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A High-Order Accurate Wavelet Method for Solving Three-Dimensional Poisson Problems

Xiaojing Liu1,2, Jizeng Wang1, Youhe Zhou1
Key Laboratory of Mechanics on Disaster and Environment in Western China, the Ministry of Education, and School of Civil Engineering and Mechanics, Lanzhou University, Lanzhou, Gansu730000, China.
Corresponding author. Email: liuxiaojing@lzu.edu.cn.

Computer Modeling in Engineering & Sciences 2015, 107(6), 433-446. https://doi.org/10.3970/cmes.2015.107.433

Abstract

Based on the approximation scheme for a L2-function defined on a three-dimensional bounded space by combining techniques of boundary extension and Coiflet-type wavelet expansion, a modified wavelet Galerkin method is proposed for solving three-dimensional Poisson problems with various boundary conditions. Such a wavelet-based solution procedure has been justified by solving five test examples. Numerical results demonstrate that the present wavelet method has an excellent numerical accuracy, a fast convergence rate, and a very good capability in handling complex boundary conditions.

Keywords

Coiflet-type wavelet, Galerkin method, three-dimensional Poisson equation, mixed boundary conditions.

Cite This Article

Liu, X., Wang, J., Zhou, Y. (2015). A High-Order Accurate Wavelet Method for Solving Three-Dimensional Poisson Problems. CMES-Computer Modeling in Engineering & Sciences, 107(6), 433–446.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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