论文标题
空间网络模型的超定位
Super-localization of spatial network models
论文作者
论文摘要
空间网络模型被用作广泛应用中的简化离散表示形式，例如血管中的流量，基于纤维的材料的弹性以及多孔材料的孔网络模型。然而，所得的线性系统通常很大且条件不佳，其数值解决方案具有挑战性。 本文提出了一种用于空间网络模型的数值均质化技术，该技术基于超级局部正交分解（Slod），该技术最近引入了用于椭圆的多尺度部分偏微分方程。它提供了与材料数据平滑度无关的近似特性的精确粗解决方案空间。平台的一个独特的卖点是，它构建了这些粗空间的几乎局部基础，与其他最先进的方法相比，在尺度上需要更少的计算，并在粗尺度上实现了改善的稀疏性。我们提供了对所提出方法的A-tosteriori分析，并在数值上确认该方法的独特定位属性。此外，我们还显示了其适用于高对比度通道材料数据的适用性。
Spatial network models are used as a simplified discrete representation in a wide range of applications, e.g., flow in blood vessels, elasticity of fiber based materials, and pore network models of porous materials. Nevertheless, the resulting linear systems are typically large and poorly conditioned and their numerical solution is challenging. This paper proposes a numerical homogenization technique for spatial network models which is based on the Super Localized Orthogonal Decomposition (SLOD), recently introduced for elliptic multiscale partial differential equations. It provides accurate coarse solution spaces with approximation properties independent of the smoothness of the material data. A unique selling point of the SLOD is that it constructs an almost local basis of these coarse spaces, requiring less computations on the fine scale and achieving improved sparsity on the coarse scale compared to other state-of-the-art methods. We provide an a-posteriori analysis of the proposed method and numerically confirm the method's unique localization properties. In addition, we show its applicability also for high-contrast channeled material data.
