Factorization-based sparse solvers and preconditioners

X.S. Li, Lawrence Berkeley National Laboratory, USA

Wednesday, June 3
at 16.15, HG D 1.1

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, the factorization-based algorithms could play a significant role in developing scalable solvers. We present our recent work in using the direct solver SuperLU code base to develop a new supernode-based ILU preconditioner and a domain-decomposition hybrid solver. Our ILU preconditioner is a modification of the classic ILUTP approach, incorporating a number of techniques to improve robustness and performance, which include the new dropping strategies that accommodate the use of supernodal structures in the factored matrix. Our hybrid solver is based on Schur complement method. We use parallel graph partitioning to obtain hierarchical interface/domain decomposition, and multiple parallel direct solvers to solve the subdomain problems simultaneously, and parallel preconditioned iterative solvers to solve the interface problem. We will demonstrate the effectiveness of our new techniques when applied to two applications, modeling next-generation particle accelerators and fusion devices.

X. Sherry Li, Lawrence Berkeley National laboratory, USA.
Joint work with Meiyue Shao and Ichitaro Yamazaki.