TY - JOUR
T1 - A Hybrid Method for Three-Dimensional Semi-Linear Elliptic Equations
AU - Huang , Jianguo
AU - Ma , Shengbiao
AU - Wang , Haoqin
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 420
EP - 434
PY - 2023
DA - 2023/04
SN - 13
DO - http://doi.org/10.4208/eajam.2022-264.091122 
UR - https://global-sci.org/intro/article_detail/eajam/21655.html
KW - Deep learning, iterative method, semi-linear elliptic equations, convergence rate analysis.
AB - <p style="text-align: justify;">This paper is concerned with a hybrid method for three-dimensional semilinear elliptic equations, constructed by combining the ideas presented in [Huang et al.,
J. Comput. Phys. 419 (2020)] and [Zhang et al., Comput. Math. Appl. 80 (2020)]. The
convergence rate analysis indicates that the method converges rapidly. Numerical examples support the theoretical results and show that the method proposed outperforms
the purely deep learning-based and traditional iterative methods.</p>