The dual continuum model serves as a powerful tool in the modeling of subsurface applications. It allows a systematic coupling of various components of the solutions. The system is of multiscale nature as it involves high heterogeneous and high contrast coefficients. To numerically compute the solutions, some types of reduced order methods are necessary. We will develop and analyze a novel multiscale method based on the recent advances in multiscale finite element methods. Our method will compute multiple local multiscale basis functions per coarse region. The idea is based on some local spectral problems, which are important to identify high contrast channels, and an energy minimization principle. Using these concepts, we show that the basis functions are localized, even in the presence of high contrast long channels and fractures. In addition, we show that the convergence of the method depends only on the coarse mesh size. Finally, we present several numerical tests to show the performance.

中文翻译：

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双连续体模型的约束能量最小化广义多尺度有限元方法

双连续介质模型是地下应用建模的强大工具。它允许系统地耦合解决方案的各种组件。该系统具有多尺度性质，因为它涉及高异质性和高对比度系数。为了数值计算解，一些类型的降阶方法是必要的。我们将基于多尺度有限元方法的最新进展开发和分析一种新的多尺度方法。我们的方法将计算每个粗略区域的多个局部多尺度基函数。这个想法基于一些局部光谱问题，这对于识别高对比度通道很重要，以及能量最小化原则。使用这些概念，我们表明即使在存在高对比度长通道和裂缝的情况下，基函数也是局部的。此外，我们表明该方法的收敛性仅取决于粗网格尺寸。最后，我们提出了几个数值测试来展示性能。