43 citations · 113 across the 11 of their papers we have counts for
11 papers
Augmented Block-Arnoldi Recycling CFD Solvers
Stephen Thomas, Alison Baker, Stephane Gaudreault
One of the limitations of recycled GCRO methods is the large amount of computation required to orthogonalize the basis vectors of the newly generated Krylov subspace for the approx…
Iterated Gauss-Seidel GMRES
Stephen Thomas, Erin Carson, Miro Rozložník +2
The GMRES algorithm of Saad and Schultz (1986) is an iterative method for approximately solving linear systems , with initial guess and residual ${\bf…
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…
ILU Smoothers for Low Mach Navier-Stokes Pressure Solvers
Stephen Thomas, Arielle Carr, Paul Mullowney +2
Incomplete LU (ILU) smoothers are effective in the algebraic multigrid (AMG) -cycle for reducing high-frequency components of the error. However, the requisite direct triangular…
Performance of Low Synchronization Orthogonalization Methods in Anderson Accelerated Fixed Point Solvers
Shelby Lockhart, David J. Gardner, Carol S. Woodward +2
Anderson Acceleration (AA) is a method to accelerate the convergence of fixed point iterations for nonlinear, algebraic systems of equations. Due to the requirement of solving a le…
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…
An overview of block Gram-Schmidt methods and their stability properties
Erin Carson, Kathryn Lund, Miroslav Rozložník +1
Block Gram-Schmidt algorithms serve as essential kernels in many scientific computing applications, but for many commonly used variants, a rigorous treatment of their stability pro…
A Survey of Numerical Methods Utilizing Mixed Precision Arithmetic
Ahmad Abdelfattah, Hartwig Anzt, Erik G. Boman +22
Within the past years, hardware vendors have started designing low precision special function units in response to the demand of the Machine Learning community and their demand for…
Low synchronization GMRES algorithms
Kasia Swirydowicz, Julien Langou, Shreyas Ananthan +2
Communication-avoiding and pipelined variants of Krylov solvers are critical for the scalability of linear system solvers on future exascale architectures. We present low synchroni…