  Four adaptations of the smoothed aggregation algebraic multigrid (SA-AMG)
method are proposed with an eye towards improving the convergence and
robustness of the solver in situations when the discretization matrix contains
many weak connections. These weak connections can cause higher than expected
levels of fill-in within the coarse discretization matrices and can also give
rise to sub-optimal smoothing within the prolongator smoothing phase. These
smoothing drawbacks are due to the relatively small size of some diagonal
entries within the filtered matrix that one obtains after dropping the weak
connections. The new algorithms consider modifications to the Jacobi-like step
that defines the prolongator smoother, modifications to the filtered matrix,
and also direct modifications to the resulting grid transfer operators.
Numerical results are given illustrating the potential benefits of the proposed
adaptations.
