A systematic comparison of coupled and distributive smoothing in multigrid for the poroelasticity system

In this paper, we present efficient multigrid methods for the system of poroelasticity equations discretized on a staggered grid. In particular, we compare two different smoothing approaches with respect to efficiency and robustness. One approach is based on the coupled relaxation philosophy. We introduce ‘cell‐wise’ and ‘line‐wise’ versions of the coupled smoothers. They are compared with a distributive relaxation, that gives us a decoupled system of equations. It can be smoothed equation‐wise with basic iterative methods. All smoothing methods are evaluated for the same poroelasticity test problems in which parameters, like the time step, or the Lamé coefficients are varied. Some highly efficient methods result, as is confirmed by the numerical experiments.