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Volume 18, Issue 3
Sparse Wavelet Element Method for Piezoelectric Equations in an Unbounded Domain

Jianguo Huang & Likun Qiu

DOI: 10.4208/nmtma.OA-2024-0137

Numer. Math. Theor. Meth. Appl., 18 (2025), pp. 733-755.

Published online: 2025-09

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  • Abstract

This paper is concerned with devising an efficient numerical method for the piezoelectric equations in an unbounded domain, which plays a fundamental role in design and analysis of microacoustic devices with piezoelectric substrate. We make use of the perfectly matched layer method to transform the underlying problem as a surrogate in a bounded domain, which is further solved by a sparse wavelet element method. The latter method can be viewed as a combination of a wavelet element method and a sparse grid method. The numerical results are performed to show the proposed method is very efficient and outperforms the usual finite element method. It can be naturally extended to two/three dimensional problems in an unbounded domain whose boundary consists of line segments or rectangles parallel to coordinate lines or planes.

  • Keywords

Piezoelectric equation, sparse grid method, sparse tensor product method, wavelet element method.

  • AMS Subject Headings

65D40, 65T60, 65N22

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-18-733, author = {Huang , Jianguo and Qiu , Likun}, title = {Sparse Wavelet Element Method for Piezoelectric Equations in an Unbounded Domain}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2025}, volume = {18}, number = {3}, pages = {733--755}, abstract = {

This paper is concerned with devising an efficient numerical method for the piezoelectric equations in an unbounded domain, which plays a fundamental role in design and analysis of microacoustic devices with piezoelectric substrate. We make use of the perfectly matched layer method to transform the underlying problem as a surrogate in a bounded domain, which is further solved by a sparse wavelet element method. The latter method can be viewed as a combination of a wavelet element method and a sparse grid method. The numerical results are performed to show the proposed method is very efficient and outperforms the usual finite element method. It can be naturally extended to two/three dimensional problems in an unbounded domain whose boundary consists of line segments or rectangles parallel to coordinate lines or planes.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2024-0137}, url = {http://global-sci.org/intro/article_detail/nmtma/24325.html} }
TY - JOUR T1 - Sparse Wavelet Element Method for Piezoelectric Equations in an Unbounded Domain AU - Huang , Jianguo AU - Qiu , Likun JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 733 EP - 755 PY - 2025 DA - 2025/09 SN - 18 DO - http://doi.org/10.4208/nmtma.OA-2024-0137 UR - https://global-sci.org/intro/article_detail/nmtma/24325.html KW - Piezoelectric equation, sparse grid method, sparse tensor product method, wavelet element method. AB -

This paper is concerned with devising an efficient numerical method for the piezoelectric equations in an unbounded domain, which plays a fundamental role in design and analysis of microacoustic devices with piezoelectric substrate. We make use of the perfectly matched layer method to transform the underlying problem as a surrogate in a bounded domain, which is further solved by a sparse wavelet element method. The latter method can be viewed as a combination of a wavelet element method and a sparse grid method. The numerical results are performed to show the proposed method is very efficient and outperforms the usual finite element method. It can be naturally extended to two/three dimensional problems in an unbounded domain whose boundary consists of line segments or rectangles parallel to coordinate lines or planes.

Huang , Jianguo and Qiu , Likun. (2025). Sparse Wavelet Element Method for Piezoelectric Equations in an Unbounded Domain. Numerical Mathematics: Theory, Methods and Applications. 18 (3). 733-755. doi:10.4208/nmtma.OA-2024-0137
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