Factorization-based Sparse Solvers and Preconditioners

Efficient solution of large-scale, ill-conditioned and highly-indefinite algebraic equations often relies on high quality preconditioners together with iterative solvers. Because of their robustness, factorizationbased algorithms play a significant role in developing scalable solvers. We discuss the state-of-the-art, high performance sparse factorization techniques which are used to build sparse direct solvers, domain-decomposition type direct/iterative hybrid solvers, and approximate factorization preconditioners. In addition to algorithmic principles, we also address the key parallelism issues and practical aspects that need to be taken under consideration in order to deliver high speed and robustness to the users of todays sophisticated high performance computers.