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.
Download or read book Scientific Computing with Multicore and Accelerators written by Jakub Kurzak and published by CRC Press. This book was released on 2010-12-07 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: The hybrid/heterogeneous nature of future microprocessors and large high-performance computing systems will result in a reliance on two major types of components: multicore/manycore central processing units and special purpose hardware/massively parallel accelerators. While these technologies have numerous benefits, they also pose substantial perfo
Download or read book Applied Parallel and Scientific Computing written by Kristján Jónasson and published by Springer Science & Business Media. This book was released on 2012-02-04 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two volume set LNCS 7133 and LNCS 7134 constitutes the thoroughly refereed post-conference proceedings of the 10th International Conference on Applied Parallel and Scientific Computing, PARA 2010, held in Reykjavík, Iceland, in June 2010. These volumes contain three keynote lectures, 29 revised papers and 45 minisymposia presentations arranged on the following topics: cloud computing, HPC algorithms, HPC programming tools, HPC in meteorology, parallel numerical algorithms, parallel computing in physics, scientific computing tools, HPC software engineering, simulations of atomic scale systems, tools and environments for accelerator based computational biomedicine, GPU computing, high performance computing interval methods, real-time access and processing of large data sets, linear algebra algorithms and software for multicore and hybrid architectures in honor of Fred Gustavson on his 75th birthday, memory and multicore issues in scientific computing - theory and praxis, multicore algorithms and implementations for application problems, fast PDE solvers and a posteriori error estimates, and scalable tools for high performance computing.
Download or read book Facing the Multicore Challenge II written by Rainer Keller and published by Springer. This book was released on 2012-05-13 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This state-of-the-art survey features topics related to the impact of multicore, manycore, and coprocessor technologies in science and for large-scale applications in an interdisciplinary environment. The papers cover issues of current research in mathematical modeling, design of parallel algorithms, aspects of microprocessor architecture, parallel programming languages, hardware-aware computing, heterogeneous platforms, manycore technologies, performance tuning, and requirements for large-scale applications. The contributions presented in this volume offer a survey on the state of the art, the concepts and perspectives for future developments. They are an outcome of an inspiring conference conceived and organized by the editors at the Karlsruhe Institute Technology (KIT) in September 2011. The twelve revised full papers presented together with two contributed papers focus on combination of new aspects of microprocessor technologies, parallel applications, numerical simulation, and software development; thus they clearly show the potential of emerging technologies in the area of multicore and manycore processors that are paving the way towards personal supercomputing and very likely towards exascale computing.
Download or read book Numerical Mathematics and Advanced Applications ENUMATH 2019 written by Fred J. Vermolen and published by Springer Nature. This book was released on 2021-04-30 with total page 1185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers outstanding papers presented at the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2019). The conference was organized by Delft University of Technology and was held in Egmond aan Zee, the Netherlands, from September 30 to October 4, 2019. Leading experts in the field presented the latest results and ideas regarding the design, implementation and analysis of numerical algorithms, as well as their applications to relevant societal problems. ENUMATH is a series of conferences held every two years to provide a forum for discussing basic aspects and new trends in numerical mathematics and scientific and industrial applications, all examined at the highest level of international expertise. The first ENUMATH was held in Paris in 1995, with successive installments at various sites across Europe, including Heidelberg (1997), Jyvaskyla (1999), lschia Porto (2001), Prague (2003), Santiago de Compostela (2005), Graz (2007), Uppsala (2009), Leicester (2011), Lausanne (2013), Ankara (2015) and Bergen (2017).
Download or read book High Performance Computing on Complex Environments written by Emmanuel Jeannot and published by John Wiley & Sons. This book was released on 2014-04-10 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: With recent changes in multicore and general-purpose computing on graphics processing units, the way parallel computers are used and programmed has drastically changed. It is important to provide a comprehensive study on how to use such machines written by specialists of the domain. The book provides recent research results in high-performance computing on complex environments, information on how to efficiently exploit heterogeneous and hierarchical architectures and distributed systems, detailed studies on the impact of applying heterogeneous computing practices to real problems, and applications varying from remote sensing to tomography. The content spans topics such as Numerical Analysis for Heterogeneous and Multicore Systems; Optimization of Communication for High Performance Heterogeneous and Hierarchical Platforms; Efficient Exploitation of Heterogeneous Architectures, Hybrid CPU+GPU, and Distributed Systems; Energy Awareness in High-Performance Computing; and Applications of Heterogeneous High-Performance Computing. • Covers cutting-edge research in HPC on complex environments, following an international collaboration of members of the ComplexHPC • Explains how to efficiently exploit heterogeneous and hierarchical architectures and distributed systems • Twenty-three chapters and over 100 illustrations cover domains such as numerical analysis, communication and storage, applications, GPUs and accelerators, and energy efficiency
Download or read book Large Scale Scientific Computing written by Ivan Lirkov and published by Springer. This book was released on 2014-06-26 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 9th International Conference on Large-Scale Scientific Computations, LSSC 2013, held in Sozopol, Bulgaria, in June 2013. The 74 revised full papers presented together with 5 plenary and invited papers were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on numerical modeling of fluids and structures; control and uncertain systems; Monte Carlo methods: theory, applications and distributed computing; theoretical and algorithmic advances in transport problems; applications of metaheuristics to large-scale problems; modeling and numerical simulation of processes in highly heterogeneous media; large-scale models: numerical methods, parallel computations and applications; numerical solvers on many-core systems; cloud and grid computing for resource-intensive scientific applications.
Download or read book Hardware Oriented Multigrid Finite Element Solvers on GPU Accelerated Clusters written by Stefan Turek and published by . This book was released on 2010 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book GPU Computing Gems Jade Edition written by and published by Elsevier. This book was released on 2011-11-02 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: GPU Computing Gems, Jade Edition, offers hands-on, proven techniques for general purpose GPU programming based on the successful application experiences of leading researchers and developers. One of few resources available that distills the best practices of the community of CUDA programmers, this second edition contains 100% new material of interest across industry, including finance, medicine, imaging, engineering, gaming, environmental science, and green computing. It covers new tools and frameworks for productive GPU computing application development and provides immediate benefit to researchers developing improved programming environments for GPUs. Divided into five sections, this book explains how GPU execution is achieved with algorithm implementation techniques and approaches to data structure layout. More specifically, it considers three general requirements: high level of parallelism, coherent memory access by threads within warps, and coherent control flow within warps. Chapters explore topics such as accelerating database searches; how to leverage the Fermi GPU architecture to further accelerate prefix operations; and GPU implementation of hash tables. There are also discussions on the state of GPU computing in interactive physics and artificial intelligence; programming tools and techniques for GPU computing; and the edge and node parallelism approach for computing graph centrality metrics. In addition, the book proposes an alternative approach that balances computation regardless of node degree variance. Software engineers, programmers, hardware engineers, and advanced students will find this book extremely usefull. For useful source codes discussed throughout the book, the editors invite readers to the following website: ..." - This second volume of GPU Computing Gems offers 100% new material of interest across industry, including finance, medicine, imaging, engineering, gaming, environmental science, green computing, and more - Covers new tools and frameworks for productive GPU computing application development and offers immediate benefit to researchers developing improved programming environments for GPUs - Even more hands-on, proven techniques demonstrating how general purpose GPU computing is changing scientific research - Distills the best practices of the community of CUDA programmers; each chapter provides insights and ideas as well as 'hands on' skills applicable to a variety of fields
Download or read book Fast Solvers for Numerical Schemes Based On Finite Element Exterior Calculus written by Lin Zhong and published by . This book was released on 2015 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite element exterior calculus (FEEC) is a framework to design and understand finite element discretizations for a wide variety of systems of partial differential equations. The applications are already made to the Hodge Laplacian, Maxwell's equations, the equations of elasticity, elliptic eigenvalue problems and etc.. In this thesis, we propose fast solvers for several numerical schemes based on the discretization of this approach and present theoretical analysis. Specifically, in the first part, we propose efficient block diagonal and block triangular preconditioners for solving the discretized linear system of the vector Laplacian by mixed finite element methods. A variable V-cycle multigrid method with the standard point-wise Gauss-Seidel smoother is proved to be a good preconditioner for the Schur complement. The major benefit of our approach is that the point-wise Gauss-Seidel smoother is more algebraic and can be easily implemented as a 'black-box' smoother. The multigrid solver for the Schur complement will be further used to build preconditioners for the original saddle point systems. In the second part, we propose a discretization method for the Darcy-Stokes equations under the framework of FEEC. The discretization is shown to be uniform with respect to the perturbation parameter. A preconditioner for the discrete system is also proposed and shown to be efficient. In the last part, we focus on the stochastic Stokes equations. The stochastic saddle-point linear systems are obtained by using finite element discretization under the framework of FEEC in physical space and generalized polynomial chaos expansion in random space. We prove the existence and uniqueness of the solutions to the continuous problem and its corresponding stochastic Galerkin discretization. Optimal error estimates are also derived. We construct block-diagonal/triangular preconditioners for use with the generalized minimum residual method and the bi-conjugate gradient stabilized method. An optimal multigrid solver is applied to efficiently solve the diagonal blocks that correspond to deterministic discrete Stokes systems. To demonstrate the efficiency and robustness of the discretization methods and proposed preconditioners, various numerical examples also are provided.
Download or read book Towards a Complete FEM Based Simulation Toolkit on GPUs written by and published by . This book was released on 2011 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Software for Exascale Computing SPPEXA 2016 2019 written by Hans-Joachim Bungartz and published by Springer Nature. This book was released on 2020-07-30 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book summarizes the research done and results obtained in the second funding phase of the Priority Program 1648 "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) presented at the SPPEXA Symposium in Dresden during October 21-23, 2019. In that respect, it both represents a continuation of Vol. 113 in Springer’s series Lecture Notes in Computational Science and Engineering, the corresponding report of SPPEXA’s first funding phase, and provides an overview of SPPEXA’s contributions towards exascale computing in today's sumpercomputer technology. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest.
Download or read book Efficient Finite Element Geometric Multigrid Solvers for Unstructured Grids on GPUs written by and published by . This book was released on 2011 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Automated Solution of Differential Equations by the Finite Element Method written by Anders Logg and published by Springer Science & Business Media. This book was released on 2012-02-24 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.
Download or read book Numerical Computations with GPUs written by Volodymyr Kindratenko and published by Springer. This book was released on 2014-07-03 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together research on numerical methods adapted for Graphics Processing Units (GPUs). It explains recent efforts to adapt classic numerical methods, including solution of linear equations and FFT, for massively parallel GPU architectures. This volume consolidates recent research and adaptations, covering widely used methods that are at the core of many scientific and engineering computations. Each chapter is written by authors working on a specific group of methods; these leading experts provide mathematical background, parallel algorithms and implementation details leading to reusable, adaptable and scalable code fragments. This book also serves as a GPU implementation manual for many numerical algorithms, sharing tips on GPUs that can increase application efficiency. The valuable insights into parallelization strategies for GPUs are supplemented by ready-to-use code fragments. Numerical Computations with GPUs targets professionals and researchers working in high performance computing and GPU programming. Advanced-level students focused on computer science and mathematics will also find this book useful as secondary text book or reference.
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 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Multigrid Framework for Variational Approaches in Medical Image Processing and Computer Vision written by Harald Köstler and published by . This book was released on 2008 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt:
