Parallel Algebraic Recursive Multilevel Solvers: Advances in Scalable and Robust High Performance Linear System Solution Methods

University Of Minnesota-Twin Cities, Minneapolis MN

Investigators

Abstract

Parallel iterative methods are leading candidates for solving large-scale engineering and scientific problems, which usually appear as sparse linear systems. However, their robustness and overall efficiency remain mixed and problem-specific. These characteristics are closely tied to the preconditioners used as inputs to these methods. Preconditioners for general sparse linear systems remain by far the biggest stumbling block to obtaining good performance for iterative solution methods on high-performance computers in engineering and scientific applications. Accordingly, the main thrust of this project is to develop a class of preconditioning techniques based on the researchers' Algebraic Recursive Multilevel Solver (ARMS) framework. The researchers will develop the new methods and test them on realistic problems arising from the researchers' collaborations. The project will develop a class of parallel multi-level ILU-type preconditioning techniques using ARMS methods. Recursive multi-level ILU methods allow the unification of many standard iterative solvers into a single generic code. Their multi-level nature allows them to bridge the gap between the excellent problem-specifc performance of multigrid methods and the general-purpose nature of preconditioned Krylov solvers. The project will examine performance and scalability for classes of existing and new procedures thus obtained, including Schwartz procedures, Schur complement methods, direct solvers, and multilevel techniques. It will also conduct extensive realistic tests. In summary, this work promises advances in three important components of developing parallel solution methods: effective and scalable algorithms, use of effective computer science tools and data structures, and testing and validation.