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


文件中的檔案:

  1. 20b8bcc8782d5b787c5b0fc35a354567.pdf

若為 zip 檔案,請下載檔案解壓縮後,用瀏覽器開啟資料夾中的 index.html 瀏覽全文。