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Volume 13, Issue 2
A Hybrid Method for Three-Dimensional Semi-Linear Elliptic Equations

Jianguo Huang, Shengbiao Ma & Haoqin Wang

East Asian J. Appl. Math., 13 (2023), pp. 420-434.

Published online: 2023-04

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  • Abstract

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.

  • AMS Subject Headings

68U99, 65N30, 65N25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-13-420, author = {Huang , JianguoMa , Shengbiao and Wang , Haoqin}, title = {A Hybrid Method for Three-Dimensional Semi-Linear Elliptic Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2023}, volume = {13}, number = {2}, pages = {420--434}, abstract = {

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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.2022-264.091122 }, url = {http://global-sci.org/intro/article_detail/eajam/21655.html} }
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 -

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.

Jianguo Huang, Shengbiao Ma & Haoqin Wang. (2023). A Hybrid Method for Three-Dimensional Semi-Linear Elliptic Equations. East Asian Journal on Applied Mathematics. 13 (2). 420-434. doi:10.4208/eajam.2022-264.091122
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