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Volume 36, Issue 2
A Sparse Grid Wavelet Galerkin Method for 3-D Static Piezoelectric Equations

Jianguo Huang & Likun Qiu

DOI: 10.4208/cicp.OA-2023-0193

Commun. Comput. Phys., 36 (2024), pp. 419-450.

Published online: 2024-09

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  • Abstract

The 3-D static piezoelectric equations with four unknowns are fundamental in studying physical behavior of piezoelectric materials. It is very challenging to numerically solve the equations efficiently due to the so-called “curse of dimensionality”. In this paper, we propose a sparse grid wavelet Galerkin method to overcome the difficulty, by combining the wavelet Galerkin method and the sparse grid technique. The error analysis is also developed in detail. Both the theoretical analysis and numerical results show the previous method outperforms the usual finite element method.

  • Keywords

Piezoelectric equations, sparse grid method, sparse tensor product method, wavelet Galerkin method.

  • AMS Subject Headings

65D40, 65N30, 65T60, 65N12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-36-419, author = {Huang , Jianguo and Qiu , Likun}, title = {A Sparse Grid Wavelet Galerkin Method for 3-D Static Piezoelectric Equations}, journal = {Communications in Computational Physics}, year = {2024}, volume = {36}, number = {2}, pages = {419--450}, abstract = {

The 3-D static piezoelectric equations with four unknowns are fundamental in studying physical behavior of piezoelectric materials. It is very challenging to numerically solve the equations efficiently due to the so-called “curse of dimensionality”. In this paper, we propose a sparse grid wavelet Galerkin method to overcome the difficulty, by combining the wavelet Galerkin method and the sparse grid technique. The error analysis is also developed in detail. Both the theoretical analysis and numerical results show the previous method outperforms the usual finite element method.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2023-0193}, url = {http://global-sci.org/intro/article_detail/cicp/23388.html} }
TY - JOUR T1 - A Sparse Grid Wavelet Galerkin Method for 3-D Static Piezoelectric Equations AU - Huang , Jianguo AU - Qiu , Likun JO - Communications in Computational Physics VL - 2 SP - 419 EP - 450 PY - 2024 DA - 2024/09 SN - 36 DO - http://doi.org/10.4208/cicp.OA-2023-0193 UR - https://global-sci.org/intro/article_detail/cicp/23388.html KW - Piezoelectric equations, sparse grid method, sparse tensor product method, wavelet Galerkin method. AB -

The 3-D static piezoelectric equations with four unknowns are fundamental in studying physical behavior of piezoelectric materials. It is very challenging to numerically solve the equations efficiently due to the so-called “curse of dimensionality”. In this paper, we propose a sparse grid wavelet Galerkin method to overcome the difficulty, by combining the wavelet Galerkin method and the sparse grid technique. The error analysis is also developed in detail. Both the theoretical analysis and numerical results show the previous method outperforms the usual finite element method.

Jianguo Huang & Likun Qiu. (2024). A Sparse Grid Wavelet Galerkin Method for 3-D Static Piezoelectric Equations. Communications in Computational Physics. 36 (2). 419-450. doi:10.4208/cicp.OA-2023-0193
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