Electromagnetic Material Interrogation Using Conductive Interfaces and Acoustic Wavefronts

161 Pages·1987·13.62 MB·English

by  H. T. Banks

Electromagnetic Material Interrogation
Using Conductive Interfaces
and Acoustic Wavefronts
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F R O N T I E RS IN
A P P L I ED MATHEMATICS
The SIAM series on Frontiers in Applied Mathematics publishes monographs dealing
with creative work in a substantive field involving applied mathematics or scientific
computation. All works focus on emerging or rapidly developing research areas that
report on new techniques to solve mainstream problems in science or engineering.
The goal of the series is to promote, through short, inexpensive, expertly written
monographs, cutting edge research poised to have a substantial impact on the solutions
of problems that advance science and technology. The volumes encompass a broad
spectrum of topics important to the applied mathematical areas of education,
government, and industry.
EDITORIAL BOARD
H.T. Banks, Editor-in-Chief, North Carolina State University
Richard Albanese, U.S. Air Force Research Laboratory, Brooks AFB
Carlos Castillo Chavez, Cornell University
Doina Cioranescu, Universite Pierre et Marie Curie (Paris VI)
Pat Hagan, NumeriX, New York
Matthias Heinkenschloss, Rice University
Belinda King, Virginia Polytechnic Institute and State University
Jeffrey Sachs, Merck Research Laboratories, Merck and Co., Inc.
Ralph Smith, North Carolina State University
Anna Tsao, Institute for Defense Analyses, Center for Computing Sciences
BOOKS PUBLISHED IN FRONTIERS
IN APPLIED MATHEMATICS
Banks, H.T., Buksas, M.W., and Lin, T., Electromagnetic Material Interrogation Using Conductive
Interfaces and Acoustic Wavefronts
Oostveen, Job, Strongly Stabilizable Distributed Parameter Systems
Griewank, Andreas, Evaluating Derivatives: Principles andTechniques of Algorithmic
Differentiation
Kelley, C. T., Iterative Methods for Optimization
Greenbaum.Anne, Iterative Methods for Solving Linear Systems
Kelley, C. T., Iterative Methods for Linear and Nonlinear Equations
Bank, Randolph E., PLTMG:A Software Package for Solving Elliptic Partial Differential Equations.
Users'Guide 7.0
More, Jorge J. and Wright, Stephen J., Optimization Software Guide
Rude, Ulrich, Mathematical and Computational Techniques for Multilevel Adaptive Methods
Cook, L. Pamela, Transonic Aerodynamics: Problems in Asymptotic Theory
Banks, H.T., Control and Estimation in Distributed Parameter Systems
Van Loan, Charles, Computational Frameworks for the Fast Fourier Transform
Van Huffel, Sabine and Vandewalle, Joos, The Total Least Squares Problem: Computational
Aspects and Analysis
Castillo, Jose E., Mathematical Aspects of Numerical Grid Generation
Bank, R. E., PLTMG: A Software Package for Solving Elliptic Partial Differential Equations.
Users'Guide 6.0
McCormick, Stephen F., Multilevel Adaptive Methods for Partial Differential Equations
Grossman, Robert, Symbolic Computation: Applications to Scientific Computing
Coleman,Thomas F. and Van Loan, Charles, Handbook for Matrix Computations
McCormick, Stephen F., Multigrid Methods
Buckmaster.John D., The Mathematics of Combustion
Ewing, Richard E., The Mathematics of Reservoir Simulation
Electromagnetic Material Interrogation
Using Conductive Interfaces
and Acoustic Wavefronts
H.T. Banks
North Carolina State University
Raleigh, North Carolina
M.W. Buksas
Los Alamos National Laboratory
Los Alamos, New Mexico
T.Lin
Virginia Polytechnic Institute and State University
Blacksburg, Virginia
Siam
Society for Industrial and Applied Mathematics
Philadelphia
Copyright © 2000 by the Society for Industrial and Applied Mathematics.
1098765432 I
All rights reserved. Printed in the United States of America. No part of this book may
be reproduced, stored, or transmitted in any manner without the written permission
of the publisher. For information, write the Society for Industrial and Applied
Mathematics, 3600 University City Science Center, Philadelphia, PA 19104-2688.
Library of Congress Cataloging-in-Publication Data
Banks, H.T.
Electromagnetic material interrogation using conductive interfaces and
acoustic wavefronts / H.T. Banks, M.W. Buksas.T. Lin.
p. cm.– (Frontiers in applied mathematics ;21)
Includes bibliographical references and index.
ISBN 0-89871-459-1
1.Acoustic emission testing. 2. Electromagnetic waves-Scattering. 3. Surfaces
(Physics) I. Buksas, M.W. II. Lin.T. Ill.Title. IV. Series
TA4I8.84.B362000
620.1'127-dc2l
00-032944
Diam
is a registered trademark.
Contents
Foreword ix
Preface xi
1 Introduction 1
2 Problem Formulation and Physical Modeling 7
2.1 Motivation 7
2.2 Estimation Methodology 15
2.3 Reduction to Specific Problems 18
2.3.1 Acoustic Reflectors 23
3 Well-Posedness 27
3.1 A Variational Formulation 27
3.2 A Semigroup Formulation 35
3.3 Enhanced Regularity of Solutions 42
3.4 Convergence of Finite Element Approximations 47
3.5 Inverse Problem Methodology 48
4 Computational Methods for Dielectrics with Supraconductive
Backing 57
4.1 The Forward Problem for the Debye Polarization Model 57
4.2 The Inverse Problem for a Debye Medium 63
4.2.1 Sample Results 65
4.2.2 Reconstruction with Inferior Accuracy 71
4.2.3 Identification of Material Depth 72
4.2.4 Results from the Two-Step Algorithm 74
4.2.5 Estimating Depth and Physical Parameters 76
4.2.6 Results for the Simultaneous Estimation of Depth and
Dielectric Parameters 77
4.3 The Forward Problem for the Lorentz Model 79
4.4 The Inverse Problem for a Lorentz Medium 85
vii
viii Contents
5 Computational Methods for General Polarization Models 89
5.1 The Forward Problem 89
5.1.1 Galerkin Methods for the History Approximation 91
5.1.2 Approximating the History ofe(t) 92
5.1.3 Implementing the Hysteresis Term 95
5.1.4 Specific Implementation: Constant Material
Parameters 96
5.2 Results of Simulations with the General Model 97
5.2.1 Dielectric Response Function Representation
of the Debye Model 97
5.2.2 DRF Representation of the Lorentz Model 99
5.3 The Inverse Problem with the General Polarization Model . . . . 101
5.3.1 Practical Conclusions 105
6 Computational Methods for Acoustically Backed Dielectrics 107
6.1 The Forward Problem with an Acoustically
Backed Layer 107
6.1.1 Numerical Methods 108
6.1.2 Simulation Results 109
6.2 Identification of Material Depth 119
7 Concluding Summary and Remarks on Potential
Applications 129
7.1 Summary of Mathematical and
Computational Results 129
7.2 Limitations and Unanswered Questions 131
7.3 Future Technological Possibilities 133
Bibliography 137
Index 145
Foreword
The human extension of visual ability has been very important to technology,
society, and culture. This extension of vision has been to the very small, the
distant, and the internal. Microscopy—viewing the small—continues to open new
doors into the structure of materials, including biological materials in their
relation to human disease. Radar systems and other airborne sensor modalities
enable environmental monitoring important to the health of our planet and
essential to flying safety. Internal imaging is central to medical diagnosis, on one
hand, and to the nondestructive assessment of the integrity of nonliving structures,
on the other.
This volume in the SIAM Frontiers in Applied Mathematics series is a milestone in
the human endeavor to extend vision. It is concerned with imaging the interior of
materials or objects and shows, in a systematic way, how internal reflecting surfaces
can be exploited to aid the process of "seeing within." Convincing evidence is
presented that highly reflective items, such as metal surfaces, can substantially aid
characterization of materials interrogated by short electromagnetic pulses. Also,
and perhaps most intriguing, the work herein suggests that slowly moving acoustic
wave structures can also serve as useful reflecting surfaces and can be tracked by
fast moving electromagnetic pulses to enhance internal visualization.
In short, I believe that this volume can foster a significant increment in imaging
technology using low energy electromagnetic radiation. The use of
electromagnetic pulses interacting with specially placed reflective surfaces,
whether solid or acoustic, is a new dimension that will substantively impact medical
imaging, subsoil investigation, and structure evaluation.
The text is accessible to the advanced undergraduate or early graduate
engineering,bioengineering, geology, and mathematics or physics student. Its
strengths include a clear discussion of materials properties from the
electromagnetic point of view, a careful formulation of the imaging problems
addressed, solid treatment of mathematical issues, and useful illustration of
computational methods and results. While confined to internal vision in one-
dimensional settings, this volume will stimulate further developments in internal
vision to include two- and three-dimensional interior assessments. It is an excellent
and robust source of applied mathematics and engineering research challenges for
the future.
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