The linear system $Ax=b$ is coming from the discretization of an elliptic PDE. Multigrid method is used in order to solve it. Suppose $c_0$ is the coarsening factor on level 0 and $c_m$ the coarsening factor on level > 0. $c_m$ is choosed to be 2 (standard coarsening) in all levels > 0. How can the choice of $c_0$ can affect Multigrid's convergence? I assume that an aggressive coarsening at the beginning may increase the number of MG iterations while reducing the convergence time. Is there any possibility the choice of $c_0$ to lead MG to diverge?