Numerical solution of three-dimensional backward heat conduction problems by the time evolution method of fundamental solutions

作者：Tsai C H; Young D L^*; Kolibal J

来源：International Journal of Heat and Mass Transfer, 2011, 54(11-12): 2446-2458.

DOI：10.1016/j.ijheatmasstransfer.2011.02.017

• Method of fundamental solutions
• Three-dimensional
• Backward heat conduction problem
• Ill-posed problem
• Diffusion 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.

• 出版日期2011-5