On the effect of partitioning schemes in semi-aggregation type techniques based on parallel pipelined iterative methods

A new parallel variant of the multi-projection method designed to solve general sparse linear systems on hybrid distributed-memory computing systems with multicore nodes is presented. The multi-projection method is an additive domain decomposition method based on semi-aggregation techniques. In the proposed variant, the multi-projection method is used as a preconditioner to a parallel preconditioned pipelined variation of the BiCGSTAB iterative method. As a domain decomposition method, it requires partitioning the graph corresponding to the coefficient matrix of the linear system, where the quality of the partitioning significantly affects convergence behavior. Thus, two new graph partitioning schemes are presented and their performance is compared against METIS with respect to the multi-projection method. The proposed graph partitioning schemes are based on Mongoose, utilizing both an iterative approach for partitioning and a hybrid multilevel approach based on METIS. Numerical results regarding the convergence behavior, the parallel performance and the scalability of the proposed scheme for several problems are given.