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

Tsung-Ming Huang Tiexiang Li Wen-Wei Lin Chin-Tien Wu

Numerical Analysis and Scientific Computing mathscidoc:1912.43744

Journal of Computational and Applied Mathematics, 244, 140-154, 2013.5
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
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@inproceedings{tsung-ming2013numerical,
  title={Numerical studies on structure-preserving algorithms for surface acoustic wave simulations},
  author={Tsung-Ming Huang, Tiexiang Li, Wen-Wei Lin, and Chin-Tien Wu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205441795673308},
  booktitle={Journal of Computational and Applied Mathematics},
  volume={244},
  pages={140-154},
  year={2013},
}
Tsung-Ming Huang, Tiexiang Li, Wen-Wei Lin, and Chin-Tien Wu. Numerical studies on structure-preserving algorithms for surface acoustic wave simulations. 2013. Vol. 244. In Journal of Computational and Applied Mathematics. pp.140-154. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205441795673308.
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