Fast Multipole Methods for the Helmholtz Equation in Three Dimensions (eBook)
426 Seiten
Elsevier Science (Verlag)
978-0-08-053159-5 (ISBN)
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
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
Front Cover 1
Fast Multipole Methods for the Helmholtz Equation in Three Dimensions 4
Copyright Page 5
Contents 8
Preface 18
Acknowledgments 24
Outline of the Book 26
Chapter 1. Introduction 32
1.1 Helmholtz Equation 32
1.2 Boundary Conditions 46
1.3 Integral Theorems 56
1.4 What is Covered in This Book and What is Not 68
Chapter 2. Elementary Solutions 70
2.1 Spherical Coordinates 70
2.2 Differentiation of Elementary Solutions 96
2.3 Sums of Elementary Solutions 104
2.4 Summary 117
Chapter 3. Translations and Rotations of Elementary Solutions 120
3.1 Expansions over Spherical Basis Functions 120
3.2 Translations of Spherical Basis Functions 124
3.3 Rotations of Elementary Solutions 148
3.4 Summary 168
Chapter 4. Multipole Methods 170
4.1 Room Acoustics: Fast Summation of Sources 170
4.2 Scattering from a Single Sphere 174
4.3 Scattering from Two Spheres 181
4.4 Scattering from N Spheres 192
4.5 On Multiple Scattering from N Arbitrary Objects 199
4.6 Summary 201
Chapter 5. Fast Multipole Methods 202
5.1 Preliminary Ideas 202
5.2 Multilevel Fast Multipole Method 227
5.3 Data Structures and Efficient Implementation 238
5.4 Summary 253
Chapter 6. Complexity and Optimizations of the MLFMM 256
6.1 Model for Level-Dependent Translation Parameters 256
6.2 Spatially Uniform Data 258
6.3 Error of MLFMM 267
6.4 Optimization 269
6.5 Non-uniform Data 279
6.6 Adaptive MLFMM 295
6.7 Summary 314
Chapter 7. Fast Translations: Basic Theory and O(p3) Methods 316
7.1 Representations of Translation and Rotation Operators 317
7.2 Rotational-coaxial translation decomposition 337
7.3 Sparse matrix decomposition of translation and rotation operators 344
7.4 Summary 369
Chapter 8. Asymptotically Faster Translation Methods 370
8.1 Fast Algorithms Based on Matrix Decompositions 371
8.2 Low- and High-Frequency Asymptotics 392
8.3 Diagonal Forms of Translation Operators 418
8.4 Summary 447
Chapter 9. Error Bounds 448
9.1 Truncation Errors for Expansions of Monopoles 448
9.2 Truncation Errors for Expansions of Multipoles 463
9.3 Translation Errors 470
9.4 Summary 493
Chapter 10. Fast Solution of Multiple Scattering Problems 496
10.1 Iterative Methods 497
10.2 Fast Multipole Method 503
10.3 Results of Computations 518
10.4 Summary 529
Color Plates 530
Bibliography 540
Index 546
| Erscheint lt. Verlag | 27.1.2005 |
|---|---|
| Sprache | englisch |
| Themenwelt | Sachbuch/Ratgeber |
| Mathematik / Informatik ► Informatik | |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| Naturwissenschaften ► Physik / Astronomie | |
| Technik ► Elektrotechnik / Energietechnik | |
| ISBN-10 | 0-08-053159-8 / 0080531598 |
| ISBN-13 | 978-0-08-053159-5 / 9780080531595 |
| Haben Sie eine Frage zum Produkt? |
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