In this work, we present a multiscale approach for the reliable coarse-scale approximation of spatial network models represented by a linear system of equations with respect to the nodes of a graph. The method is based on the ideas of the Localized Orthogonal Decomposition (LOD) strategy and is constructed in a fully algebraic way. This allows to apply the method to geometrically challenging objects such as corrugated cardboard. In particular, the method can also be applied to finite difference or finite element discretizations of elliptic partial differential equations, yielding an approximation with similar properties as the LOD in the continuous setting. We present a rigorous error analysis of the proposed method under suitable assumptions on the network. Moreover, numerical examples are presented that underline our theoretical results.

翻译：本文提出了一种针对空间网络模型的多尺度方法，旨在对由节点图上的线性方程组表示的空间网络进行可靠的粗尺度近似。该方法基于局部正交分解（LOD）策略的思想，并以完全代数方式构建，从而能够应用于几何上具有挑战性的物体（如瓦楞纸板）。特别地，该方法还可用于椭圆型偏微分方程的有限差分或有限元离散化，得到与连续情形下LOD具有相似性质的近似。我们在网络满足适当假设的条件下，对所提方法进行了严格的误差分析。此外，数值算例进一步验证了我们的理论结果。