Numerical Solution of Three-Dimensional Backward Heat Conduction Problems By the Time Evolution Method of Fundamental Solutions
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.
International Journal of Heat and Mass Transfer
(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.
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