66 citations · 94 across the 5 of their papers we have counts for
6 papers
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…
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…
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…
Scalability of High-Performance PDE Solvers
Paul Fischer, Misun Min, Thilina Rathnayake +8
Performance tests and analyses are critical to effective HPC software development and are central components in the design and implementation of computational algorithms for achiev…
Acceleration of tensor-product operations for high-order finite element methods
Kasia Świrydowicz, Noel Chalmers, Ali Karakus +1
This paper is devoted to GPU kernel optimization and performance analysis of three tensor-product operators arising in finite element methods. We provide a mathematical background…