Numerical studies on structure-preserving algorithms for surface acoustic wave simulations

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

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We study the generalized eigenvalue problems (GEPs) derived from modeling the surface acoustic wave in piezoelectric materials with periodic inhomogeneity. The eigenvalues appear in the reciprocal pairs due to periodic boundary conditions in the modeling. By transforming the GEP into a T-palindromic quadratic eigenvalue problem (TPQEP), the reciprocal relationship of the eigenvalues can be maintained. In this paper, we outline four recently developed structure-preserving algorithms, SA, SDA, TSHIRA and GTSHIRA, for solving the TPQEP. Numerical comparisons on the accuracy and the computational costs of these algorithm are presented. The eigenvalues close to unit circle on the complex plane are of interest in the area of filter and sensor designs. Our numerical results show that the Arnoldi-type structure-preserving algorithms TSHIRA and GTSHIRA with "re-symplectic" and "re-bi- isotropic" processes, respectively, are as accurate as the SA and SDA algorithms, and more efficient in finding these eigenvalues.

Original languageEnglish
Pages (from-to)140-154
Number of pages15
JournalJournal of Computational and Applied Mathematics
Volume244
Issue number1
DOIs
Publication statusPublished - 2013 Jan 7

Fingerprint

Surface Acoustic Wave
Surface waves
Numerical Study
Acoustic waves
Quadratic Eigenvalue Problem
Eigenvalue
Generalized Eigenvalue Problem
Simulation
Arnoldi
Piezoelectric Material
Piezoelectric materials
Numerical Comparisons
Periodic Boundary Conditions
Unit circle
Modeling
Inhomogeneity
Argand diagram
Computational Cost
Boundary conditions
Filter

Keywords

  • Palindromic quadratic eigenvalue problem
  • Structure-preserving
  • Surface acoustic wave

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

Numerical studies on structure-preserving algorithms for surface acoustic wave simulations. / Hwang, Tsung-Min; Li, Tiexiang; Lin, Wen Wei; Wu, Chin Tien.

In: Journal of Computational and Applied Mathematics, Vol. 244, No. 1, 07.01.2013, p. 140-154.

Research output: Contribution to journalArticle

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N2 - We study the generalized eigenvalue problems (GEPs) derived from modeling the surface acoustic wave in piezoelectric materials with periodic inhomogeneity. The eigenvalues appear in the reciprocal pairs due to periodic boundary conditions in the modeling. By transforming the GEP into a T-palindromic quadratic eigenvalue problem (TPQEP), the reciprocal relationship of the eigenvalues can be maintained. In this paper, we outline four recently developed structure-preserving algorithms, SA, SDA, TSHIRA and GTSHIRA, for solving the TPQEP. Numerical comparisons on the accuracy and the computational costs of these algorithm are presented. The eigenvalues close to unit circle on the complex plane are of interest in the area of filter and sensor designs. Our numerical results show that the Arnoldi-type structure-preserving algorithms TSHIRA and GTSHIRA with "re-symplectic" and "re-bi- isotropic" processes, respectively, are as accurate as the SA and SDA algorithms, and more efficient in finding these eigenvalues.

AB - We study the generalized eigenvalue problems (GEPs) derived from modeling the surface acoustic wave in piezoelectric materials with periodic inhomogeneity. The eigenvalues appear in the reciprocal pairs due to periodic boundary conditions in the modeling. By transforming the GEP into a T-palindromic quadratic eigenvalue problem (TPQEP), the reciprocal relationship of the eigenvalues can be maintained. In this paper, we outline four recently developed structure-preserving algorithms, SA, SDA, TSHIRA and GTSHIRA, for solving the TPQEP. Numerical comparisons on the accuracy and the computational costs of these algorithm are presented. The eigenvalues close to unit circle on the complex plane are of interest in the area of filter and sensor designs. Our numerical results show that the Arnoldi-type structure-preserving algorithms TSHIRA and GTSHIRA with "re-symplectic" and "re-bi- isotropic" processes, respectively, are as accurate as the SA and SDA algorithms, and more efficient in finding these eigenvalues.

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