论文标题
离散断裂网络的域分解方法的可伸缩性弱
Weak scalability of domain decomposition methods for discrete fracture networks
论文作者
论文摘要
离散的断裂网络（DFN）是复杂的三维结构，其特征在于平面多边形裂缝的相互作用，并用于模拟断裂培养基中的流动。尽管适合域分解（DD）技术，但在DD方法中应用DFN的作品相对较少。在本手稿中，我们介绍了应用于DFNS的优化Schwarz方法（OSM）的理论研究。有趣的是，我们证明，在适当的假设下，在域分解的合适假设下，OSM可以弱扩展（即它们在许多迭代中收敛到给定的耐受性）。在最近的工作显示DD方法较弱的DD方法的特定几何配置，即使没有粗空间，这种贡献符合对DD方法弱的可伸缩性的重新兴趣。尽管简化了可能在实践中可能违反的假设，但我们的分析提供了启发式方法，以最大程度地减少现实环境中的计算工作。最后，我们强调，提出的方法可以直接推广以研究应用于DFN的其他经典DD方法。
Discrete Fracture Networks (DFNs) are complex three-dimensional structures characterized by the intersections of planar polygonal fractures, and are used to model flows in fractured media. Despite being suitable for Domain Decomposition (DD) techniques, there are relatively few works on the application of DD methods to DFNs. In this manuscript, we present a theoretical study of Optimized Schwarz Methods (OSMs) applied to DFNs. Interestingly, we prove that the OSMs can be weakly scalable (that is, they converge to a given tolerance in a number of iterations independent of the number of fractures) under suitable assumptions on the domain decomposition. This contribution fits in the renewed interest on the weak scalability of DD methods after recent works showed weak scalability of DD methods for specific geometric configurations, even without coarse spaces. Despite simplifying assumptions which may be violated in practice, our analysis provides heuristics to minimize the computational efforts in realistic settings. Finally, we emphasize that the methodology proposed can be straightforwardly generalized to study other classical DD methods applied to DFNs.
