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Author : Mark Francis Adams
Publisher :
ISBN 13 :
Total Pages : 432 pages
Book Rating : 4.:/5 (34 download)
Download or read book Multigrid Equation Solvers of Large Scale Nonlinear Finite Element Simulations written by Mark Francis Adams and published by . This book was released on 1998 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Stefan Reitzinger
Publisher :
ISBN 13 : 9783854872597
Total Pages : 117 pages
Book Rating : 4.8/5 (725 download)
Download or read book Algebraic Multigrid Methods for Large Scale Finite Element Equations written by Stefan Reitzinger and published by . This book was released on 2001 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : James H Bramble
Publisher : Routledge
ISBN 13 : 1351429868
Total Pages : 176 pages
Book Rating : 4.3/5 (514 download)
Download or read book Multigrid Methods written by James H Bramble and published by Routledge. This book was released on 2019-01-22 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multigrid methods are among the most efficient iterative methods for the solution of linear systems which arise in many large scale scientific calculations. Every researcher working with the numerical solution of partial differential equations should at least be familiar with this powerful technique. This invaluable book presents results concerning the rates of convergence of multigrid iterations.
Author :
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (684 download)
Download or read book Multigrid and Krylov Solvers for Large Scale Finite Element Groundwater Flow Simulations on Distributed Memory Parallel Platforms written by and published by . This book was released on 1997 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this report we present parallel solvers for large linear systems arising from the finite-element discretization of the three-dimensional steady-state groundwater flow problem. Our solvers are based on multigrid and Krylov subspace methods. The parallel implementation is based on a domain decomposition strategy with explicit message passing using NX and MPI libraries. We have tested our parallel implementations on the Intel Paragon XP/S 150 supercomputer using up to 1024 parallel processors and on other parallel platforms such as SGI/Power Challenge Array, Cray/SGI Origin 2000, Convex Exemplar SPP-1200, and IBM SP using up to 64 processors. We show that multigrid can be a scalable algorithm on distributed memory machines. We demonstrate the effectiveness of parallel multigrid based solvers by solving problems requiring more than 70 million nodes in less than a minute. This is more than 25 times faster than the diagonal preconditioned conjugate gradient method which is one of the more popular methods for large sparse linear systems. Our results also show that multigrid as a stand alone solver works best for problems with smooth coefficients, but for rough coefficients it is best used as a preconditioner for a Krylov subspace method such as the conjugate gradient method. We show that even for extremely heterogeneous systems the multigrid pre-conditioned conjugate gradient method is at least 10 times faster than the diagonally preconditioned conjugate gradient method.
Author : Timothy J. Barth
Publisher : Springer Science & Business Media
ISBN 13 : 3642562051
Total Pages : 396 pages
Book Rating : 4.6/5 (425 download)
Download or read book Multiscale and Multiresolution Methods written by Timothy J. Barth and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many computionally challenging problems omnipresent in science and engineering exhibit multiscale phenomena so that the task of computing or even representing all scales of action is computationally very expensive unless the multiscale nature of these problems is exploited in a fundamental way. Some diverse examples of practical interest include the computation of fluid turbulence, structural analysis of composite materials, terabyte data mining, image processing, and a multitude of others. This book consists of both invited and contributed articles which address many facets of efficient multiscale representation and scientific computation from varied viewpoints such as hierarchical data representations, multilevel algorithms, algebraic homogeni- zation, and others. This book should be of particular interest to readers interested in recent and emerging trends in multiscale and multiresolution computation with application to a wide range of practical problems.
Author : William L. Briggs
Publisher : SIAM
ISBN 13 : 9780898714623
Total Pages : 318 pages
Book Rating : 4.7/5 (146 download)
Download or read book A Multigrid Tutorial written by William L. Briggs and published by SIAM. This book was released on 2000-07-01 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Author : Achi Brandt
Publisher : SIAM
ISBN 13 : 9781611970753
Total Pages : 239 pages
Book Rating : 4.9/5 (77 download)
Download or read book Multigrid Techniques written by Achi Brandt and published by SIAM. This book was released on 2011-01-01 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic text presents the best practices of developing multigrid solvers for large-scale computational problems in science and engineering. By representing a problem at multiple scales and employing suitable interscale interactions, multigrid avoids slowdown due to stiffness and reduces the computational cost of classical algorithms by orders of magnitude. Starting from simple examples, this book guides the reader through practical stages for developing reliable multigrid solvers, methodically supported by accurate performance predictors. The revised edition presents discretization and fast solution of linear and nonlinear partial differential systems; treatment of boundary conditions, global constraints and singularities; grid adaptation, high-order approximations, and system design optimization; applications to fluid dynamics, from simple models to advanced systems; new quantitative performance predictors, a MATLAB sample code, and more. Readers will also gain access to the Multigrid Guide 2.0 Web site, where updates and new developments will be continually posted, including a chapter on Algebraic Multigrid.
Author : Ulrich Trottenberg
Publisher : Academic Press
ISBN 13 : 9780127010700
Total Pages : 652 pages
Book Rating : 4.0/5 (17 download)
Download or read book Multigrid Methods written by Ulrich Trottenberg and published by Academic Press. This book was released on 2001 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Author : Dominik Göddeke
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 3832527680
Total Pages : 300 pages
Book Rating : 4.8/5 (325 download)
Download or read book Fast and Accurate Finite-Element Multigrid Solvers for PDE Simulations on GPU Clusters written by Dominik Göddeke and published by Logos Verlag Berlin GmbH. This book was released on 2011 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation demonstrates that graphics processors (GPUs) as representatives of emerging many-core architectures are very well-suited for the fast and accurate solution of large, sparse linear systems of equations, using parallel multigrid methods on heterogeneous compute clusters. Such systems arise for instance in the discretisation of (elliptic) partial differential equations with finite elements. Fine-granular parallelisation techniques and methods to ensure accuracy are developed that enable at least one order of magnitude speedup over highly-tuned conventional CPU implementations, without sacrificing neither accuracy nor functionality.
Author : Michael A. Heroux
Publisher : SIAM
ISBN 13 : 0898716195
Total Pages : 407 pages
Book Rating : 4.8/5 (987 download)
Download or read book Parallel Processing for Scientific Computing written by Michael A. Heroux and published by SIAM. This book was released on 2006-01-01 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientific computing has often been called the third approach to scientific discovery, emerging as a peer to experimentation and theory. Historically, the synergy between experimentation and theory has been well understood: experiments give insight into possible theories, theories inspire experiments, experiments reinforce or invalidate theories, and so on. As scientific computing has evolved to produce results that meet or exceed the quality of experimental and theoretical results, it has become indispensable.Parallel processing has been an enabling technology in scientific computing for more than 20 years. This book is the first in-depth discussion of parallel computing in 10 years; it reflects the mix of topics that mathematicians, computer scientists, and computational scientists focus on to make parallel processing effective for scientific problems. Presently, the impact of parallel processing on scientific computing varies greatly across disciplines, but it plays a vital role in most problem domains and is absolutely essential in many of them. Parallel Processing for Scientific Computing is divided into four parts: The first concerns performance modeling, analysis, and optimization; the second focuses on parallel algorithms and software for an array of problems common to many modeling and simulation applications; the third emphasizes tools and environments that can ease and enhance the process of application development; and the fourth provides a sampling of applications that require parallel computing for scaling to solve larger and realistic models that can advance science and engineering. This edited volume serves as an up-to-date reference for researchers and application developers on the state of the art in scientific computing. It also serves as an excellent overview and introduction, especially for graduate and senior-level undergraduate students interested in computational modeling and simulation and related computer science and applied mathematics aspects.Contents List of Figures; List of Tables; Preface; Chapter 1: Frontiers of Scientific Computing: An Overview; Part I: Performance Modeling, Analysis and Optimization. Chapter 2: Performance Analysis: From Art to Science; Chapter 3: Approaches to Architecture-Aware Parallel Scientific Computation; Chapter 4: Achieving High Performance on the BlueGene/L Supercomputer; Chapter 5: Performance Evaluation and Modeling of Ultra-Scale Systems; Part II: Parallel Algorithms and Enabling Technologies. Chapter 6: Partitioning and Load Balancing; Chapter 7: Combinatorial Parallel and Scientific Computing; Chapter 8: Parallel Adaptive Mesh Refinement; Chapter 9: Parallel Sparse Solvers, Preconditioners, and Their Applications; Chapter 10: A Survey of Parallelization Techniques for Multigrid Solvers; Chapter 11: Fault Tolerance in Large-Scale Scientific Computing; Part III: Tools and Frameworks for Parallel Applications. Chapter 12: Parallel Tools and Environments: A Survey; Chapter 13: Parallel Linear Algebra Software; Chapter 14: High-Performance Component Software Systems; Chapter 15: Integrating Component-Based Scientific Computing Software; Part IV: Applications of Parallel Computing. Chapter 16: Parallel Algorithms for PDE-Constrained Optimization; Chapter 17: Massively Parallel Mixed-Integer Programming; Chapter 18: Parallel Methods and Software for Multicomponent Simulations; Chapter 19: Parallel Computational Biology; Chapter 20: Opportunities and Challenges for Parallel Computing in Science and Engineering; Index.
Author : Stephen F. McCormick
Publisher : SIAM
ISBN 13 : 1611971055
Total Pages : 292 pages
Book Rating : 4.6/5 (119 download)
Download or read book Multigrid Methods written by Stephen F. McCormick and published by SIAM. This book was released on 1987-12-01 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thoughtful consideration of the current level of development of multigrid methods, this volume is a carefully edited collection of papers that addresses its topic on several levels. The first three chapters orient the reader who is familiar with standard numerical techniques to multigrid methods, first by discussing multigrid in the context of standard techniques, second by detailing the mechanics of use of the method, and third by applying the basic method to some current problems in fluid dynamics. The fourth chapter provides a unified development, complete with theory, of algebraic multigrid (AMG), which is a linear equation solver based on multigrid principles. The last chapter is an ambitious development of a very general theory of multigrid methods for variationally posed problems. Included as an appendix is the latest edition of the Multigrid Bibliography, an attempted compilation of all existing research publications on multigrid.
Author :
Publisher :
ISBN 13 :
Total Pages : 18 pages
Book Rating : 4.:/5 (946 download)
Download or read book Performance of Algebraic Multigrid Preconditioners for Large-Scale Finite Element Simulations written by and published by . This book was released on 2015 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Roger Patrick Pawlowski
Publisher :
ISBN 13 :
Total Pages : 89 pages
Book Rating : 4.:/5 (316 download)
Download or read book Robust Large-scale Parallel Nonlinear Solvers for Simulations written by Roger Patrick Pawlowski and published by . This book was released on 2005 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: This report documents research to develop robust and efficient solution techniques for solving large-scale systems of nonlinear equations. The most widely used method for solving systems of nonlinear equations is Newton's method. While much research has been devoted to augmenting Newton-based solvers (usually with globalization techniques), little has been devoted to exploring the application of different models. Our research has been directed at evaluating techniques using different models than Newton's method: a lower order model, Broyden's method, and a higher order model, the tensor method. We have developed large-scale versions of each of these models and have demonstrated their use in important applications at Sandia. Broyden's method replaces the Jacobian with an approximation, allowing codes that cannot evaluate a Jacobian or have an inaccurate Jacobian to converge to a solution. Limited-memory methods, which have been successful in optimization, allow us to extend this approach to large-scale problems. We compare the robustness and efficiency of Newton's method, modified Newton's method, Jacobian-free Newton-Krylov method, and our limited-memory Broyden method. Comparisons are carried out for large-scale applications of fluid flow simulations and electronic circuit simulations. Results show that, in cases where the Jacobian was inaccurate or could not be computed, Broyden's method converged in some cases where Newton's method failed to converge. We identify conditions where Broyden's method can be more efficient than Newton's method. We also present modifications to a large-scale tensor method, originally proposed by Bouaricha, for greater efficiency, better robustness, and wider applicability. Tensor methods are an alternative to Newton-based methods and are based on computing a step based on a local quadratic model rather than a linear model. The advantage of Bouaricha's method is that it can use any existing linear solver, which makes it simple to write and easily portable. However, the method usually takes twice as long to solve as Newton-GMRES on general problems because it solves two linear systems at each iteration. In this paper, we discuss modifications to Bouaricha's method for a practical implementation, including a special globalization technique and other modifications for greater efficiency. We present numerical results showing computational advantages over Newton-GMRES on some realistic problems. We further discuss a new approach for dealing with singular (or ill-conditioned) matrices. In particular, we modify an algorithm for identifying a turning point so that an increasingly ill-conditioned Jacobian does not prevent convergence.
Author :
Publisher :
ISBN 13 :
Total Pages : 702 pages
Book Rating : 4.:/5 (31 download)
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Valeria V. Krzhizhanovskaya
Publisher : Springer Nature
ISBN 13 : 3030504204
Total Pages : 648 pages
Book Rating : 4.0/5 (35 download)
Download or read book Computational Science – ICCS 2020 written by Valeria V. Krzhizhanovskaya and published by Springer Nature. This book was released on 2020-06-19 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: The seven-volume set LNCS 12137, 12138, 12139, 12140, 12141, 12142, and 12143 constitutes the proceedings of the 20th International Conference on Computational Science, ICCS 2020, held in Amsterdam, The Netherlands, in June 2020.* The total of 101 papers and 248 workshop papers presented in this book set were carefully reviewed and selected from 719 submissions (230 submissions to the main track and 489 submissions to the workshops). The papers were organized in topical sections named: Part I: ICCS Main Track Part II: ICCS Main Track Part III: Advances in High-Performance Computational Earth Sciences: Applications and Frameworks; Agent-Based Simulations, Adaptive Algorithms and Solvers; Applications of Computational Methods in Artificial Intelligence and Machine Learning; Biomedical and Bioinformatics Challenges for Computer Science Part IV: Classifier Learning from Difficult Data; Complex Social Systems through the Lens of Computational Science; Computational Health; Computational Methods for Emerging Problems in (Dis-)Information Analysis Part V: Computational Optimization, Modelling and Simulation; Computational Science in IoT and Smart Systems; Computer Graphics, Image Processing and Artificial Intelligence Part VI: Data Driven Computational Sciences; Machine Learning and Data Assimilation for Dynamical Systems; Meshfree Methods in Computational Sciences; Multiscale Modelling and Simulation; Quantum Computing Workshop Part VII: Simulations of Flow and Transport: Modeling, Algorithms and Computation; Smart Systems: Bringing Together Computer Vision, Sensor Networks and Machine Learning; Software Engineering for Computational Science; Solving Problems with Uncertainties; Teaching Computational Science; UNcErtainty QUantIficatiOn for ComputationAl modeLs *The conference was canceled due to the COVID-19 pandemic.
Author : V.V. Shaidurov
Publisher : Springer Science & Business Media
ISBN 13 : 940158527X
Total Pages : 345 pages
Book Rating : 4.4/5 (15 download)
Download or read book Multigrid Methods for Finite Elements written by V.V. Shaidurov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multigrid Methods for Finite Elements combines two rapidly developing fields: finite element methods, and multigrid algorithms. At the theoretical level, Shaidurov justifies the rate of convergence of various multigrid algorithms for self-adjoint and non-self-adjoint problems, positive definite and indefinite problems, and singular and spectral problems. At the practical level these statements are carried over to detailed, concrete problems, including economical constructions of triangulations and effective work with curvilinear boundaries, quasilinear equations and systems. Great attention is given to mixed formulations of finite element methods, which allow the simplification of the approximation of the biharmonic equation, the steady-state Stokes, and Navier--Stokes problems.
Author : Mark Adams
Publisher :
ISBN 13 :
Total Pages : 21 pages
Book Rating : 4.:/5 (416 download)
Download or read book Parallel Multigrid Algorithms for Unstructured 3D Large Deformation Elasticity and Plasticity Finite Element Problems written by Mark Adams and published by . This book was released on 1999 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:
