In this paper, we consider a time-dependent discrete network model with highly varying connectivity. The approximation by time is performed using an implicit scheme. We propose the coarse scale approximation construction of network models based on the Generalized Multiscale Finite Element Method. An accurate coarse-scale approximation is generated by solving local spectral problems in sub-networks. Convergence analysis of the proposed method is presented for semi-discrete and discrete network models. We establish the stability of the multiscale discrete network. Numerical results are presented for structured and random heterogeneous networks.

翻译：本文研究具有高度变化连通性的时间相关离散网络模型。时间近似采用隐式格式，提出基于广义多尺度有限元方法的网络模型粗尺度近似构建方案。通过求解子网络中的局部谱特征问题生成精确的粗尺度近似，并给出了所提方法在半离散与离散网络模型中的收敛性分析。建立了多尺度离散网络的稳定性。数值结果分别针对结构化与随机异质网络进行展示。