Scalable Hybrid Parallel ILU Preconditioner to Solve Sparse Linear Systems

Incomplete LU (ILU) preconditioners are widely used to improve the convergence of general-purpose large sparse linear systems in computational simulations because of their robustness, accuracy, and usability as a black-box preconditioner. However, the ILU factorization and the subsequent triangular solve are sequential for sparse matrices in their original form. Multilevel nested dissection (MLND) ordering can resolve that issue and expose some parallelism. This work investigates the parallel efficiency of a hybrid parallel ILU preconditioner that combines a restricted additive Schwarz (RAS) method on the process level with a shared memory parallel MLND Crout ILU method on the core level. We employ the GASPI programming model to efficiently implement the data exchange on the process level. We show the scalability results of our approach for the convection-diffusion problem.