An efficient and accurate method for transient heat conduction in 1D periodic structures

An efficient and accurate method is proposed for solving transient heat conduction in a one-dimensional (1D) periodic structure. Based on the physical features of transient heat conduction, the periodic property of the structure and the physical meaning of the matrix exponential, the sparsity of the matrix exponential corresponding to the 1D periodic structure and the repeatability of the elements in the matrix are proved in detail in this paper. According to the algebraic structure of the matrix exponential and the precise integration method (PIM), an efficient and accurate method is proposed by computing the matrix exponential corresponding to a representative periodic structure (RPS) with a few unit cells instead of computing the matrix exponential corresponding to the entire periodic structure. The proposed method achieves significantly improved computational efficiency in terms of both CPU time and memory. Meanwhile, the method inherits the accuracy and stability of the original PIM. Those merits of the proposed method are verified through two numerical examples.