標題: | A ROBUST NUMERICAL ALGORITHM FOR COMPUTING MAXWELL'S TRANSMISSION EIGENVALUE PROBLEMS |
作者: | Huang, Tsung-Ming Huang, Wei-Qiang Lin, Wen-Wei 應用數學系 丘成桐中心 Department of Applied Mathematics Shing-Tung Yau Center |
關鍵字: | transmission eigenvalues;Maxwell's equations;quadratic eigenvalue problems;secant-type iteration;LOBPCG |
公開日期: | 1-一月-2015 |
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 Nedelec 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. |
URI: | http://dx.doi.org/10.1137/15M1018927 http://hdl.handle.net/11536/129459 |
ISSN: | 1064-8275 |
DOI: | 10.1137/15M1018927 |
期刊: | SIAM JOURNAL ON SCIENTIFIC COMPUTING |
Volume: | 37 |
Issue: | 5 |
起始頁: | 0 |
結束頁: | 0 |
顯示於類別: | 期刊論文 |