Fast Parallel Direct Linear Solvers and Preconditioners
TimeMonday, 18 November 20198:30am - 12pm
DescriptionMatrix factorizations and the accompanying solution algorithms (e.g., triangular solution associated with the LU factorization) are often the most robust algorithmic choices for linear systems from multi-physics and multi-scale simulations. They are indispensable tools for building various algebraic equation solvers. They can be used as direct solvers, as coarse-grid solvers in multigrid, or as preconditioners for iterative solvers. As we are approaching the exascale computing era, demand for algorithm innovation is increasingly high. It is imperative to develop optimal-complexity scalable algorithms both in flop count and more importantly in data movement, such as, in the form of communication-avoiding formulations, and low-rank and butterfly compressions. On the software and implementation side, it is imperative to exploit multiple levels of parallelism presented by the heterogeneous node architectures through well orchestrated use of MPI, OpenMP and GPU programming like CUDA.
In this tutorial, we will present our recently developed novel techniques to address scalability gaps. We will demonstrate their efficacies through three solver libraries: SuperLU, STRUMPACK and ButterflyPACK, with representative use cases from simulations and data analytics. Through hands-on exercises, the participants will learn how to use each solver most effectively for their target problems and parallel machines.