Multiscale asymptotic method for heat transfer equations in lattice-type structures
Fang-Man Zhai 1, Li-Qun Cao 11 State Key Laboratory of Scientific and Engineering Computing , Institute of Computational Mathematics and Science-Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China.
In this paper, we discuss the initial-boundary value problem for the heat transfer equation in lattice-type structures that arises from the aerospace industry and the structural engineering. The main results obtained in this paper are the convergence theorems by using the homogenization method and the multiscale asymptotic method (see Theorems 2.1 and 2.2). Some numerical examples are given for three types of lattice structures. These numerical results suggest that the first-order multiscale method should be a better choice compared with the homogenization method and the second-order multiscale method for solving the heat transfer equations in lattice-type structures.
AMS subject classifications: 65F10, 65W05
Key words: Homogenization, multiscale asymptotic expansion, parabolic equation, lattice-type structure, multiscale finite element method.
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