Hiding global synchronization latency in the preconditioned conjugate gradient algorithm

P Ghysels, W Vanroose - Parallel Computing, 2014 - Elsevier
Scalability of Krylov subspace methods suffers from costly global synchronization steps that
arise in dot-products and norm calculations on parallel machines. In this work, a modified …

Hiding global communication latency in the GMRES algorithm on massively parallel machines

P Ghysels, TJ Ashby, K Meerbergen… - SIAM journal on scientific …, 2013 - SIAM
In the generalized minimal residual method (GMRES), the global all-to-all communication
required in each iteration for orthogonalization and normalization of the Krylov base vectors …

[KİTAP][B] Communication-avoiding Krylov subspace methods in theory and practice

EC Carson - 2015 - search.proquest.com
Advancements in the field of high-performance scientific computing are necessary to
address the most important challenges we face in the 21st century. From physical modeling …

Krylov methods for nonsymmetric linear systems

G Meurant, JD Tebbens - Cham: Springer, 2020 - Springer
Solving systems of algebraic linear equations is among the most frequent problems in
scientific computing. It appears in many areas like physics, engineering, chemistry, biology …

Benchmarks of cuda-based GMRES solver for Toeplitz and Hankel matrices and applications to topology optimization of photonic components

IB Minin, SA Matveev, MV Fedorov, IE Zacharov… - Computational …, 2021 - Springer
Generalized Minimal Residual Method (GMRES) was benchmarked on many types of GPUs
for solving linear systems based on dense and sparse matrices. However, there are still no …

s-step Krylov subspace methods as bottom solvers for geometric multigrid

S Williams, M Lijewski, A Almgren… - 2014 IEEE 28th …, 2014 - ieeexplore.ieee.org
Geometric multigrid solvers within adaptive mesh refinement (AMR) applications often reach
a point where further coarsening of the grid becomes impractical as individual sub domain …

Predict-and-recompute conjugate gradient variants

T Chen, E Carson - SIAM Journal on Scientific Computing, 2020 - SIAM
The standard implementation of the conjugate gradient algorithm suffers from
communication bottlenecks on parallel architectures, due primarily to the two global …

Low-synchronization Arnoldi Methods for the Matrix Exponential with Application to Exponential Integrators

T Tafolla, S Gaudreault, M Tokman - arxiv preprint arxiv:2410.14917, 2024 - arxiv.org
High order exponential integrators require computing linear combination of exponential like
$\varphi $-functions of large matrices $ A $ times a vector $ v $. Krylov projection methods …

Comparative performance modeling of parallel preconditioned krylov methods

K Sood, B Norris, E Jessup - 2017 IEEE 19th International …, 2017 - ieeexplore.ieee.org
Many scientific and engineering computations rely on the scalable solution of large sparse
linear systems. Preconditioned Krylov methods are widely used and offer many algorithmic …

On the convergence rate of variants of the conjugate gradient algorithm in finite precision arithmetic

A Greenbaum, H Liu, T Chen - SIAM Journal on Scientific Computing, 2021 - SIAM
We consider three mathematically equivalent variants of the conjugate gradient (CG)
algorithm and how they perform in finite precision arithmetic. It was shown in [Greenbaum …