Features
- Cover Type: Hard Cover with 426 pages
- Published by: Elsevier Science January 27, 2005
- Written in: English
- ISBN 10 Number: 0080443710
- ISBN 13 Number: 978-0080443713
-
Book Dimensions:
9.1 x 6.1 x 1.1 inches
- Weighs: 2 pounds
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 ten 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
Reader ReviewsLink 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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