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 - <p style="text-align: justify;">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.</p>