Open Access

ARTICLE

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

by Chih-Wen Chang¹, Chein-Shan Liu²

1 Grid Applied Technology Division, National Center for High-Performance Computing, Taichung 40763, Taiwan. Corresponding author, E-mail: d93510002@ntou.edu.tw
2 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.

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Keywords

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