A MULTISCALE FINITE ELEMENT METHOD FOR PDES WITH OSCILLATORY COEFFICIENTS
A MULTISCALE FINITE ELEMENT METHOD FOR PDES WITH OSCILLATORY COEFFICIENTS
复制标题
具有振荡系数的偏微分方程的多尺度有限元方法
DOI：
--
复制
发表时间：
1997
期刊：
影响因子：
--
通讯作者：
Xiao
中科院分区：
文献类型：
--
作者：
T. Hou;Xiao
提出了求解高振荡系数偏微分方程的多尺度有限元方法。MFEM提供了一个通用的、系统的框架，可以在不直接求解小尺度细节的情况下有效地捕获大尺度解。这是通过构造适应微分算子局部性质的多尺度有限元基函数来实现的。基函数的构造从元素到元素完全解耦；因此，该方法自然适用于并行计算。我们简要概述了该方法的分析，重点介绍了“尺度共振”效应及其分辨率-一种过采样技术。然后，通过数值实验验证了该方法的准确性和有效性。
We present a multiscale finite element method (MFEM) for solving partial differential equations with highly oscillatory coefficients. MFEM provides a general and systematic framework for effectively capturing the large scale solutions without directly resolving the small scale details. This is accomplished by constructing the multiscale finite element base functions that are adaptive to the local property of the differential operator. The construction of the base functions is fully decoupled from element to element; thus the method is naturally adapted to parallel computing. We briefly overview the analysis of the method, emphasizing on the “scale resonance” effect and its resolution—an over-sampling technique. Then, we demonstrate the accuracy and efficiency of the method through numerical experiments.