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A Backward Group Preserving Scheme for Multi-Dimensional Backward Heat Conduction Problems

Chih-Wen Chang1, Chein-Shan Liu2
Grid Applied Technology Division, National Center for High-Performance Computing, Taichung 40763, Taiwan. Corresponding author, E-mail: d93510002@ntou.edu.tw
Department of Civil Engineering, National Taiwan University, Taipei 10617, Taiwan

Computer Modeling in Engineering & Sciences 2010, 59(3), 239-274. https://doi.org/10.3970/cmes.2010.059.239

Abstract

In this article, we propose a backward group preserving scheme (BGPS) to tackle the multi-dimensional backward heat conduction problem (BHCP). The BHCP is well-known as severely ill-posed because the solution does not continuously depend on the given data. When eight numerical examples (including nonlinear and nonhomogeneous BHCP, and Neumann and Robin conditions of homogeneous BHCP) are examined, we find that the BGPS is applicable to the multi-dimensional BHCP. Even with noisy final data, the BGPS is also robust against disturbance. The one-step BGPS effectively reconstructs the initial data from the given final data, which with a suitable grid length produces a highly accurate solution never seen before. The results are very important in the computations of multi-dimensional BHCP.

Keywords

Nonlinear backward heat conduction problem, Strongly ill-posed problem, Nonhomogeneous heat conduction equation, Backward group preserving scheme (BGPS), Group preserving scheme (GPS)

Cite This Article

Chang, C., Liu, C. (2010). A Backward Group Preserving Scheme for Multi-Dimensional Backward Heat Conduction Problems. CMES-Computer Modeling in Engineering & Sciences, 59(3), 239–274.



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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