Parallel And Sequential Methods For Ordinary Differential Equations
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Parallel And Sequential Methods For Ordinary Differential Equations
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Author : Kevin Burrage
language : en
Publisher:
Release Date : 1995
Parallel And Sequential Methods For Ordinary Differential Equations written by Kevin Burrage and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Differential equations categories.
Computer Methods For Ordinary Differential Equations And Differential Algebraic Equations
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Author : Uri M. Ascher
language : en
Publisher: SIAM
Release Date : 1998-01-01
Computer Methods For Ordinary Differential Equations And Differential Algebraic Equations written by Uri M. Ascher and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Mathematics categories.
Designed for those people who want to gain a practical knowledge of modern techniques, this book contains all the material necessary for a course on the numerical solution of differential equations. Written by two of the field's leading authorities, it provides a unified presentation of initial value and boundary value problems in ODEs as well as differential-algebraic equations. The approach is aimed at a thorough understanding of the issues and methods for practical computation while avoiding an extensive theorem-proof type of exposition. It also addresses reasons why existing software succeeds or fails. This book is a practical and mathematically well-informed introduction that emphasizes basic methods and theory, issues in the use and development of mathematical software, and examples from scientific engineering applications. Topics requiring an extensive amount of mathematical development, such as symplectic methods for Hamiltonian systems, are introduced, motivated, and included in the exercises, but a complete and rigorous mathematical presentation is referenced rather than included.
High Performance Computing In Science And Engineering Garching Munich 2007
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Author : Siegfried Wagner
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-22
High Performance Computing In Science And Engineering Garching Munich 2007 written by Siegfried Wagner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-22 with Mathematics categories.
For the fourth time, the Leibniz Supercomputing Centre (LRZ) and the Com- tence Network for Technical, Scienti c High Performance Computing in Bavaria (KONWIHR) publishes the results from scienti c projects conducted on the c- puter systems HLRB I and II (High Performance Computer in Bavaria). This book reports the research carried out on the HLRB systems within the last three years and compiles the proceedings of the Third Joint HLRB and KONWIHR Result and Reviewing Workshop (3rd and 4th December 2007) in Garching. In 2000, HLRB I was the rst system in Europe that was capable of performing more than one Tera op/s or one billion oating point operations per second. In 2006 it was replaced by HLRB II. After a substantial upgrade it now achieves a peak performance of more than 62 Tera op/s. To install and operate this powerful system, LRZ had to move to its new facilities in Garching. However, the situation regarding the need for more computation cycles has not changed much since 2000. The demand for higher performance is still present, a trend that is likely to continue for the foreseeable future. Other resources like memory and disk space are currently in suf cient abundance on this new system.
Time Parallel Methods For Accelerating The Solution Of Structural Dynamics Problems
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Author : Julien Remi Cortial
language : en
Publisher: Stanford University
Release Date : 2011
Time Parallel Methods For Accelerating The Solution Of Structural Dynamics Problems written by Julien Remi Cortial and has been published by Stanford University this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
The classical approach for solving evolution Partial Differential Equations (PDEs) using a parallel computer consists in first partitioning the spatial domain and assigning each subdomain to a processor to achieve space-parallelism, then advancing the solution sequentially. However, enabling parallelism along the time dimension, despite its intrinsic difficulty, can be of paramount importance to fast computations when space-parallelism is unfeasible, cannot fully exploit a massively parallel machine or when near-real-time prediction is desired. The aforementioned objective can be achieved by applying classical domain decomposition principles to the time axis. The latter is first partitioned into time-slices to be processed independently. Starting with approximate seed information that provides a set of initial conditions, the response is then advanced in parallel in each time-slice using a standard time-stepping integrator. This decomposed solution exhibits discontinuities or jumps at the time-slice boundaries if the initial guess is not accurate. Applying a Newton-like approach to the time-dependent system, a correction function is then computed to improve the accuracy of the seed values and the process is repeated until convergence is reached. Methods based on the above concept have been successfully applied to various problems but none was found to be competitive for even for the simplest of second-order hyperbolic PDEs, a class of equations that covers the field of structural dynamics among others. To overcome this difficulty, a key idea is to improve the sequential propagator used for correcting the seed values, observing that the original evolution problem and the derived corrective one are closely related. The present work first demonstrates how this insight can be brought to fruition in the context of linear oscillators, with numerical examples featuring structural models ranging from academic to more challenging large-scale ones. An extension of this method to nonlinear equations is then developed and its concrete application to geometrically nonlinear transient dynamics is presented. Finally, it is shown how the time-reversibility property that characterizes some of the above problems can be exploited to develop a new framework that provides an increased speed-up factor.
High Performance Computing And Networking
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Author : Peter Sloot
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-04-15
High Performance Computing And Networking written by Peter Sloot and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-04-15 with Computers categories.
Proceedings -- Parallel Computing.
Solving Differential Equations By Multistep Initial And Boundary Value Methods
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Author : L Brugnano
language : en
Publisher: CRC Press
Release Date : 1998-05-22
Solving Differential Equations By Multistep Initial And Boundary Value Methods written by L Brugnano and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-05-22 with Mathematics categories.
The numerical approximation of solutions of differential equations has been, and continues to be, one of the principal concerns of numerical analysis and is an active area of research. The new generation of parallel computers have provoked a reconsideration of numerical methods. This book aims to generalize classical multistep methods for both initial and boundary value problems; to present a self-contained theory which embraces and generalizes the classical Dahlquist theory; to treat nonclassical problems, such as Hamiltonian problems and the mesh selection; and to select appropriate methods for a general purpose software capable of solving a wide range of problems efficiently, even on parallel computers.
Proceedings Of The Fourth Siam Conference On Parallel Processing For Scientific Computing
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Author : J. J. Dongarra
language : en
Publisher: SIAM
Release Date : 1990-01-01
Proceedings Of The Fourth Siam Conference On Parallel Processing For Scientific Computing written by J. J. Dongarra and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with Computers categories.
Proceedings -- Parallel Computing.
Multiple Shooting And Time Domain Decomposition Methods
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Author : Thomas Carraro
language : en
Publisher: Springer
Release Date : 2015-10-26
Multiple Shooting And Time Domain Decomposition Methods written by Thomas Carraro and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-26 with Mathematics categories.
This book offers a comprehensive collection of the most advanced numerical techniques for the efficient and effective solution of simulation and optimization problems governed by systems of time-dependent differential equations. The contributions present various approaches to time domain decomposition, focusing on multiple shooting and parareal algorithms. The range of topics covers theoretical analysis of the methods, as well as their algorithmic formulation and guidelines for practical implementation. Selected examples show that the discussed approaches are mandatory for the solution of challenging practical problems. The practicability and efficiency of the presented methods is illustrated by several case studies from fluid dynamics, data compression, image processing and computational biology, giving rise to possible new research topics. This volume, resulting from the workshop Multiple Shooting and Time Domain Decomposition Methods, held in Heidelberg in May 2013, will be of great interest to applied mathematicians, computer scientists and all scientists using mathematical methods.
Numerical Methods For Ordinary Differential Equations
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Author : Alfredo Bellen
language : en
Publisher: Springer
Release Date : 2006-11-14
Numerical Methods For Ordinary Differential Equations written by Alfredo Bellen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Developments in numerical initial value ode methods were the focal topic of the meeting at L'Aquila which explord the connections between the classical background and new research areas such as differental-algebraic equations, delay integral and integro-differential equations, stability properties, continuous extensions (interpolants for Runge-Kutta methods and their applications, effective stepsize control, parallel algorithms for small- and large-scale parallel architectures). The resulting proceedings address many of these topics in both research and survey papers.
Euro Par 2007 Parallel Processing
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Author : Anne-Marie Kermarrec
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-14
Euro Par 2007 Parallel Processing written by Anne-Marie Kermarrec and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-14 with Computers categories.
This book constitutes the refereed proceedings of the 13th International Conference on Parallel Computing, Euro-Par 2007, held in Dresden, Rennes, France, August 28-31, 2007. The 89 revised papers presented were carefully reviewed and selected from 333 submissions. The papers are organized in topical sections on support tools and environments; performance prediction and evaluation; scheduling and load balancing; compilers for high performance; parallel and distributed databases; grid and cluster computing; peer-to-peer computing; distributed systems and algorithms; parallel and distributed programming; parallel numerical algorithms; distributed and high-performance multimedia; theory and algorithms for parallel computation; high performance networks; mobile and ubiquitous computing.