【作者】 唐闻瑜；

【导师】 岳兴业；

【作者基本信息】 苏州大学 ， 计算数学， 2005， 硕士

【摘要】 本文考虑了带有振荡系数的椭圆问题。我们采用一类多尺度方法(Heterogeneous Multiscale Method,简称HMM)来进行求解。HMM包括两部分的内容:一是在宏观尺度网格上选择一个宏观算法;二是通过解局部的细网格问题来估算未知的宏观尺度数据。所以这一方法的关键:一是如何选择宏观算法;二是如何估算未知的宏观数据。我们采用了一类考虑数值积分影响的有限体积法(Finite Volume Method,简称FVM)作为宏观算法。于是得到一类多尺度有限体积法(HMM-FVM)。我们分析了此多尺度有限体积法的误差,并给出了数值算例来验证该多尺度有限体积法有较好的收敛阶。更多还原

【Abstract】 In this paper we consider the elliptic PDE with oscillating coefficients. We adopt heterogeneous multiscale method (HMM) to solve the problem. HMM consists of two components : selection of a macroscopic solver on a macroscale grid, and estimating the missing macroscale data by solving locally the fine scale problem. So the key of this method is how to select a macroscopic solver and how to estimate the missing macroscale data. A kind of finite volume method(FVM) that considers the effects of numerical integration is used as the macroscopic solver in HMM. Then we get the method named HMM-FVM. We present the error estimate and show some numerical examples to confirm that HMM-FVM has good convergent order.更多还原