Parallel Incomplete Cholesky Preconditioners Based on the Non-Overlapping Data Distribution

The paper analyses various parallel incomplete factorizations based on the non-overlapping domain decomposition. The general framework is applied to the investigation of the preconditioning step in cg-like methods. Under certain conditions imposed on the nite element mesh, all matrix and vector types given by the special data distribution can be used in the matrix-by-vector multiplications. Not only the well-known domain decomposition preconditioners t into the concept but also parallelized global incomplete factorizations are feasible. Additionally, those global incomplete factorizations can be used as smoothers in parallel multigrid methods. Numerical results on a parallel machine with distributed memory are presented.