66 citations · 190 across the 14 of their papers we have counts for
6 papers · 1 filter
Neumann Series in GMRES and Algebraic Multigrid Smoothers
Stephen Thomas, Arielle Carr, Paul Mullowney +2
Neumann series underlie both Krylov methods and algebraic multigrid smoothers. A low-synch modified Gram-Schmidt (MGS)-GMRES algorithm is described that employs a Neumann series to…
A Hybrid Direct-Iterative Method for Solving KKT Linear Systems
Shaked Regev, Nai-Yuan Chiang, Eric Darve +4
We propose a solution strategy for linear systems arising in interior method optimization, which is suitable for implementation on hardware accelerators such as graphical processin…
Efficient Exascale Discretizations: High-Order Finite Element Methods
Tzanio Kolev, Paul Fischer, Misun Min +27
Efficient exploitation of exascale architectures requires rethinking of the numerical algorithms used in many large-scale applications. These architectures favor algorithms that ex…
Linear solvers for power grid optimization problems: a review of GPU-accelerated linear solvers
Kasia Swirydowicz, Eric Darve, Wesley Jones +5
The linear equations that arise in interior methods for constrained optimization are sparse symmetric indefinite and become extremely ill-conditioned as the interior method converg…
Low-Synch Gram-Schmidt with Delayed Reorthogonalization for Krylov Solvers
Daniel Bielich, Julien Langou, Stephen Thomas +3
The parallel strong-scaling of Krylov iterative methods is largely determined by the number of global reductions required at each iteration. The GMRES and Krylov-Schur algorithms e…
Two-Stage Gauss--Seidel Preconditioners and Smoothers for Krylov Solvers on a GPU cluster
Luc Berger-Vergiat, Brian Kelley, Sivasankaran Rajamanickam +5
Gauss-Seidel (GS) relaxation is often employed as a preconditioner for a Krylov solver or as a smoother for Algebraic Multigrid (AMG). However, the requisite sparse triangular solv…