Download or read book Utilizing Parallelism in the Conjugate Gradient Algorithm written by and published by . This book was released on 2019 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper develops the original conjugate gradient method and the idea of preconditioning a system. I also propose a unique type of additive-Schwarz preconditioner that can be solved in parallel, which creates a speed increase for large systems. To show this, I developed a C++11 linear algebra library used in conjunction with the OpenMP parallel computing library to empirically show a speed increase.

Download or read book Parallel Conjugate Gradient Algorithm with Local Decomposition written by P. Laurent-Gengoux and published by . This book was released on 1988 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Parallelization of the Preconditioned Conjugate Gradient Method Using a Processor Array written by Robert A. M. Allen and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Parallel Incomplete Cholesky Conjugate Gradient Algorithm written by Vikram V. Shanbhag and published by . This book was released on 1990 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Parallel Conjugate Gradient written by and published by . This book was released on 2000 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Conjugate Gradient (CG) algorithm is perhaps the best-known iterative technique to solve sparse linear systems that are symmetric and positive definite. A sparse matrix-vector multiply (SPMV) usually accounts for most of the floating-point operations with a CG iteration. In this paper, we investigate the effects of various ordering and partitioning strategies on the performance of parallel CG and SPMV using different programming and architectures. Results show that for this class of applications, ordering significantly improves overall performance, that cache reuse may be more important than reducing communication, and that it is possible to achieve message passing performance using shared memory constructs through careful data ordering and distribution. However, a multithreaded implementation of CG on the Tera MTA does not require special ordering or partitioning to obtain high efficiency and scalability.

Download or read book Parallel Implementation of Incomplete Cholesky Conjugate Gradient Algorithm written by Hazera Rahman and published by . This book was released on 1995 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Parallel Numerical Algorithms written by David E. Keyes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, designed for computational scientists and engineers working on applications requiring the memories and processing rates of large-scale parallelism, leading algorithmicists survey their own field-defining contributions, together with enough historical and bibliographical perspective to permit working one's way to the frontiers. This book is distinguished from earlier surveys in parallel numerical algorithms by its extension of coverage beyond core linear algebraic methods into tools more directly associated with partial differential and integral equations - though still with an appealing generality - and by its focus on practical medium-granularity parallelism, approachable through traditional programming languages. Several of the authors used their invitation to participate as a chance to stand back and create a unified overview, which nonspecialists will appreciate.

Download or read book Parallel Algorithms in Computational Science and Engineering written by Ananth Grama and published by Springer Nature. This book was released on 2020-07-06 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume highlights two areas of fundamental interest in high-performance computing: core algorithms for important kernels and computationally demanding applications. The first few chapters explore algorithms, numerical techniques, and their parallel formulations for a variety of kernels that arise in applications. The rest of the volume focuses on state-of-the-art applications from diverse domains. By structuring the volume around these two areas, it presents a comprehensive view of the application landscape for high-performance computing, while also enabling readers to develop new applications using the kernels. Readers will learn how to choose the most suitable parallel algorithms for any given application, ensuring that theory and practicality are clearly connected. Applications using these techniques are illustrated in detail, including: Computational materials science and engineering Computational cardiovascular analysis Multiscale analysis of wind turbines and turbomachinery Weather forecasting Machine learning techniques Parallel Algorithms in Computational Science and Engineering will be an ideal reference for applied mathematicians, engineers, computer scientists, and other researchers who utilize high-performance computing in their work.

Download or read book Parallel Solution of Large Sparse Linear Systems by the Conjugate Gradient Algorithm written by P.J. Elger and published by . This book was released on 1993 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Multitasking a Parallel Conjugate Gradient Algorithm on Cray YMP8 864 written by Pankaj Arora and published by . This book was released on 1992 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Parallel Implementation of the Block Conjugate Gradient Algorithm written by University of Maryland at College Park. Dept. of Computer Science and published by . This book was released on 1986 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Parallel Iterative Solution of Sparse Linear Systems Using Orderings from Graph Coloring Heuristics written by and published by . This book was released on 1990 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: The efficiency of a parallel implementation of the conjugate gradient method preconditioned by an incomplete Cholesky factorization can vary dramatically depending on the column ordering chosen. One method to minimize the number of major parallel steps is to choose an ordering based on a coloring of the symmetric graph representing the nonzero adjacency structure of the matrix. In this paper, we compare the performance of the preconditioned conjugate gradient method using these coloring orderings with a number of standard orderings on matrices arising from applications in structural engineering. Because optimal colorings for these systems may not be a priori known: we employ several graph coloring heuristics to obtain consistent colorings. Based on lower bounds obtained from the local structure of these systems, we find that the colorings determined by these heuristics are nearly optimal. For these problems, we find that the increase in parallelism afforded by the coloring-based orderings more than offsets any increase in the number of iterations required for the convergence of the conjugate gradient algorithm.

Download or read book Parallel Processing and Applied Mathematics written by Roman Wyrzykowski and published by Springer. This book was released on 2018-03-22 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two-volume set LNCS 10777 and 10778 constitutes revised selected papers from the 12th International Conference on Parallel Processing and Applied Mathematics, PPAM 2017, held in Lublin, Poland, in September 2017. The 49 regular papers presented in this volume were selected from 98 submissions. For the workshops and special sessions, that were held as integral parts of the PPAM 2017 conference, a total of 51 papers was accepted from 75 submissions. The papers were organized in topical sections named as follows: Part I: numerical algorithms and parallel scientific computing; particle methods in simulations; task-based paradigm of parallel computing; GPU computing; parallel non-numerical algorithms; performance evaluation of parallel algorithms and applications; environments and frameworks for parallel/distributed/cloud computing; applications of parallel computing; soft computing with applications; and special session on parallel matrix factorizations. Part II: workshop on models, algorithms and methodologies for hybrid parallelism in new HPC systems; workshop power and energy aspects of computations (PEAC 2017); workshop on scheduling for parallel computing (SPC 2017); workshop on language-based parallel programming models (WLPP 2017); workshop on PGAS programming; minisymposium on HPC applications in physical sciences; minisymposium on high performance computing interval methods; workshop on complex collective systems.

Download or read book Investigations Into the Suitability of Parallel Computing Architectures for the Solution of Sparse Matrices Using the Preconditioned Conjugate Gradient Method written by Otman Abubaker El-Ghajiji and published by . This book was released on 1995 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Advances in Parallel Algorithms written by Ivan Dimov and published by IOS Press. This book was released on 1994 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents an overview of research in the subjects of computational linear algebra, Monte Carlo algorithms and parallel algorithms in discrete mathematics. Topics covered include theoretical investigations of numerical analysis and parallel algorithms, and practical large-scale problem solving such as modelling of semiconductor devices, ballistic trajectory estimations and the simulation of distributed memory parallel computers.

Download or read book An Implementation of a Conjugate Gradient Algorithm on a Transputer Network written by Manoranjan Jha and published by . This book was released on 1990 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "In this report we describe how parallelism can be achieved in the conjugate gradient algorithm for solving linear equations. Both full and sparse version codes are implemented and respective speed up for both cases are discussed."

Download or read book The SSOR Preconditioned Conjugate Gradient Method on Parallel Computers written by Courtenay T. Vaughan and published by . This book was released on 1989 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: