On algebraic multilevel methods for non-symmetric systems - convergence results.
Christian Mense, Reinhard Nabben · 2008
We analyze algebraic multilevel methods applied to non-symmetric M -matrices. Two types of multilevel approximate block factorizations are consider ed. The first one is related to the AMLI method. The second method is the multiplicative counterpart of the AMLI approach which we call the multiplicative algebraic multilevel (MAMLI) method. The MAMLI method is closely related to certain geometric and algebraic multigrid methods, such as the AMGr method. Although these multilevel methods work very well in practice for many problems, not much is known about theoretical convergence properties for non-symmetric problems. Here, we establish convergence results and comparison results betw een AMLI and MAMLI multilevel methods applied to non-symmetric M -matrices.