Hierarchically Low-Rank Structured Approximate Factorization using Randomized Sampling}

Talk
Sherry Li
Lawrence Berkeley Laboratory
Time: 
09.26.2016 15:00 to 16:00
Location: 

AVW 4172

Many extreme-scale simulation codes encompass multiphysics componentsin multiple spatial and length scales.The resulting discretized sparse linear systems can be highly indefinite,nonsymmetric and extremely ill-conditioned. For such problems,factorization based algorithms are often the most robust algorithmicchoices among many alternatives, either being used as direct solvers,or as coarse-grid solvers in multigrid, or as preconditioners foriterative solvers which otherwise rarely converge.We present our recent research on novel factorization algorithmsthat are efficient for solving such problems.We incorporate data-sparse low-rank structures, such ashierarchical matrix algebra, to achieve lower arithmetic andcommunication complexity as well as robust preconditioner.We will illustrate both theoretical and practical aspects of the methods,and demonstrate their performance on newer parallel machines,using a variety of real world problems.