Large-Scale Structures in Acoustics and Electromagnetics

Proceedings of a Symposium

Board on Mathematical Sciences

Commission on Physical Sciences, Mathematics, and Applications

National Research Council

National Academy Press
Washington, D.C.
1996



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Large-Scale Structures in Acoustics and Electromagnetics: Proceedings of a Symposium Large-Scale Structures in Acoustics and Electromagnetics Proceedings of a Symposium Board on Mathematical Sciences Commission on Physical Sciences, Mathematics, and Applications National Research Council National Academy Press Washington, D.C. 1996

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Large-Scale Structures in Acoustics and Electromagnetics: Proceedings of a Symposium NOTICE: The project that is the subject of this report was approved by the Governing Board of the National Research Council, whose members are drawn from the councils of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The National Academy of Sciences is a private, nonprofit, self-perpetuating society of distinguished scholars engaged in scientific and engineering research, dedicated to the furtherance of science and technology and to their use for the general welfare. Upon the authority of the charter granted to it by the Congress in 1863, the Academy has a mandate that requires it to advise the federal government on scientific and technical matters. Dr. Bruce Alberts is president of the National Academy of Sciences. The National Academy of Engineering was established in 1964, under the charter of the National Academy of Sciences, as a parallel organization of outstanding engineers. It is autonomous in its administration and in the selection of its members, sharing with the National Academy of Sciences the responsibility for advising the federal government. The National Academy of Engineering also sponsors engineering programs aimed at meeting national needs, encourages education and research, and recognizes the superior achievement of engineers. Dr. Harold Liebowitz is president of the National Academy of Engineering. The Institute of Medicine was established in 1970 by the National Academy of Sciences to secure the services of eminent members of appropriate professions in the examination of policy matters pertaining to the health of the public. The Institute acts under the responsibility given to the National Academy of Sciences by its congressional charter to be an adviser to the federal government and, upon its own initiative, to identify issues of medical care, research, and education. Dr. Kenneth I. Shine is president of the Institute of Medicine. The National Research Council was organized by the National Academy of Sciences in 1916 to associate the broad community of science and technology with the Academy’s purposes of furthering knowledge and advising the federal government. Functioning in accordance with general policies determined by the Academy, the Council has become the principal operating agency of both the National Academy of Sciences and the National Academy of Engineering in providing services to the government, the public, and the scientific and engineering communities. The Council is administered jointly by both Academies and the Institute of Medicine. Dr. Bruce Alberts and Dr. Harold Liebowitz are chairman and vice-chairman, respectively, of the National Research Council. The National Research Council established the Board on Mathematical Sciences in 1984. The objectives of the Board are to maintain awareness and active concern for the health of the mathematical sciences and to serve as the focal point in the National Research Council for issues connected with the mathematical sciences. In addition, the Board conducts studies for federal agencies and maintains liaison with the mathematical sciences communities and academia, professional societies, and industry. This material is based on work supported by the National Science Foundation under Grant No. DMS-9525898 and relates to Department of Navy Grant N00014-94-1-0571 issued by the Office of Naval Research. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the sponsors. The United States government has a royalty-free license throughout the world in all copyrightable material contained herein. Library of Congress Catalog Card Number 95-70716 International Standard Book Number 0-309-05337-4 Additional copies of this report are available from: National Academy Press 2101 Constitution Avenue, N.W. Box 285Washington, D.C. 20055800-624-6242; 202-334-3313 (in the Washington Metropolitan Area) B-665 Copyright 1996 by the National Academy of Sciences. All rights reserved. Printed in the United States of America

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Large-Scale Structures in Acoustics and Electromagnetics: Proceedings of a Symposium BOARD ON MATHEMATICAL SCIENCES AVNER FRIEDMAN, University of Minnesota, Chair JEROME SACKS, National Institute of Statistical Sciences, Vice-Chair LOUIS AUSLANDER, City University of New York HYMAN BASS, Columbia University PETER E. CASTRO, Eastman Kodak Company FAN R.K. CHUNG, University of Pennsylvania R. DUNCAN LUCE, University of California, Irvine PAUL S. MUHLY, University of Iowa GEORGE NEMHAUSER, Georgia Institute of Technology ANIL NERODE, Cornell University INGRAM OLKIN, Stanford University RONALD F. PEIERLS, Brookhaven National Laboratory DONALD ST.P. RICHARDS, University of Virginia MARY F. WHEELER, Rice University ROBERT ZIMMER, University of Chicago Ex Officio Member JON R. KETTENRING, Bell Communications Research Chair, Committee on Applied and Theoretical Statistics Staff JOHN R. TUCKER, Director RUTH E. O'BRIEN, Staff Associate JOHN W. ALEXANDER, Program Officer BARBARA W. WRIGHT, Administrative Assistant

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Large-Scale Structures in Acoustics and Electromagnetics: Proceedings of a Symposium COMMISSION ON PHYSICAL SCIENCES, MATHEMATICS, AND APPLICATIONS ROBERT J. HERMANN, United Technologies Corporation, Chair STEPHEN L. ADLER, Institute for Advanced Study PETER M. BANKS, Environmental Research Institute of Michigan SYLVIA T. CEYER, Massachusetts Institute of Technology L. LOUIS HEGEDUS, W.R. Grace and Co. JOHN E. HOPCROFT, Cornell University RHONDA J. HUGHES, Bryn Mawr College SHIRLEY A. JACKSON, U.S. Nuclear Regulatory Commission KENNETH I. KELLERMANN, National Radio Astronomy Observatory KEN KENNEDY, Rice University THOMAS A. PRINCE, California Institute of Technology JEROME SACKS, National Institute of Statistical Sciences L.E. SCRIVEN, University of Minnesota LEON T. SILVER, California Institute of Technology CHARLES P. SLICHTER, University of Illinois at Urbana-Champaign ALVIN W. TRIVELPIECE, Oak Ridge National Laboratory SHMUEL WINOGRAD, IBM T.J. Watson Research Center CHARLES A. ZRAKET, Mitre Corporation (retired) NORMAN METZGER, Executive Director

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Large-Scale Structures in Acoustics and Electromagnetics: Proceedings of a Symposium Preface In response to a request from the Office of Naval Research, the Board on Mathematical Sciences convened a symposium, "Large-Scale Structures in Acoustics and Electromagnetics," on September 26-27, 1994, in Washington, D.C. The symposium's main theme, the dynamics of large-scale structures, refers to structures that are large relative to their operating wavelengths. Large-scale structures typically involve many substructures and are characterized by an extended range of scales. Examples include large man-made objects in the ocean such as naval and maritime vessels, aerospace vehicles, and densely packed microelectronic and optical integrated circuits. Analytical, computational, and experimental procedures for studying large-scale structures entail an extremely large number of degrees of freedom. The excitation of large-scale structures can yield both linear and nonlinear responses, with similar effects in surrounding media. The dynamics of the substructures and their interfaces include time-variant, dispersive, and dissipative aspects. The symposium focused on computational methods required to determine the dynamics of large-scale electromagnetic, acoustic, and mechanical systems. Over the past two decades, long-dominant frequency-domain methods have been complemented and occasionally supplanted by a growing collection of time-domain techniques. For example, in structural acoustics two recent procedures involve high-order expansions in time, and temporal finite elements. Another noteworthy example is research on integrated microwave and optical circuits that involves electromagnetic and optical scattering and propagation theories, quantum electronics, and solid-state physics. Speakers were advised that one purpose of the symposium was to stimulate discussions of the efficiency, accuracy, and areas of applicability of time- and frequency-domain computational procedures. Another purpose was to address the interplay of time- and frequency-domain computational procedures and experimental procedures with respect to the future goal of comparing them. The symposium emphasized the relationship and synergy between time- and frequency-domain methods rather than their individual advantages, since information that allows a direct comparison between the two types of methods often is not available. This symposium helped to clarify the roles of and relationships between time-domain and frequency-domain methods in electromagnetics and acoustics. It also inaugurated an exchange of ideas and perspectives between investigators involved mainly with acoustics and others concerned principally with electromagnetics. Chapters 1, 2, 6, and 9 of these Proceedings describe results using mostly time-domain methods in elasto-acoustics problems derived primarily from fluid-solid interactions of the kind that occur in submarine detection. Chapters 4, 5, 7, 8, and 10 similarly describe spatial frequency range results for electromagnetic systems. Chapter 3 describes a unique, successful attempt at generalizing the problems in a mathematically useful way. A number of the papers address the relative applicability of time-domain and fast (or rather, discrete) Fourier transform methods, adaptive grid techniques, error estimates, costs of computation, and so on, to issues arising in other fields. Regardless of the domain in which the model of a large structure is formulated, a key issue is how computer cost scales with increasing model complexity and model size in wavelengths. For the most part, the papers in this volume emphasize analytical issues and how good a particular approach is for addressing the problem at hand. For constructing models of large-scale, complex structures, hybrid approaches are required and a multidisciplinary approach is de rigueur. The ideal model would simultaneously be efficient enough to be affordable and to permit quantifiable trade-offs between accuracy and efficiency, and would also provide a known, and preferably selectable, amount of accuracy. Several papers address issues such as computer time involved, the number of iterations required to reach

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Large-Scale Structures in Acoustics and Electromagnetics: Proceedings of a Symposium acceptable convergence, and similar concerns, and a few describe how the cost, or equivalently the total operation count, depends on spatial frequency. Chapter 1 describes significant spatial adaptation techniques that are extremely important for ensuring accuracy and efficiency and also addresses the problem of spectral density that haunts the middle frequency range of elasto-acoustic systems. Chapter 2 demonstrates the use of reduced-order models that capture, to acceptable accuracy, a physical behavior of interest—a technique that may substantially improve modeling efficiency for problems amenable to such an approach. The analytically elegant Chapter 3 presents various modeling approaches in an overall analytical framework that may be most relevant as a means for the systematic development of hybrid models. Chapter 4, which tackles some impressively complex problems in ultrafast optical pulses, provides evidence for the computational benefits of the use of hybrid models and points up the challenges posed by a three-dimensional setting with, presumably, its commensurate increased computer costs. Chapter 5 usefully discusses computational electromagnetics from the initial perspective of computational fluid dynamics, and describes some nice results for this computer-intensive approach. Impressive results showing the benefits of adapting a spatial grid to satisfy an error criterion are given in Chapter 6. Chapter 7 discusses the use of reduced-order models in a hierarchical way that seems well suited to that particular physical setting and elsewhere, and that, at least conceptually, offers hope that hybrid models of problems consisting only of wave fields might be similarly, if for different reasons, addressed. An interesting synthesis and analysis problem for large-scale integrated photonic devices and circuits is discussed in Chapter 8. Chapter 9's preconditioners (an approach to improving the model formulation prior to interaction) lead to, among other things, iterative convergence rates that are almost frequency- and discretization-independent; if this independence were to remain true for general problems, a significant advance could result: time-harmonic iterative solutions might be achieved at a cost proportional to the total number of spatial unknowns. Chapter 10 provides a comprehensive discussion of methods being pursued in electromagnetics to reduce the operation count, describes how such methods work, and presents explicit operation-count scaling laws. Chapter 11, the record of an open discussion in which symposium participants tried to come to grips with the symposium's main theme, is particularly useful. There it is noted, for example, that much of the person-effort needed for numerical modeling is associated with grid generation, so that being able to avoid grid generation would be extremely beneficial. Avoidance of remeshing is particularly important as well when adapting field sampling for error reduction. Furthermore, since error estimation is not in general well developed for computational electromagnetics, the value and reliability of any computed result must be regarded with skepticism until independent confirming data are obtained. Also, knowledge of spatial or temporal errors is needed to determine whether fields are being undersampled, causing decreased accuracy, or oversampled, causing an expenditure of excessive computer time. Thus the importance of error estimation and validation of computed results in computational electromagnetics can hardly be overstated. Chapter 11 also points out the opportunity to compile the common analytical features of electromagnetics and acoustics and to tabulate the most efficient kinds of codes for modeling various kinds of structures. Also of value would be the development of a modeling handbook that catalogs solved problems (according to type and complexity together with the codes used for their solutions, and so forth), and that includes negative as well as positive results so that others can learn what does and does not work. The symposium's concluding discussion further raised the crucial question of what is really sought in scientific computing, which all too often is done with no regard for whether all the resulting data are needed. If computing entailed no cost penalty, all would be fine, but that is hardly ever the case. Thus, when computing the input impedance of an antenna, with everything else being equal, it would almost

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Large-Scale Structures in Acoustics and Electromagnetics: Proceedings of a Symposium always be better to develop an iterative solution rather than compute a factored—or, even worse, an inverted—solution matrix. As reflected in the symposium papers and in the discussion, numerous research opportunities exist, including enunciating the scaling laws for some of the techniques discussed and addressing the question, Are electromagnetic systems immune to the spectral density problem (addressed in Chapter 1) because they have lower-order field equations? The presentations collected in this volume point out interrelationships and opportunities for future development of heretofore mostly separate research approaches, and so inspire coordinated progress in understanding the behavior of large-scale structures. The papers and discussion help clarify issues and, in emphasizing scientific bridges and methodological commonalities, indicate new and beneficial research directions. It is hoped that they will stimulate investigations of these related frequency- and time-domain approaches and how to use them together to achieve even greater progress in acoustics and electromagnetics, as well as exploration of cross-cutting fundamental questions whose answers would directly benefit efforts in these areas.

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Large-Scale Structures in Acoustics and Electromagnetics: Proceedings of a Symposium Contents     OPENING REMARKS Fred E. Saalfeld   1     INTRODUCTION John R. Tucker   4 1   HIGH-ORDER, MULTILEVEL, ADAPTIVE TIME-DOMAIN METHODS FOR STRUCTURAL ACOUSTICS SIMULATIONS J. Tinsley Oden, Andrzej Safjan, Po Geng, Leszek Demkowicz   5 2   DISTRIBUTED FEEDBACK RESONATORS Hermann A. Haus   50 3   ACOUSTIC, ELASTODYNAMIC, AND ELECTROMAGNETIC WAVEFIELD COMPUTATION - A STRUCTURED APPROACH BASED ON RECIPROCITY Adrianus T. de Hoop, MaartenV. de Hoop   72 4   NUMERICAL MODELING OF THE INTERACTIONS OF ULTRAFAST OPTICAL PULSES WITH NONRESONANT AND RESONANT MATERIALS AND STRUCTURES Richard W.Ziolkowski, Justin B. Judkins   89 5   ALGORITHMIC ASPECTS AND SUPERCOMPUTING TRENDS IN COMPUTATIONAL ELECTROMAGNETICS Vijaya Shankar, William F. Hall, Alireza Mohammadian,Chris Rowell   103 6   ADAPTIVE FINITE ELEMENT METHODS FOR THE HELMHOLTZ EQUATION IN EXTERIOR DOMAINS James R. Stewart, Thomas J.R. Hughes   122 7   MODELING OF OPTICALLY "ASSISTED" PHASED ARRAY RADAR Alan Rolf Mickelson   143 8   Synthesis and Analysis of Large-Scale Integrated Photonic Devices and Circuits Lakshman S. Tamil, Arthur K. Jordan   162 9   DESIGN AND ANALYSIS OF FINITE ELEMENT METHODS FOR TRANSIENT AND TIME-HARMONIC STRUCTURAL ACOUSTICS Peter M. Pinsky, M. Malhotra,Lonny L. Thompson   183

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Large-Scale Structures in Acoustics and Electromagnetics: Proceedings of a Symposium 10   AN OVERVIEW OF THE APPLICATIONS OF THE METHODS OF MOMENTS TO LARGE BODIES IN ELECTROMAGNETICS EDWARD H. NEWMAN, I. TEKIN   204 11   DISCUSSION   221     APPENDICES   241     A Symposium Agenda   243     B Speakers   246     C Symposium Participants   250

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Large-Scale Structures in Acoustics and Electromagnetics: Proceedings of a Symposium Large-Scale Structures in Acousticsand Electromagnetics Proceedings of a Symposium

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