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