Fast Multipole Methods for the Helmholtz Equation in Three Dimensions [Hardcover]

Nail A Gumerov (Author), Ramani Duraiswami (Author)

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Product Details

Hardcover: 426 pages
Publisher: Elsevier Science; 1 edition (Jan 27 2005)
Language: English
ISBN-10: 0080443710
ISBN-13: 978-0080443713
Product Dimensions: 24 x 15.4 x 2.7 cm
Shipping Weight: 921 g

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Product Description

Book Description

This is the only book which provides a comprehensive coverage of this topic in one volume

Product Description

This volume in the Elsevier Series in Electromagnetism presents a detailed, in-depth and self-contained treatment of the Fast Multipole Method and its applications to the solution of the Helmholtz equation in three dimensions. The Fast Multipole Method was pioneered by Rokhlin and Greengard in 1987 and has enjoyed a dramatic development and recognition during the past two decades. This method has been described as one of the best 10 algorithms of the 20th century. Thus, it is becoming increasingly important to give a detailed exposition of the Fast Multipole Method that will be accessible to a broad audience of researchers. This is exactly what the authors of this book have accomplished.

For this reason, it will be a valuable reference for a broad audience of engineers, physicists and applied mathematicians.

The Only book that provides comprehensive coverage of this topic in one location.

Presents a review of the basic theory of expansions of the Helmholtz equation solutions

Comprehensive description of both mathematical and practical aspects of the fast multipole method and it's applications to issues described by the Helmholtz equation

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Front Cover | Copyright | Table of Contents | Excerpt | Index

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Amazon.com: 5.0 out of 5 stars (1 customer review)

1 of 12 people found the following review helpful

5.0 out of 5 stars Some additional content from the book, Jan 3 2006

By Ramani Duraiswami - Published on Amazon.com

This review is from: Fast Multipole Methods for the Helmholtz Equation in Three Dimensions (Hardcover)

Link to the table of contents, book outline and preface

http://www.umiacs.umd.edu/~ramani/FMM_HELMHOLTZ/prelims.pdf

Link to Chapter 1 of the book

http://www.umiacs.umd.edu/~ramani/FMM_HELMHOLTZ/Introduction.pdf

Link to the cover

http://www.umiacs.umd.edu/~ramani/FMM_HELMHOLTZ/GumerovWT.pdf

Short table of contents

Preface xvii

Acknowledgments xxiii

Outline of the Book xxv

Chapter 1. Introduction 1

1.1 Helmholtz Equation 1

1.2 Boundary Conditions 15

1.3 Integral Theorems 25

1.4 What is Covered in This Book and What is Not 37

Chapter 2. Elementary Solutions 39

2.1 Spherical Coordinates 39

2.2 Differentiation of Elementary Solutions 65

2.3 Sums of Elementary Solutions 73

2.4 Summary 86

Chapter 3. Translations and Rotations of Elementary Solutions 89

3.1 Expansions over Spherical Basis Functions 89

3.2 Translations of Spherical Basis Functions 93

3.3 Rotations of Elementary Solutions 117

3.4 Summary 137

Chapter 4. Multipole Methods 139

4.1 Room Acoustics: Fast Summation of Sources 139

4.2 Scattering from a Single Sphere 143

4.3 Scattering from Two Spheres 150

4.4 Scattering from N Spheres 161

4.5 On Multiple Scattering from N Arbitrary Objects 168

4.6 Summary 170

Chapter 5. Fast Multipole Methods 171

5.1 Preliminary Ideas 171

5.2 Multilevel Fast Multipole Method 196

5.3 Data Structures and Efficient Implementation 207

5.4 Summary 222

Chapter 6. Complexity and Optimizations of the MLFMM 225

6.1 Model for Level-Dependent Translation Parameters 225

6.2 Spatially Uniform Data 227

6.3 Error of MLFMM 236

6.4 Optimization 238

6.5 Non-uniform Data 248

6.6 Adaptive MLFMM 264

6.7 Summary 283

Chapter 7. Fast Translations: Basic Theory and O(p^3) Methods 285

7.1 Representations of Translation and Rotation Operators 286

7.2 Rotational-coaxial translation decomposition 306

7.3 Sparse matrix decomposition of translation and rotation operators 313

7.4 Summary 338

Chapter 8. Asymptotically Faster Translation Methods 339

8.1 Fast Algorithms Based on Matrix Decompositions 340

8.2 Low- and High-Frequency Asymptotics 361

8.3 Diagonal Forms of Translation Operators 387

8.4 Summary 416

Chapter 9. Error Bounds 417

9.1 Truncation Errors for Expansions of Monopoles 417

9.2 Truncation Errors for Expansions of Multipoles 432

9.3 Translation Errors 439

9.4 Summary 462

Chapter 10. Fast Solution of Multiple Scattering

Problems 465

10.1 Iterative Methods 466

10.2 Fast Multipole Method 472

10.3 Results of Computations 487

10.4 Summary 498

Color Plates 499

Bibliography 509

Index 515

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