We develop a partially explicit time discretization based on the framework of constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) for the problem of linear poroelasticity with high contrast. Firstly, dominant basis functions generated by the CEM-GMsFEM approach are used to capture important degrees of freedom and it is known to give contrast-independent convergence that scales with the mesh size. In typical situation, one has very few degrees of freedom in dominant basis functions. This part is treated implicitly. Secondly, we design and introduce an additional space in the complement space and these degrees are treated explicitly. We also investigate the CFL-type stability restriction for this problem, and the restriction for the time step is contrast independent.

翻译：基于约束能量最小化广义多尺度有限元方法框架，针对高对比度线性孔隙弹性问题，我们开发了一种部分显式时间离散格式。首先，采用CEM-GMsFEM方法生成的主基函数用于捕捉重要自由度，已知该方法能够提供与网格尺寸成比例的对比度无关收敛性。在典型情形下，主基函数中自由度数量极少，此部分采用隐式处理。其次，设计并引入补充空间中的附加空间，这些自由度采用显式处理。我们还研究了该问题的CFL型稳定性限制条件，且时间步长的限制与对比度无关。