通用多尺度有限元法（GMsFEM）用于各向异性介质中的弹性波传播
Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media
AI总结：
本文提出了一种通用多尺度有限元法，用于高效模拟各向异性介质中的弹性波传播，通过多尺度基函数减少自由度并保持精度。
摘要：
开发快速且准确的数值方法对于地震波传播以表征复杂地质结构和油气储层至关重要。然而，传统数值建模方法如有限差分法和有限元法在应用于非常大的模型时计算成本变得不可接受。我们提出了一种通用多尺度有限元法（GMsFEM）用于各向异性介质中的弹性波传播，其中我们从多个局部问题构造基函数，用于粗节点支持或粗元素的边界和内部。多尺度基函数的应用可以捕捉细尺度介质属性变化，并允许我们大大减少实现建模所需的自由度，与传统波动方程有限元法相比，同时将误差限制在较低水平。我们制定了多尺度方法的连续伽辽金和间断伽辽金公式，两者各有优缺点。将多尺度方法应用于三个异质模型显示，我们的多尺度方法可以有效模拟各向异性介质中的弹性波传播，并在建模系统中显著减少自由度。
英文摘要：
It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale medium property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.
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