Peter M. van den Berg - Forward and Inverse Scattering Algorithms Based on Contrast Source Integral Equations

1. Chapter 1
2. Chapter 2
3. Chapter 3
4. Chapter 4
5. Chapter 6

1. Chapter 1
2. Chapter 2
3. Chapter 3
4. Chapter 4
5. Chapter 5
6. Chapter 6

Peter M. van den Berg
Applied Sciences
Delft University of Technology
Delft, Netherlands

This edition first published 2021

2021 John Wiley & Sons, Inc.

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Library of Congress CataloginginPublication Data

Names: van den Berg, Peter. M., author.

Title: Forward and inverse scattering algorithms based on contrast source

integral equations / Peter M. van den Berg.

Description: Hoboken, NJ : Wiley, [2020] | Includes bibliographical

references and index.

Identifiers: LCCN 2020030605 (print) | LCCN 2020030606 (ebook) | ISBN

9781119741541 (hardback) | ISBN 9781119741572 (adobe pdf) | ISBN

9781119741565 (epub)

Subjects: LCSH: Wave equation. | Scattering (Mathematics) | Integral

equations. | Fourier transformations. | Optical data

processingMathematical models. | Computeraided designMathematical

models.

Classification: LCC QC174.26.W28 B464 2020 (print) | LCC QC174.26.W28

(ebook) | DDC 515/.353dc23

LC record available at https://lccn.loc.gov/2020030605

LC ebook record available at https://lccn.loc.gov/2020030606

Cover Design: Wiley

Cover Image: tatianazaets/Getty Images

To Corrievan Ravesteijn

As Professor at Delft University of Technology in the period from 1981 to 2014, I learned that university students have great difficulty implementing numerical methods to solve the forward and inverse scattering problem. PhD students need at least one year to understand the theory of wavefield scattering in complex configurations and to cast the problem into an effective numerical formulation. Currently, the scientific community is putting increasing pressure not only to publish the theory and the numerical results but also to store codes and numerical data. In current practice, many scientific works explain the physical problem and the relevant mathematics, and list numerical codes in printed form in an appendix or online on the World Wide Web. I believe that in textbooks, theoretical formulation, numerical discretization, and digital coding should be presented as a coherent package.

Therefore in 2015, I started to work on the book Forward and Inverse Scattering Algorithms Based on Contrast Source Integral Equations. The book provides a link between the fundamental scattering theory, as educated at universities, and its discrete counterpart. Next, I convert the discrete formulation into numerical codes and I include them in the book. This is of extreme importance for the development of graduate education, doctoral, and postdoctoral research. The examples are made as simple as possible and serve as canonical problems throughout the book. It can be used either as a starting point or as a benchmark for existing or new methods. I chose Matlab as a software platform because more and more universities use Matlab in teaching. Students are trained to use Matlab as an interactive tool not only to perform the assigned exercises but also to understand the essence of the mathematical problem. It stimulates creative thinking.

The goal I set to myself is that every theoretical problem is formulated in such a way that all physical configurations are discretized in a uniform way. The associated computer code must be executed as quickly as possible with minimal storage requirements, while remaining userfriendly. I consider it the most important requirement. Students should recognize the common thread running through the various Matlab codes. In this book, I organized a Matlab structure so that every code listing does not exceed the end of a page. The description of a Matlab function is paged as close as possible to the theoretical and numerical formulations, enabling easy comparison of the two formulations. Furthermore, the choice for Matlab facilitates a simple conversion to C and C++, also for calling Matlab from C or C++.

The codes for solving the forward scattering problem have been developed exclusively to serve the purpose of the present book. All forward codes are written in such a way they can be used for 1D, 2D, and 3D configurations. To compare the numerical results with analytical results, this book only discusses the canonical examples of a homogeneous scatterer, namely the slab in 1D, the circle cylinder in 2D, and the sphere in 3D. For these types of scatterers, the analytical solution for the wavefield presentations in terms of plane waves (1D), radial waves (2D), and spherical waves (3D) are given with the associated codes.

A similar numerical strategy is used for the inverse scattering problem. In the absence of real measurement data, for software development purposes, synthetic data must be used, but with a different calculation model than the discrete numerical model. For that reason, I use the analytical data determined by the canonical objects.