A block-asynchronous relaxation method for graphics processing units
TLDR
This paper develops asynchronous iteration algorithms in CUDA and compares them with parallel implementations of synchronous relaxation methods on CPU- or GPU-based systems and identifies the high potential of the asynchronous methods for Exascale computing.About:
This article is published in Journal of Parallel and Distributed Computing.The article was published on 2013-12-01 and is currently open access. It has received 28 citations till now. The article focuses on the topics: Asynchronous communication & CUDA.read more
Figures
Table V: Variations of the convergence behavior for 100 solver runs on FV3. 
Figure 5: Convergence for test matrix FV1 
Figure 16: Average iteration timings of CPU/GPU implementations depending on total iteration number, test matrix FV3. 
Table VII: Average iteration timings in seconds. 
Figure 17: Time to solution for CHEM97ZTZ. 
Figure 18: Time to solution for FV1.
Citations
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Book ChapterDOI
GPU-accelerated asynchronous error correction for mixed precision iterative refinement
TL;DR: A mixed precision iterative refinement algorithm is derived using a block-asynchronous iteration as an error correction solver, and its performance is compared with a pure implementation of a blocksynchronous iteration and an iteratives refinement method using double precision for the error Correction solver.
Book ChapterDOI
Domain Overlap for Iterative Sparse Triangular Solves on GPUs
TL;DR: It is demonstrated that moderate directed overlap with subdomain scheduling can improve convergence and time-to-solution for sparse triangular factors from incomplete factorizations.
Book ChapterDOI
Weighted block-asynchronous iteration on GPU-Accelerated systems
TL;DR: This paper introduces different weighting techniques similar to those applied in block-smoothers for multigrid methods and observes that using weights may accelerate the convergence rate of block-asynchronous iteration considerably.
Journal ArticleDOI
GPU implementation of Jacobi Method and Gauss-Seidel Method for Data Arrays that Exceed GPU-dedicated Memory Size
TL;DR: A predictive mathematical model for computation duration is proposed that allows to find optimal algorithm parameters and computation experiment results have shown the model to be accurate enough to predict optimal algorithms parameters.
Journal ArticleDOI
Reducing the effect of global synchronization in delayed gradient methods for symmetric linear systems
TL;DR: This paper explores the cyclic formulations of lagged gradient methods and s-dimensional methods for reducing global synchronizations and concludes that these formulations perform better than traditional methods in view of both iteration count and computing time.
References
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Book
Iterative Methods for Sparse Linear Systems
TL;DR: This chapter discusses methods related to the normal equations of linear algebra, and some of the techniques used in this chapter were derived from previous chapters of this book.
Journal ArticleDOI
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
Youcef Saad,Martin H. Schultz +1 more
TL;DR: An iterative method for solving linear systems, which has the property of minimizing at every step the norm of the residual vector over a Krylov subspace.
Book
Iterative Methods for Linear and Nonlinear Equations
TL;DR: Preface How to Get the Software How to get the Software Part I.
Journal ArticleDOI
The International Exascale Software Project roadmap
Jack Dongarra,Pete Beckman,Terry Moore,Patrick Aerts,Giovanni Aloisio,Jean-Claude Andre,David Barkai,Jean-Yves Berthou,Taisuke Boku,Bertrand Braunschweig,Franck Cappello,Barbara Chapman,Xuebin Chi,Alok Choudhary,Sudip S. Dosanjh,Thom H. Dunning,Sandro Fiore,Al Geist,Bill Gropp,Robert W. Harrison,Mark Hereld,Michael A. Heroux,Adolfy Hoisie,Koh Hotta,Zhong Jin,Yutaka Ishikawa,Fred Johnson,Sanjay Kale,Richard Kenway,David E. Keyes,Bill Kramer,Jesús Labarta,Alain Lichnewsky,Thomas Lippert,Bob Lucas,Barney Maccabe,Satoshi Matsuoka,Paul Messina,Peter Michielse,Bernd Mohr,Matthias S. Mueller,Wolfgang E. Nagel,Hiroshi Nakashima,Michael E. Papka,Daniel A. Reed,Mitsuhisa Sato,Edward Seidel,John Shalf,David Skinner,Marc Snir,Thomas Sterling,Rick Stevens,Frederick H. Streitz,Bob Sugar,Shinji Sumimoto,William Tang,John Taylor,Rajeev Thakur,Anne E. Trefethen,Mateo Valero,Aad J. van der Steen,Jeffrey S. Vetter,Peg Williams,Robert W. Wisniewski,Katherine Yelick +64 more
TL;DR: The work of the community to prepare for the challenges of exascale computing is described, ultimately combing their efforts in a coordinated International Exascale Software Project.
Journal ArticleDOI
Asynchronous Iterative Methods for Multiprocessors
TL;DR: A class of asynchronous iterative methods is presented for solving a system of equations corresponding to a parallel implementation on a multiprocessor system with no synchronization between cooperating processes to show clearly the advantage of purely asynchronous Iterative methods.