Model Reduction for Circuit Simulation
Simulation based on mathematical models plays a major role in computer aided design of integrated circuits (ICs). Decreasing structure sizes, increasing packing densities and driving frequencies require the use of refined mathematical models, and to take
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Peter Benner Michael Hinze E. Jan W. ter Maten •
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Editors
Model Reduction for Circuit Simulation
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Editors Prof. Dr. Peter Benner Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 39106 Magdeburg Germany e-mail: [email protected]
Dr. E. Jan W. ter Maten Department of Mathematics & Computer Science Eindhoven University of Technology Den Dolech 2, HG 8.02, P.O. Box 513 5600 MB Eindhoven The Netherlands e-mail: [email protected]
Prof. Michael Hinze Dept. Mathematik Universität Hamburg Bundesstr. 55 20146 Hamburg Germany e-mail: [email protected]
ISSN 1876-1100
e-ISSN 1876-1119
ISBN 978-94-007-0088-8
e-ISBN 978-94-007-0089-5
DOI 10.1007/978-94-007-0089-5 Springer Dordrecht Heidelberg London New york Ó Springer Science+Business Media B.V. 2011 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Cover design: eStudio Calamar, Berlin/Figueres Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
Simulation plays a major role in computer aided design of integrated circuits (ICs). Mathematical models describe the dynamical processes and interactions of electrical devices. Verification of a circuit’s behavior by means of solving these model equations in time and frequency domain is a mandatory task in the design process. The structures’ sizes are decreasing, the packing density increases and so do the driving frequencies. This requires to use refined models and to take into account secondary, parasitic effects. The very high dimensional problems that emerge in this way may be solvable with the help of computer algebra in an unreasonable amount of time only. Clearly, this conflicts with the short time-to-market demands in industry. Model order reduction (MOR) presents a way out of this dilemma. Redundancies are resolved, less relevant quantities are replaced by the most significant ones. In this way, the problem’s complexity is reduced, keeping the main characteristics. Solving lower dimensional problems one can get statements on the circuit’s performance more quickly. This book surveys the state of the art in the challenging research field of MOR for integrated circuits (ICs), and also addresses future research directions in this area. Special emphasis is put on aspects stemming from miniaturization to nanoscale. Contributions cover complexity reduction using e.g., balanced truncation, Pad´e-approximation/Krylov-techniques, or POD approaches. For semiconductor applications, a focus is on generalizing current techniques to differential algebraic equations, on including design parameters, on preserv
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