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

Tsung-Min Hwang, Wen Wei Lin, Chin Tien Wu

Research output: Contribution to journalArticle

2 Citations (Scopus)

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
Publication statusPublished - 2013 May 14

Fingerprint

Acoustic resonators
Arnoldi
Hamiltonians
Generalized Eigenvalue Problem
Surface Waves
Constitutive equations
Surface waves
Wave propagation
Wave Propagation
Eigenvalue Problem
Transducers
Quadratic Eigenvalue Problem
Arnoldi Method
Finite element method
Electrodes
Eigenvalue
Mesh Refinement
Constitutive Equation
Resonator
Transducer

Keywords

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

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

Structure-preserving Arnoldi-type algorithm for solving eigenvalue problems in leaky surface wave propagation. / Hwang, Tsung-Min; Lin, Wen Wei; Wu, Chin Tien.

In: Applied Mathematics and Computation, Vol. 219, No. 19, 14.05.2013, p. 9947-9958.

Research output: Contribution to journalArticle

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AB - 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.

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