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 language | English |
|---|---|
| Pages (from-to) | 140-154 |
| Number of pages | 15 |
| Journal | Journal of Computational and Applied Mathematics |
| Volume | 244 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2013 Jan 7 |
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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 journal › Article
}
TY - JOUR
T1 - Numerical studies on structure-preserving algorithms for surface acoustic wave simulations
AU - Hwang, Tsung-Min
AU - Li, Tiexiang
AU - Lin, Wen Wei
AU - Wu, Chin Tien
PY - 2013/1/7
Y1 - 2013/1/7
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.
KW - Palindromic quadratic eigenvalue problem
KW - Structure-preserving
KW - Surface acoustic wave
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U2 - 10.1016/j.cam.2012.11.020
DO - 10.1016/j.cam.2012.11.020
M3 - Article
AN - SCOPUS:84871800357
VL - 244
SP - 140
EP - 154
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
SN - 0377-0427
IS - 1
ER -