Smoothed Aggregation for Nonsymmetric Linear Systems

Abstract: Smoothed Aggregation (SA) is a technique from algebraic multigrid methods (AMG) which has shown very promising results when solving systems of linear equations with symmetric system matrices, but suboptimal results for nonsymmetric system matrices. The purpose of this thesis is to investigate the method EMIN(r) and a closely related method EMIN proposed by Sala and Tuminaro. EMIN(r) and EMIN were built on the success of SA in symmetric systems, but perform better in nonsymmetric systems. These methods have a more costly set-up, but promising results were found, in particular when performing one time-step of linear advection at extremely high CFL numbers.