Reduced-Basis Approach for Homogenization beyond the Periodic Setting
Reduced-Basis Approach for Homogenization beyond the Periodic Setting
复制标题
超出周期性设置的均质化的减基方法
DOI：
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发表时间：
2007
影响因子：
1.6
通讯作者：
S. Boyaval
中科院分区：
文献类型：
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作者：
S. Boyaval
考虑椭圆型偏微分方程均匀化的平均系数的计算。在该问题中，与许多多尺度问题一样，需要在微观尺度上进行大量由宏观尺度参数化的类似计算。这是一个非常适合模型简化尝试的框架。这项工作的目的是展示减少基的方法如何允许人们在不损失任何精度的情况下加速大量细胞问题的计算。这种减基方法的基本组成部分是后验误差估计，它为感兴趣的输出提供了明确的误差界限，以及一个分为离线和在线阶段的近似过程，它解耦了近似空间的生成及其对Galerkin投影的使用。
We consider the computation of averaged coefficients for the homogenization of elliptic partial differential equations. In this problem, like in many multiscale problems, a large number of similar computations parameterized by the macroscopic scale is required at the microscopic scale. This is a framework very well suited for model reduction attempts. The purpose of this work is to show how the reduced-basis approach allows one to speed up the computation of a large number of cell problems without any loss of precision. The essential components of this reduced-basis approach are the a posteriori error estimation, which provides sharp error bounds for the outputs of interest, and an approximation process divided into offline and online stages, which decouples the generation of the approximation space and its use for Galerkin projections.