Additive multilevel preconditioners based on bilinear interpolation, matrix-dependent geometric coarsening and algebraic multigrid coarsening for second-order elliptic PDEs

Abstract

In this paper, we study additive multilevel preconditioners based on bilinear interpolation, matrix-dependent interpolations and the algebraic multigrid approach. We consider second-order elliptic problems, including strong elliptic ones, singular perturbation problems and problems with locally strongly varying or discontinuous coefficient functions. We report on the results of our numerical experiments which show that especially the method based on algebraic multigrid is mostly robust also in the additive case.