Method of Moments for 2D Scattering Problems E-Book

Christophe Bourlier

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 166

Veröffentlichungsjahr: 2013

Beschreibung

Electromagnetic wave scattering from randomly rough surfaces in the presence of scatterers is an active, interdisciplinary area of research with myriad practical applications in fields such as optics, acoustics, geoscience and remote sensing.

In this book, the Method of Moments (MoM) is applied to compute the field scattered by scatterers such as canonical objects (cylinder or plate) or a randomly rough surface, and also by an object above or below a random rough surface. Since the problem is considered to be 2D, the integral equations (IEs) are scalar and only the TE (transverse electric) and TM (transverse magnetic) polarizations are addressed (no cross-polarizations occur). In Chapter 1, the MoM is applied to convert the IEs into a linear system, while Chapter 2 compares the MoM with the exact solution of the field scattered by a cylinder in free space, and with the Physical Optics (PO) approximation for the scattering from a plate in free space. Chapter 3 presents numerical results, obtained from the MoM, of the coherent and incoherent intensities scattered by a random rough surface and an object below a random rough surface. The final chapter presents the same results as in Chapter 3, but for an object above a random rough surface. In these last two chapters, the coupling between the two scatterers is also studied in detail by inverting the impedance matrix by blocks.

Leseprobe

Contents

Preface

Introduction

1 Integral Equations for a Single Scatterer: Method of Moments and Rough Surfaces

1.1. Introduction

1.2. Integral equations

1.3. Method of moments with point-matching method

1.4. Application to a surface

1.5. Forward–Backward (FB) method

1.6. Random rough surface generation

2 Validation of the Method of Moments for a Single Scatterer

2.1. Introduction

2.2. Solutions of a scattering problem

2.3. Comparison with the exact solution of a circular cylinder in free space

2.4. PO approximation

2.5. FB method

2.6. Conclusion

3 Scattering from Two Illuminated Scatterers

3.1. Introduction

3.2. Integral equations and method of moments

3.3. Efficient inversion of the impedance matrix: E-PILE method for two scatterers

3.4. E-PILE method combined with PO and FB

3.5. Conclusion

4 Scattering from Two Scatterers Where Only One Is Illuminated

4.1. Introduction

4.2. Integral equations and method of moments

4.3. Efficient inversion of the impedance matrix: PILE method

4.4. PILE method combined with FB or PO

4.5. Conclusion

Appendix MatLab Codes

Bibliography

Index

First published 2013 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

ISTE Ltd

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John Wiley & Sons, Inc.

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USA

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© ISTE Ltd 2013

The rights of Christophe Bourlier, Nicolas Pinel and Gildas Kubické to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2013941777

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

ISSN: 2051-2481 (Print)

ISSN: 2051-249X (Online)

ISBN: 978-1-84821-472-9

Preface

Electromagnetic wave scattering from randomly rough surfaces in the presence of scatterers is an active, interdisciplinary area of research with countless practical applications in fields such as optics, acoustics, geoscience and remote sensing. In the last four decades, considerable theoretical progress has been made in elucidating and understanding the scattering processes involved in such problems. Numerical simulations allow us to solve the Maxwell equations exactly, without the limitations of asymptotic approaches whose regimes of validity are often difficult to assess. The purpose of this book is to present both asymptotic approaches, such as the Kirchhoff approximation, and numerical methods, such as the method of moments (MoM), in order to solve scattering from rough surfaces.

Excellent textbooks on this subject are available and this book focuses on some scattering problems such as the scattering from a rough surface, a rough layer, a coated cylinder and an object near a rough surface. Although the scattering problem is assumed to be two-dimensional (invariant with respect to a direction), the problem is of practical interest because large problems can easily be solved, unlike a direct three-dimensional scattering problem, for which the equations are more complicated (because they are vectorial). Indeed, due to computing time and memory space requirements, the size of the problem to be solved is reduced. Nevertheless, advanced numerical methods can handle large problems, but the complexity of programming significantly increases.

This book is intended both for graduate students who wish to learn about scattering by rough surfaces and engineers or researchers who have to solve such problems. Adding a scatterer near a rough surface, from the MoM, the problem size increases significantly and in order to solve this problem using a standard personal computer, in Chapters 3 and 4, a versatile method, which has been developed in the last decade, is presented in detail.

The increasingly important role of numerical simulations in solving electromagnetic wave scattering problems has motivated us to provide the readers with computer codes on topics relevant to the book. These computer codes are written in the MatLab programming language. They are provided for two main purposes. The first purpose is to provide the readers a hands-on training for performing numerical experiments, through which the concepts of the book can be better communicated. The second purpose is to give new researchers a set of basic tools with which they could quickly build on their own projects.

To have the MatLab programs, please send an email to Dr. C. Bourlier at [email protected] by providing a receipt of the purchase of this book.

My thanks go to several people who made this book possible. I am grateful to Professor Joseph Saillard (retired), for suggesting writing this book, and both Professors Saillard and Serge Toutain (retired) for giving me the means to develop this research. I would like to acknowledge Drs N. Déchamps and G. Kubické, the PhD students whom I co-supervised and who developed the PILE and E-PILE methods thoroughly presented in this book. I would also like to thank the National Center for Scientific Research by whom I am employed, and the DGA (Direction Générale de l’Armement) for their financial support.

Christophe BOURLIERJune 2013

Introduction

In this book, the method of moments (MoM) is addressed to compute the field scattered by scatterers such as canonical objects (cylinder or plate) or a randomly rough surface, and also by an object above or below a random rough surface. Because the problem is considered two-dimensional (2D), the integral equations (IEs) are scalar and only the transverse electric (TE) and transverse magnetic (TM) polarizations are considered (no cross polarizations occur). Chapter 1 analyzes how the MoM with the point-matching method and pulse basic functions is applied to convert the IEs into a linear system. In addition, Chapter 1 presents the statistical parameters necessary to generate Gaussian random rough surfaces. Chapter 2 compares the MoM with the exact solution of the field scattered by a circular cylinder in free space, and with the physical optics (PO) approximation for the scattering from a plate in free space. Chapter 3 presents numerical results, obtained from the MoM combined with the efficient E-PILE method, of the scattering from two illuminated scatterers and shows how the E-PILE algorithm can be hybridized with asymptotic or rigorous methods valid for the scattering from a single scatterer (alone). Chapter 4 presents the same results as those in Chapter 3 but for an object above a random rough surface or for a coated (circular or elliptical) cylinder. In the last two chapters, the coupling between the two scatterers is also studied in detail by inverting the impedance matrix by blocks.

1

Integral Equations for a Single Scatterer: Method of Moments and Rough Surfaces

1.1. Introduction

In this chapter, the integral equations (IEs) are addressed to derive the field scattered by a single scatterer in free space. They are obtained by introducing the Green function concept and by applying the boundary conditions onto the scatterer. In addition, the IEs are converted into a linear system by using the method of moments (MoM) with the point-matching method. The impedance matrix is then expressed for any shape of the object. The special case of a perfectly conducting (PC) object is also discussed. This chapter also presents the necessary statistical parameters to generate a random rough surface.