Increasing Locality in Sparse Solvers

Luke Olson, University of Illinois at Urbana-Champaign

Usage Details

Large, sparse linear systems of equations arise in many high performance scientific simulations, and solving them represents a major computational component.  Krylov subspace methods have historically been considered some of the most efficient methods to solve these systems due to their low computational requirements per iteration and the ability to be preconditioned, yielding quick convergence. However, Krylov solvers, as well as the multilevel solvers used to precondition them, require large amounts of communication with little on-node computation per iteration resulting in poor scalability and efficiency on current parallel machines such as Blue Waters. The focus of this work is on increasing locality in Krylov and multilevel solvers by designing solvers and preconditioners based on enlarged Krylov methods, which have an increase in on-node computation due to a block structure.  In this sense, Blue Waters is a critical resource for the study as both traditional CPU compute nodes are available as well as nodes with accelerators.