An efficient numerical algorithm for computing densely distributed positive interior transmission eigenvalues

Tiexiang Li, Tsung-Min Hwang, Wen Wei Lin, Jenn Nan Wang

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number035009
JournalInverse Problems
Volume33
Issue number3
DOIs
Publication statusPublished - 2017 Feb 7

Fingerprint

Quadratic Eigenvalue Problem
Distributed computer systems
Distributed Computing
Numerical Algorithms
Interior
Transmission Problem
Efficient Algorithms
Eigenvalue
Eigenvalue Problem
Computer simulation
Maxwell equations
Jacobi-Davidson Method
Deflation
Numerical Simulation
Maxwell's equations
Finite element method
Nonlinear Function
Piecewise Linear
Governing equation
Transverse

Keywords

  • Tellegen model
  • non-equivalence deflation
  • quadratic Jacobi-Davidson method
  • two-dimensional transmission eigenvalue problem

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics

Cite this

An efficient numerical algorithm for computing densely distributed positive interior transmission eigenvalues. / Li, Tiexiang; Hwang, Tsung-Min; Lin, Wen Wei; Wang, Jenn Nan.

In: Inverse Problems, Vol. 33, No. 3, 035009, 07.02.2017.

Research output: Contribution to journalArticle

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