Two-Level Finite Difference Methods for Simulating the High-Dimensional Lagging Models of Heat Conduction

Heat transfer at microscale plays an important role in microtechnology applications. First, this paper is concerned with the numerical solution of a two-dimensional (2D) heat transfer equation at microscale through a second-order alternating direction implicit (ADI) method. By the discrete energy method, it is shown that the ADI solution converges to the exact solution with a convergence order of O(τ²+h²_x+h²_y) in L²-norm. Second, the ADI method is generalized to numerically solve the three-dimensional (3D) problem, and provides numerical solutions of order two in both time and space. Finally, numerical results testify the temporal and spatial accuracy of the ADI method.