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

Tsung Ming Huang, Tiexiang Li, Wen Wei Lin, Chin Tien Wu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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
Issue number1
Publication statusPublished - 2013


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

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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