In this paper, we propose to use modified B-splines spanned on several macroelements as a basis for building the multiscale finite element method (MsFEM) trail functions. The main benefit of our approach is that the calculations of a multiscale function are done in one step on the whole support, in contrast to standard MsFEM shape functions that are evaluated coarse element by element and require a cumbersome gluing. Selected numerical experiments for flow in porous media with periodic and random material properties distributions were performed to test our modified MsFEM with the new basis functions. We found that the method indeed improves standard MsFEM for fast oscillating material properties. We observed that the resonance effect, when the ratio of inclusion size and coarse mesh size approaches 1 (ε/H → 1) can be reduced by increasing the order of B-splines.

中文翻译：

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多尺度有限元方法与等几何分析的耦合

在本文中，我们建议使用跨越多个宏元素的修饰B样条作为构建多尺度有限元方法（MsFEM）追踪函数的基础。我们的方法的主要好处是，与标准MsFEM形状函数（逐个元素进行评估并需要繁琐的胶合）相比，多尺度函数的计算在整个支架上一步完成。对具有周期性和随机材料特性分布的多孔介质中的流动进行了选定的数值实验，以测试具有新基础函数的改进MsFEM。我们发现，该方法确实提高了标准MsFEM的快速振荡材料性能。我们观察到共振效应，