標題: An efficient numerical algorithm for computing densely distributed positive interior transmission eigenvalues
作者: Li, Tiexiang
Huang, Tsung-Ming
Lin, Wen-Wei
Wang, Jenn-Nan
應用數學系
Department of Applied Mathematics
關鍵字: two-dimensional transmission eigenvalue problem;Tellegen model;quadratic Jacobi-Davidson method;non-equivalence deflation
公開日期: 1-Mar-2017
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.
URI: http://dx.doi.org/10.1088/1361-6420/aa5475
http://hdl.handle.net/11536/144298
ISSN: 0266-5611
DOI: 10.1088/1361-6420/aa5475
期刊: INVERSE PROBLEMS
Volume: 33
Appears in Collections:Articles