Algebraische Mehrgittermethoden mit alternativen starken Verbindungen

This thesis introduces the AscAMG preconditioner, a parallel Algebraic Multigrid Preconditioner for scalar, elliptic H1-problems that has been developed for NGSolve. The method gets is name from an alternative way to define strong connections that is based on a replacement matrix. This leads directly to a new variation of the smoothed prolongation method commonly found in aggregation based Multigrid solvers. The parallelization of the method is described in detail and scalable smoothers are found and discussed. After demonstrating the scalability of the method to at least 1800 cores with numerical results, conclusions are drawn and an outlook on possible future developments of the method is given