The paper analyzes various parallel matrix-vector multiplications with different matrix and vector types resulting from a non-overlapping domain decomposition. Under certain requirements to the f.e. mesh all given matrix and vector types can be used in the multiplication. The general framework is applied to the investigation of the preconditioning step in cg-like methods. Not only the well-known domain decomposition preconditioners fit into the concept but also parallelized global incomplete factorizations are feasible. Additionally, those global incomplete factorizationscan can be used as smoothers in global multilevel methods. Numerical results on a SPMD parallel machine are presented.

Keywords : Parallel iterative solvers, Incomplete Factorization, Preconditioning, Domain decomposition, Finite element method.