Time Integration Methods
With a discretization in time like the Störmer-Verlet method from Section 3.1, the solution of the continuous Newton’s equations is computed only approximately at selected points along the time axis. There, approximations to the values at later points in
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Michael Griebel Stephan Knapek Gerhard Zumbusch
Numerical Simulation in Molecular Dynamics Numerics, Algorithms, Parallelization, Applications
With 180 Figures, 43 in Color, and 63 Tables
123
Michael Griebel
Stephan Knapek
Institut für Numerische Simulation Universität Bonn Wegelerstr. 6 53115 Bonn, Germany e-mail: [email protected]
e-mail: [email protected]
Gerhard Zumbusch Institut für Angewandte Mathematik Friedrich-Schiller-Universität Jena Ernst-Abbe-Platz 2 07743 Jena, Germany e-mail: [email protected]
Library of Congress Control Number: 2007928345
Mathematics Subject Classification (2000): 68U20, 70F10, 70H05, 83C10, 65P10, 31C20, 65N06, 65T40, 65Y05, 68W10, 65Y20
ISSN 1611-0994 ISBN 978-3-540-68094-9 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com © Springer-Verlag Berlin Heidelberg 2007 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: by the authors using a Springer TEX macro package Cover design: WMX Design GmbH, Heidelberg Production: LE-TEX Jelonek, Schmidt & Vöckler GbR, Leipzig Printed on acid-free paper 46/3180/YL - 5 4 3 2 1 0
Preface
The rapid development of parallel computing systems made it possible to recreate and predict physical processes on computers. Nowadays, computer simulations complement and even substitute experiments. Moreover, simulations allow to study processes that cannot be analyzed directly through experiments. This accelerates the development of new products since costly physical experiments can be avoided. Additionally, the quality of products can be improved by the investigation of phenomena not previously accessible. Hence, computer simulation plays a decisive role especially in the development of new substances in the material sciences as well as in biotechnology and nanotechnology. Many interesting processes cannot be described nor understood in their entirety in a continuum model, but have to be studied with molecular or atomic models. The numerical simulation of models on this length scale usually relies on particle methods and other methods of molecular dynamics. Areas of application range from physics, biology, and chemistry to modern material sciences. The fundamental mathemat
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