This book details the development of techniques and ideas from the radial basis function. It begins with a mathematical description of the basic concept of radial function method with chapters progressively delving into the derivation and construction of radial basis functions for large-scale wave propagation problems including singularity problems, high-frequency wave problems and large-scale computation problems. This reference, written by experts in numerical analysis, demonstrates how the functions arise naturally in mathematical analyses of structures responding to external loads. Readers are also equipped with mathematical knowledge about the radial basis function for understanding key algorithms required for practical solutions.
The book is designed to make information about radial basis function methods more accessible to research scientists, professional engineers and postgraduate students, with a specific focus on large-scale wave propagation problems.
Key Features:
- Introduces basic concepts of radial basis function methods
- Provides detailed derivations of several radial basis functions
- Explains complex problems using simple language
- Contains a wide range of numerical examples to demonstrate applications of relevant functions
- Combines the radial basis function with other known numerical methods (boundary element methods and differential equations).
- Includes references and appropriate chapter appendices
- Includes MATLAB codes for origin intensity factors and nearly singular factors for radial basis calculations
The book is designed to make information about radial basis function methods more accessible to research scientists, professional engineers and postgraduate students, with a specific focus on large-scale wave propagation problems.
Table of Contents
Chapter 1 Introduction To Radial Basis Function Method1.1. Historical Background
1.2. Overview Of Rbf In Large Scale High-Frequency Wave Propagation Computing
1.3. Numerical Methods Using Rbf For Simulating Wave Propagation Problems
1.4. Chapter Arrangement
- References
Chapter 2 Singular Boundary Method Analysis Of Obliquely Incident Water Wave Passing Through Submerged Breakwater
2.1. Mathematical Formulation
2.2. Singular Boundary Method For 2-D Modified Helmholtz Problems
2.3. Numerical Experiments
- Conclusions
- Appendix A. Fundamental Solution And Origin Intensity Factor Of Laplace Equation, Helmholtz Equation, And Modified Helmholtz Equation
- Appendix B. Relationship Of The Origin Intensity Factor For Interior And Exterior Problems
- References
Chapter 3 Singular Boundary Method For Three-Dimensional Low And Middle Frequency Acoustic Problems
3.1. Introduction
3.2. Singular Boundary Method Based On The Burton-Miller Formulations
3.3. Origin Intensity Factor For Helmholtz Equation
3.4. The Regularized Singular Boundary Method For Near-Boundary And Boundary Solutions
3.5. Numerical Experiments
- Conclusion
- Appendix. Fundamental Solution And Oif Of Laplace Equation, Helmholtz Equation And Modified Helmholtz Equation
- References
Chapter 4 Rbf Based On The Modified Fundamental Solutions For High-Frequency Acoustic Problems
4.1. Introduction
4.2. Modified Singular Boundary Method
4.3. Dual-Level Method Of Fundamental Solutions
4.4. Numerical Experiments
- Conclusions
- Appendix. Influence Of The Fictitious Boundary On Results
- References
Chapter 5 Modified Dual-Level Fast Multipole Algorithm For Three- Dimensional Potential Problems
5.1. Introduction
5.2. Basic Formulations Of The Boundary Element Method
5.3. Basic Formulations Of The Fast Multipole Boundary Element Method
5.4. The Modified Dual-Level Fast Multipole Algorithm
5.5. Complexity Analysis Of The Mdfma As A Potential Model
5.6. Numerical Results And Discussion
- Conclusions
- Appendix. The Pseudocode Of The Mdfma
- References
Chapter 6 Modified Dual-Level Fast Multipole Algorithm Based On The Burton-Miller Formulation For Large-Scale Sound Field Analysis
6.1. Introduction
6.2. Formulations Of The Boundary Element Method
6.3. Formulations Of The Fast Multipole Boundary Element Method Based On The Burton-Miller Formulation
6.4. The Dual-Level Fast Multipole Boundary Element Method Based On The Burton-Miller Formulation
6.5. Numerical Results And Discussions
- Conclusions
- References
Chapter 7 Time-Dependent Singular Boundary Method For Scalar Wave Equation
7.1. Introduction
7.2. Time-Dependent Singular Boundary Method For 2-D Wave Equations
7.3. Time-Dependent Singular Boundary Method For 3-D Wave Equations
7.4. Numerical Example
- Conclusions
- References
Chapter 8 Regularized Method Of Moments For Time-Harmonic Electromagnetic Scattering
8.1. Introduction
8.2. The Regularized Method Of Moments For Three-Dimensional Electromagnetic Scattering
8.3. Numerical Example
- Conclusions
- References
- Subject Index
Author
- Jun-Pu Li
- Qinghua Qin
