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The application of dimension split method in the three‐dimensional heat equation |
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| Authors: | Jianping Zhao Yanren Hou Haibiao Zheng Yongfei Li Haifeng Wang |
| Affiliation: | 1. College of Mathematics and System Sciences, Xinjiang University, Urumuqi;2. China and Xijiang Institute of Ecology and Geography, Chinese Academy of Sciences, Urumqi, China;3. School of Mathematics and Statistics and Center for Computational Geosciences, Xi'an Jiaotong University, Xi'an, China;4. Department of Mathematics, East China Normal Univesity, Shanghai, China;5. Huawei Technologies Co., Ltd., Wuhan, China |
| Abstract: | A dimension splitting method (DSM) with Crank–Nicolson time discrete strategy for a three‐dimensional heat equation is proposed. The basic idea is to simulate the three‐Dimensional problem by numerically solving a series of two‐dimensional problems in parallel fashion. Convergence and error estimation for the DSM scheme are derived in the paper. Numerical experiments demonstrate the feasibility and efficiency of the DSM scheme. Copyright © 2016 John Wiley & Sons, Ltd. |
| Keywords: | dimension splitting method domain decomposition method heat equation Crank– Nicolson scheme parallel computing |