Hiding global synchronization latency in the preconditioned conjugate gradient algorithm
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 …
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
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 …
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 …
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 …
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
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 …
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
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 …
a point where further coarsening of the grid becomes impractical as individual sub domain …
Predict-and-recompute conjugate gradient variants
The standard implementation of the conjugate gradient algorithm suffers from
communication bottlenecks on parallel architectures, due primarily to the two global …
communication bottlenecks on parallel architectures, due primarily to the two global …
Low-synchronization Arnoldi Methods for the Matrix Exponential with Application to Exponential Integrators
High order exponential integrators require computing linear combination of exponential like
$\varphi $-functions of large matrices $ A $ times a vector $ v $. Krylov projection methods …
$\varphi $-functions of large matrices $ A $ times a vector $ v $. Krylov projection methods …
Comparative performance modeling of parallel preconditioned krylov methods
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 …
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
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 …
algorithm and how they perform in finite precision arithmetic. It was shown in [Greenbaum …