Numerical Solution of Three-Dimensional Backward Heat Conduction Problems By the Time Evolution Method of Fundamental Solutions
Document Type
Article
Publication Date
5-1-2011
Department
Mathematics
School
Mathematics and Natural Sciences
Abstract
The time evolution method of fundamental solutions (MFS) is proposed to solve three-dimensional backward heat conduction problems (BHCPs). The time evolution MFS is obtained through the linear super-position of diffusion fundamental solutions. Through a correct treatment of temporal evolution, the MFS can be implemented to solve strongly ill-posed problems. The numerical results demonstrate the accuracy and stability of the MFS for three-dimensional BHCPs with high levels of noise. This represents the first implementation of MFS to solve three-dimensional BHCPs, and demonstrates that time evolution MFS is a stable and powerful numerical scheme which has the potential to significantly improve the solution of three-dimensional backward heat conduction problems. (C) 2011 Elsevier Ltd. All rights reserved.
Publication Title
International Journal of Heat and Mass Transfer
Volume
54
Issue
41225
First Page
2446
Last Page
2458
Recommended Citation
Tsai, C.,
Young, D.,
Kolibal, J.
(2011). Numerical Solution of Three-Dimensional Backward Heat Conduction Problems By the Time Evolution Method of Fundamental Solutions. International Journal of Heat and Mass Transfer, 54(41225), 2446-2458.
Available at: https://aquila.usm.edu/fac_pubs/455