雙曲問題的多尺度方法

Abstract

本文中，我們將發展雙曲問題的多尺度方法。我們的方法建立在 HMM 的架構上。HMM 的架構是在 [Commun. Math. Sci. 1 (1) 87] 所提出的。該架構包含兩部分 ：微尺度上的問題(原方程度)和宏觀問題。藉由解宏觀問題，我們所需的計算時間將比直接解原問題，要少得多。除了方法的描述外，我們也呈現一些數值的結果，以及誤差的分析。

In this thesis, we design a numerical method to solve multiscale hyperbolic problems. This method is based on the framework HMM, introduced in [Commun. Math. Sci. 1 (1) 87]. The HMM framework contains two main components: microscopic problem (orginal equation) and macroscopic problem. By solving the macroscopic probem, our cost is much lower than solving the original equation directly. We describe the details of the HMM method and present some numerical results. Finally, we analyze the errors of the HMM method.