Hybrid Parallel ILU Preconditioner in Linear Solver Library GaspiLS

Krylov subspace solvers such as GMRES and preconditioners such as incomplete LU (ILU) are the most commonly used methods to solve general-purpose, large-scale linear systems in simulations efficiently. Parallel Krylov subspace solvers and preconditioners with good scalability features are required to exploit the increasing parallelism provided by modern hardware fully. As such, they are crucial for productivity. They provide a high-level abstraction to the details of a complex hybrid parallel implementation which is easy to use for the domain expert. However, the ILU factorization and the subsequent triangular solve are sequential in their basic form. We use a multilevel nested dissection (MLND) ordering to resolve that issue and expose some parallelism. We investigate 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 thread level. We employ the PGAS based programming model GASPI to efficiently implement the data exchange across processes. We demonstrate the scalability of our approach for the convection-diffusion problem as a representative of a large class of engineering problems up to 64 sockets (1280 cores) and show comparable baseline performance against the linear solver library PETSc. The RAS preconditioned GMRES solver achieves about 80% parallel efficiency on 1280 cores. Our implementation provides a generic, algebraic, scalable, and efficient preconditioner that enables productivity for the domain expert in solving large-scale sparse linear systems.