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：我们基于约束能量最小化广义多尺度有限元方法（CEM-GMsFEM）框架，针对高对比度线性孔隙弹性问题发展了一种部分显式时间离散化方法。首先，采用CEM-GMsFEM方法生成的主控基函数来捕捉重要自由度，已知该方法能给出与网格尺寸成比例的对比度无关收敛性。在典型情况下，主控基函数中仅有极少数自由度，这部分采用隐式处理。其次，我们在补空间中设计并引入一个附加空间，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，发现时间步长的限制条件与对比度无关。