Grid Application Division, National Center for High-Performance Computing, Taichung 40763,Taiwan
Department of Civil Engineering, National Taiwan University, Taipei 10617, Taiwan. Corresponding author, Tel.:+886-2-33664233. E-mail: liucs@ntu.edu.tw
Department of Systems Engineering and Naval Architecture, National Taiwan Ocean University, Keelung 20224, Taiwan
Abstract:
In this article, we propose a semi-analytical method to tackle the two-dimensional backward heat conduction problem (BHCP) by using a quasi-boundary idea. First, the Fourier series expansion technique is employed to calculate the temperature field u(x, y, t) at any time t < T. Second, we consider a direct regularization by adding an extra termau(x, y, 0) to reach a second-kind Fredholm integral equation for u(x, y, 0). The termwise separable property of the kernel function permits us to obtain a closed-form regularized solution. Besides, a strategy to choose the regularization parameter is suggested. When several numerical examples were tested, we find that the proposed scheme is robust and applicable to the two-dimensional BHCP.
