) for which the spectrum contains many zero eigenvalues and the coefficient matrices consist of patterns in the matrix form XY-1Z, both of which prevent existing eigenvalue solvers from being efficient. To remedy these difficulties, we rewrite the QEP as a particular nonlinear eigenvalue problem and develop a secant-type iteration, together with an indefinite locally optimal block preconditioned conjugate gradient (LOBPCG) method, to sequentially compute the desired positive eigenvalues. Furthermore, we propose a novel method to solve the linear systems in each iteration of LOBPCG. Intensive numerical experiments show that our proposed method is robust, although the desired real eigenvalues are surrounded by complex eigenvalues.

KW - LOBPCG

KW - Maxwell's equations

KW - Quadratic eigenvalue problems

KW - Secant-type iteration

KW - Transmission eigenvalues

UR - http://www.scopus.com/inward/record.url?scp=84945919789&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84945919789&partnerID=8YFLogxK

U2 - 10.1137/15M1018927

DO - 10.1137/15M1018927

M3 - Article

AN - SCOPUS:84945919789

VL - 37

SP - A2403-A2423

JO - SIAM Journal of Scientific Computing

JF - SIAM Journal of Scientific Computing

SN - 0036-1445

IS - 5

ER -