Step 2 -- Multilevel Preconditioners

These preconditioners are implemented by the ML library, by class ML_Epetra::MultiLevelPreconditioner, which is available here.

ML is Sandia's main multigrid preconditioning package. ML is designed to solve large sparse linear systems of equations arising primarily from elliptic PDE discretizations.

If you want to analyze the performances of multigrid preconditioners, first click on Multilevel Preconditioners to visualize the list of parameters, then set Analyze Multilevel Preconditioners to Yes. You still need to specify several parameters; probably, the most important ones are the Maximum coarse size and the Smoother type for the different levels. Level 0 is the finest level.

Typically, you should first try lightweight smoothers on the finest levels (0, 1), and something stronger on the other levels. If this does not suffice, then try a stronger smoothers also for levels 0 and 1.

If the problem is symmetric, Damping factor for aggregation should be 1.333; for highly non-symmetric problems, instead, 0.0 is a safer choice.