Direct Methods for Sparse Linear Systems

Author: Timothy A. Davis

Publisher: SIAM

ISBN: 9780898718881

Category: Linear systems

Page: 217

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Presents the fundamentals of sparse matrix algorithms to provide the requisite background. The book includes CSparse, a concise downloadable sparse matrix package that illustrates the algorithms and theorems presented in the book and equips readers with the tools necessary to understand larger and more complex software packages.

Numerische Mathematik

Eine Einführung anhand von Differentialgleichungsproblemen; Band 1: Stationäre Probleme

Author: Walter Zulehner

Publisher: Springer-Verlag

ISBN: 3764384271

Category: Mathematics

Page: 150

View: 4652

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"Numerik", in zwei Bänden, ist eine Einführung in die Numerische Mathematik anhand von Differenzialgleichungsproblemen. Gegliedert nach elliptischen, parabolischen und hyperbolischen Differenzialgleichungen, erläutert sie zunächst jeweils die Diskretisierung solcher Probleme. Als Diskretisierungstechniken stehen Finite-Elemente-Methoden im Raum und (partitionierte) Runge-Kutta-Methoden in der Zeit im Vordergrund. Die diskretisierten Gleichungen motivieren die Diskussion von Methoden für endlichdimensionale (nicht)lineare Gleichungen, die anschließend als eigenständige Themen behandelt werden. Ein in sich geschlossenes Bild.

CRC Handbook of Thermal Engineering

Author: Raj P. Chhabra

Publisher: CRC Press

ISBN: 149871529X

Category: Science

Page: 1649

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The CRC Handbook of Thermal Engineering, Second Edition, is a fully updated version of this respected reference work, with chapters written by leading experts. Its first part covers basic concepts, equations and principles of thermodynamics, heat transfer, and fluid dynamics. Following that is detailed coverage of major application areas, such as bioengineering, energy-efficient building systems, traditional and renewable energy sources, food processing, and aerospace heat transfer topics. The latest numerical and computational tools, microscale and nanoscale engineering, and new complex-structured materials are also presented. Designed for easy reference, this new edition is a must-have volume for engineers and researchers around the globe.

Computer Algebra in Scientific Computing

18th International Workshop, CASC 2016, Bucharest, Romania, September 19-23, 2016, Proceedings

Author: Vladimir P. Gerdt,Wolfram Koepf,Werner M. Seiler,Evgenii V. Vorozhtsov

Publisher: Springer

ISBN: 3319456415

Category: Computers

Page: 513

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This book constitutes the proceedings of the 18th International Workshop on Computer Algebra in Scientific Computing, CASC 2016, held in Bucharest, Romania, in September 2016. The 32 papers presented in this volume were carefully reviewed and selected from 39 submissions. They deal with cutting-edge research in all major disciplines of Computer Algebra.

Understanding and Implementing the Finite Element Method

Author: Mark S. Gockenbach

Publisher: SIAM

ISBN: 0898716144

Category: Mathematics

Page: 363

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The ?nite element method is the most powerful general-purpose technique for comput­ing accurate solutions to partial differential equations. Understanding and Implementing the Finite Element Method is essential reading for those interested in understanding both the theory and the implementation of the ?nite element method for equilibrium problems. This book contains a thorough derivation of the finite element equations as well as sections on programming the necessary calculations, solving the finite element equations, and using a posteriori error estimates to produce validated solutions. Accessible introductions to advanced topics, such as multigrid solvers, the hierarchical basis conjugate gradient method, and adaptive mesh generation, are provided. Each chapter ends with exercises to help readers master these topics. Understanding and Implementing the Finite Element Method includes a carefully documented collection of MATLAB® programs implementing the ideas presented in the book. Readers will bene?t from a careful explanation of data structures and speci?c coding strategies and will learn how to write a ?nite element code from scratch. Students can use the MATLAB codes to experiment with the method and extend them in various ways to learn more about programming ?nite elements. This practical book should provide an excellent foundation for those who wish to delve into advanced texts on the subject, including advanced undergraduates and beginning graduate students in mathematics, engineering, and the physical sciences.Preface; Part I: The Basic Framework for Stationary Problems. Chapter 1: Some Model PDEs; Chapter 2: The weak form of a BVP; Chapter 3: The Galerkin method; Chapter 4: Piecewise polynomials and the finite element method; Chapter 5: Convergence of the finite element method; Part II Data Structures and Implementation. Chapter 6: The mesh data structure; Chapter 7: Programming the finite element method: Linear Lagrange triangles; Chapter 8: Lagrange triangles of arbitrary degree; Chapter 9: The finite element method for general BVPs; Part III: Solving the Finite Element Equations. Chapter 10: Direct solution of sparse linear systems; Chapter 11: Iterative methods: Conjugate gradients; Chapter 12: The classical stationary iterations; Chapter 13: The multigrid method; Part IV: Adaptive Methods. Chapter 14: Adaptive mesh generation; Chapter 15: Error estimators and indicators; Bibliography; Index.


Parallel Programming

for Multicore and Cluster Systems

Author: Thomas Rauber,Gudula Rünger

Publisher: Springer Science & Business Media

ISBN: 3642378013

Category: Computers

Page: 516

View: 2039

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Innovations in hardware architecture, like hyper-threading or multicore processors, mean that parallel computing resources are available for inexpensive desktop computers. In only a few years, many standard software products will be based on concepts of parallel programming implemented on such hardware, and the range of applications will be much broader than that of scientific computing, up to now the main application area for parallel computing. Rauber and Rünger take up these recent developments in processor architecture by giving detailed descriptions of parallel programming techniques that are necessary for developing efficient programs for multicore processors as well as for parallel cluster systems and supercomputers. Their book is structured in three main parts, covering all areas of parallel computing: the architecture of parallel systems, parallel programming models and environments, and the implementation of efficient application algorithms. The emphasis lies on parallel programming techniques needed for different architectures. For this second edition, all chapters have been carefully revised. The chapter on architecture of parallel systems has been updated considerably, with a greater emphasis on the architecture of multicore systems and adding new material on the latest developments in computer architecture. Lastly, a completely new chapter on general-purpose GPUs and the corresponding programming techniques has been added. The main goal of the book is to present parallel programming techniques that can be used in many situations for a broad range of application areas and which enable the reader to develop correct and efficient parallel programs. Many examples and exercises are provided to show how to apply the techniques. The book can be used as both a textbook for students and a reference book for professionals. The material presented has been used for courses in parallel programming at different universities for many years.

Large-Scale PDE-Constrained Optimization

Author: Lorenz T. Biegler,Omar Ghattas,Matthias Heinkenschloss,Bart van Bloemen Waanders

Publisher: Springer Science & Business Media

ISBN: 364255508X

Category: Mathematics

Page: 349

View: 2710

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Optimal design, optimal control, and parameter estimation of systems governed by partial differential equations (PDEs) give rise to a class of problems known as PDE-constrained optimization. The size and complexity of the discretized PDEs often pose significant challenges for contemporary optimization methods. With the maturing of technology for PDE simulation, interest has now increased in PDE-based optimization. The chapters in this volume collectively assess the state of the art in PDE-constrained optimization, identify challenges to optimization presented by modern highly parallel PDE simulation codes, and discuss promising algorithmic and software approaches for addressing them. These contributions represent current research of two strong scientific computing communities, in optimization and PDE simulation. This volume merges perspectives in these two different areas and identifies interesting open questions for further research.

Numerical Methods II - Roots and Equation Systems

Author: Boris Obsieger

Publisher: university-books.eu

ISBN: 9537919021

Category:

Page: 260

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Numerički postupci II: Korjeni i sustavi jednadžbi Numerische Methoden II: Wurzeln und sistems gleichungs Métodos Numéricos II: Raíces y sistems de ecuaciones Численные методы II: Корни и системс уравнений

Fundamentals of Engineering Numerical Analysis

Author: Parviz Moin

Publisher: Cambridge University Press

ISBN: 0521711231

Category: Mathematics

Page: 241

View: 1953

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This text introduces numerical methods and shows how to develop, analyze, and use them. Complete MATLAB programs are now available at www.cambridge.org/Moin, and more than 30 exercises have been added. This thorough and practical book is a first course in numerical analysis for new graduate students in engineering and physical science.

Euro-Par’ 99 Parallel Processing

5th International Euro-Par Conference Toulouse, France, August 31–September 3, 1999 Proceedings

Author: Patrick Amestoy,Philippe Berger,Michel Daydé,Iain Duff,Valerie Fraysse,Luc Giraud,Daniel Ruiz

Publisher: Springer Science & Business Media

ISBN: 3540664432

Category: Computers

Page: 1503

View: 9135

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Euro-Parisaninternationalconferencededicatedtothepromotionandadvan- ment of all aspects of parallel computing. The major themes can be divided into the broad categories of hardware, software, algorithms and applications for p- allel computing. The objective of Euro-Par is to provide a forum within which to promote the development of parallel computing both as an industrial te- nique and an academic discipline, extending the frontier of both the state of the art and the state of the practice. This is particularly important at a time when parallel computing is undergoing strong and sustained development and experiencing real industrial take-up. The main audience for and participants in Euro-Parareseenasresearchersinacademicdepartments,governmentlabora- ries and industrial organisations. Euro-Par’s objective is to become the primary choice of such professionals for the presentation of new results in their specic areas. Euro-Par is also interested in applications which demonstrate the e - tiveness of the main Euro-Par themes. There is now a permanent Web site for the series http://brahms. fmi. uni-passau. de/cl/europar where the history of the conference is described. Euro-Par is now sponsored by the Association of Computer Machinery and the International Federation of Information Processing. Euro-Par’99 The format of Euro-Par’99follows that of the past four conferences and consists of a number of topics eachindividually monitored by a committee of four. There were originally 23 topics for this year’s conference. The call for papers attracted 343 submissions of which 188 were accepted. Of the papers accepted, 4 were judged as distinguished, 111 as regular and 73 as short papers.

Computational Partial Differential Equations

Numerical Methods and Diffpack Programming

Author: Hans Petter Langtangen

Publisher: Springer Science & Business Media

ISBN: 9783540434160

Category: Computers

Page: 862

View: 325

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This text teaches finite element methods and basic finite difference methods from a computational point of view. It emphasizes developing flexible computer programs using the numerical library Diffpack, which is detailed for problems including model equations in applied mathematics, heat transfer, elasticity, and viscous fluid flow. This edition offers new applications and projects, and all program examples are available on the Internet.

Algorithmen - Eine Einführung

Author: Thomas H. Cormen,Charles E. Leiserson,Ronald Rivest,Clifford Stein

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110522012

Category: Computers

Page: 1339

View: 4986

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Der "Cormen" bietet eine umfassende und vielseitige Einführung in das moderne Studium von Algorithmen. Es stellt viele Algorithmen Schritt für Schritt vor, behandelt sie detailliert und macht deren Entwurf und deren Analyse allen Leserschichten zugänglich. Sorgfältige Erklärungen zur notwendigen Mathematik helfen, die Analyse der Algorithmen zu verstehen. Den Autoren ist es dabei geglückt, Erklärungen elementar zu halten, ohne auf Tiefe oder mathematische Exaktheit zu verzichten. Jedes der weitgehend eigenständig gestalteten Kapitel stellt einen Algorithmus, eine Entwurfstechnik, ein Anwendungsgebiet oder ein verwandtes Thema vor. Algorithmen werden beschrieben und in Pseudocode entworfen, der für jeden lesbar sein sollte, der schon selbst ein wenig programmiert hat. Zahlreiche Abbildungen verdeutlichen, wie die Algorithmen arbeiten. Ebenfalls angesprochen werden Belange der Implementierung und andere technische Fragen, wobei, da Effizienz als Entwurfskriterium betont wird, die Ausführungen eine sorgfältige Analyse der Laufzeiten der Programme mit ein schließen. Über 1000 Übungen und Problemstellungen und ein umfangreiches Quellen- und Literaturverzeichnis komplettieren das Lehrbuch, dass durch das ganze Studium, aber auch noch danach als mathematisches Nachschlagewerk oder als technisches Handbuch nützlich ist. Für die dritte Auflage wurde das gesamte Buch aktualisiert. Die Änderungen sind vielfältig und umfassen insbesondere neue Kapitel, überarbeiteten Pseudocode, didaktische Verbesserungen und einen lebhafteren Schreibstil. So wurden etwa - neue Kapitel zu van-Emde-Boas-Bäume und mehrfädigen (engl.: multithreaded) Algorithmen aufgenommen, - das Kapitel zu Rekursionsgleichungen überarbeitet, sodass es nunmehr die Teile-und-Beherrsche-Methode besser abdeckt, - die Betrachtungen zu dynamischer Programmierung und Greedy-Algorithmen überarbeitet; Memoisation und der Begriff des Teilproblem-Graphen als eine Möglichkeit, die Laufzeit eines auf dynamischer Programmierung beruhender Algorithmus zu verstehen, werden eingeführt. - 100 neue Übungsaufgaben und 28 neue Problemstellungen ergänzt. Umfangreiches Dozentenmaterial (auf englisch) ist über die Website des US-Verlags verfügbar.


Direct methods for sparse matrices

Author: Iain S. Duff,A. M. Erisman,John Ker Reid

Publisher: Oxford University Press, USA

ISBN: N.A

Category: Mathematics

Page: 341

View: 9367

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This book provides practical approaches to the efficient use of sparsity--a key to solving large problems in many fields, including computational science and engineering, where mathematical models give rise to very large systems of linear equations. The emphasis is on practicality, with conclusions based on concrete experience. Non-numeric computing techniques have been included as well as frequent illustrations in an attempt to bridge the gap between the written word and the working computer code. Exercises have been included to strengthen understanding of the material as well as to extend it for students and researchers in engineering, mathematics, and computer science.


Hierarchische Matrizen

Algorithmen und Analysis

Author: Wolfgang Hackbusch

Publisher: Springer Science & Business Media

ISBN: 3642002218

Category: Mathematics

Page: 451

View: 682

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Bei der Diskretisierung von Randwertaufgaben und Integralgleichungen entstehen große, eventuell auch voll besetzte Matrizen. In dem Band stellt der Autor eine neuartige Methode dar, die es erstmals erlaubt, solche Matrizen nicht nur effizient zu speichern, sondern auch alle Matrixoperationen einschließlich der Matrixinversion bzw. der Dreieckszerlegung approximativ durchzuführen. Anwendung findet diese Technik nicht nur bei der Lösung großer Gleichungssysteme, sondern auch bei Matrixgleichungen und der Berechnung von Matrixfunktionen.

Computational Techniques for Fluid Dynamics 1

Fundamental and General Techniques

Author: Clive A.J. Fletcher

Publisher: Springer Science & Business Media

ISBN: 364258229X

Category: Science

Page: 401

View: 1335

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This well-known 2-volume textbook provides senior undergraduate and postgraduate engineers, scientists and applied mathematicians with the specific techniques, and the framework to develop skills in using the techniques in the various branches of computational fluid dynamics. A solutions manual to the exercises is in preparation.

Spectral Methods

Fundamentals in Single Domains

Author: Claudio Canuto,M. Yousuff Hussaini,Alfio Quarteroni,Thomas A. Zang

Publisher: Springer Science & Business Media

ISBN: 3540307265

Category: Science

Page: 581

View: 7179

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Since the publication of "Spectral Methods in Fluid Dynamics" 1988, spectral methods have become firmly established as a mainstream tool for scientific and engineering computation. The authors of that book have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then. This latest book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is also greatly expanded.

The Schur Complement and Its Applications

Author: Fuzhen Zhang

Publisher: Springer Science & Business Media

ISBN: 0387242732

Category: Mathematics

Page: 295

View: 9516

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This book describes the Schur complement as a rich and basic tool in mathematical research and applications and discusses many significant results that illustrate its power and fertility. Coverage includes historical development, basic properties, eigenvalue and singular value inequalities, matrix inequalities in both finite and infinite dimensional settings, closure properties, and applications in statistics, probability, and numerical analysis.