Open Access

ARTICLE

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

Xiaojing Liu^1,2, Jizeng Wang¹, Youhe Zhou¹

1 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.
2 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.

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Keywords

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