Structure-preserving Arnoldi-type algorithm for solving eigenvalue problems in leaky surface wave propagation

Tsung Ming Huang, Wen-Wei Lin*, Chin-Tien Wu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We study the generalized eigenvalue problems (GEPs) that arise from modeling leaky surface wave propagation in an acoustic resonator with an infinite amount of periodically arranged interdigital transducers. The constitutive equations are discretized by finite element methods with mesh refinements along the electrode interfaces and corners. The nonzero eigenvalues of the resulting GEP appear in reciprocal pairs (λ,1/λ). We transform the GEP into a T-palindromic quadratic eigenvalue problem (TPQEP) to reveal the important reciprocal relationships of the eigenvalues. The TPQEP is then solved by a structure-preserving algorithm incorporating a generalized T-skew-Hamiltonian implicitly restarted Arnoldi method so that the reciprocal relationship of the eigenvalues may be automatically preserved. Compared with applying the Arnoldi method to solve the GEPs, our numerical results show that the eigenpairs produced by the proposed structure-preserving method not only preserve the reciprocal property but also possess high efficiency and accuracy.

Original languageEnglish
Pages (from-to)9947-9958
Number of pages12
JournalApplied Mathematics and Computation
Volume219
Issue number19
DOIs
StatePublished - 14 May 2013

Keywords

  • GTSHIRA Mesh refinement
  • Leaky SAW
  • Palindromic quadratic eigenvalue problem
  • Structure-preserving

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