Multiscale Modeling &Simulation, Volume 18, Issue 2, Page 1153-1177, January 2020.
In the framework of generalized finite element methods for elliptic equations with rough coefficients, efficiency and accuracy of the numerical method depend critically on the use of appropriate basis functions. This work explores several random sampling strategies that construct approximations to the optimal set of basis functions of a given dimension, and proposes a quantitative criterion to analyze and compare these sampling strategies. Numerical evidence shows that the best results are achieved by two strategies, Random Gaussian and Smooth Boundary sampling.

中文翻译：

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广义有限元法中基函数构造的随机抽样

《多尺度建模与仿真》，第18卷，第2期，第1153-1177页，2020
年1月。在具有粗糙系数的椭圆方程的广义有限元方法的框架内，数值方法的效率和准确性主要取决于适当基函数的使用。这项工作探索了几种随机抽样策略，这些策略构造了给定维的最佳基础函数集的近似值，并提出了定量标准来分析和比较这些抽样策略。数值证据表明，通过两种策略（随机高斯采样和平滑边界采样）可获得最佳结果。