Some studies of the AMG performance in critical situations

Klaus Stüben


Algebraic multigrid has shown to be very efficient and robust for the solution of various types of linear algebraic systems of equations, in particular those arising from the discretization of scalar partial differential equations. Major research is focusing on the extension of AMG to systems of partial differential equations, for which a robustness and efficiency comparable to that of the scalar case has not yet been reached. But even for certain scalar problems, the performance of AMG may substantially deteriorate. We will discuss several critical situations and possible remedies for some particular scalar and systems problems.