Fast Multipole Methods for the Helmholtz Equation in Three Dimensions (Elsevier Series in Electromagnetism) [Hardcover]

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

Book Description

ISBN-10: 0080443710 | ISBN-13: 978-0080443713 | Publication Date: February 10, 2005 | Edition: 1

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

Editorial Reviews

Book Description

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

Product Details

• Hardcover: 426 pages
• Publisher: Elsevier Science; 1 edition (February 10, 2005)
• Language: English
• ISBN-10: 0080443710
• ISBN-13: 978-0080443713
• Product Dimensions: 9.5 x 6.1 x 1.1 inches
• Shipping Weight: 2 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #2,397,577 in Books (See Top 100 in Books)

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1 of 11 people found the following review helpful:

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

By 

Ramani Duraiswami (College Park, MD USA) - See all my reviews
(REAL NAME)   

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