摘要
本文主要讨论一类重要的数学物理问题，即双曲型波动问题。首先，我们利用均匀化和多尺度渐近展开法求解周期复合材料振荡系数双曲型波动问题，在假定振荡系数具有双尺度，且关于快尺度是周期的条件下，我们得到了一个在实际计算时更易操作的渐近展开式，并给出了这种方法的一个详尽的收敛性分析。其次，我们利用多尺度有限元法讨论了小周期复合材料振荡系数双曲型波动方程的半离散解逼近，并给出了相应的误差估计。
A class of important mathematical physics problems, i.e. hyperbolic type wave problems are discussed in this paper. First, we use homogenization theory and multiscale asymptotic expansion to resolve hyperbolic type wave problems with rapidly oscillating coefficients in periodic composite materials. We capture a more easily operated asymptotic expansion when computed in practice under the assumption that the oscillating coefficients is of two scales and is periodic in the fast scale, and provide a detailed convergence analysis of our method. Second, we use multiscale finite element method to discuss the approximation of semi-discrete resolution about the hyperbolic type wave equation with rapidly oscillating in small periodic composite materials, and provide its error estimates.
引文
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