A parallel hybrid sparse linear system solver

Abstract

We present a parallel hybrid sparse linear system solver that is suitable for the solution of large sparse linear systems on parallel computing platforms. This study is motivated by the lack of robustness of Krylov subspace iterative schemes with “black-box” preconditioners, such as incomplete LU-factorizations and the lack of scalability of direct sparse system solvers. Our hybrid solver is as robust as direct solvers and as scalable as iterative solvers. Our method relies on weighted symmetric and nonsymmetric matrix reordering for bringing the largest elements on or closer to the main diagonal resulting in a very effective extracted banded preconditioner. Systems involving the extracted banded preconditioner are solved via a member of the recently developed SPIKE family of algorithms. The effectiveness of our method is demonstrated by solving large sparse linear systems that arise in various applications such as computational electromagnetics and nonlinear optimizations. We compare the performance and scalability of our solvers to well known direct and iterative solver packages such as ILUPACK and MUMPS. Finally, we present a highly accurate model for predicting the parallel scalability of our solver on architectures with more nodes than the platform on which our experiments have been performed.