Authors: Jun-Pu Li, Qing-Hua Qin

Radial Basis Function Methods for Large-Scale Wave Propagation

eBook: US $49 Special Offer (PDF + Printed Copy): US $59
Printed Copy: US $83
Library License: US $196
ISBN: 978-1-68108-899-0 (Print)
ISBN: 978-1-68108-898-3 (Online)
Year of Publication: 2021
DOI: 10.2174/97816810889831210101

Introduction

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.

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.

Audience: research scientists and postgraduate students in physics, engineering and mathematics, as well as professional engineers in construction, civil and communications engineering.

Preface

- Pp. i-iii (3)
Jun-Pu Li, Qing-Hua Qin
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Acknowledgements

- Pp. iv
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Introduction to Radial Basis Function Method

- Pp. 1-17 (17)
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Singular Boundary Method Analysis of Obliquely Incident Water Wave Passing through Submerged Breakwater

- Pp. 18-29 (12)
Jun-Pu Li, Qing-Hua Qin
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Singular Boundary Method for Three-Dimensional Low and Middle Frequency Acoustic Problems

- Pp. 30-50 (21)
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RBF Based on the Modified Fundamental Solutions for High-Frequency Acoustic Problems

- Pp. 51-68 (18)
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Modified Dual-Level Fast Multipole Algorithm For Three-Dimensional Potential Problems

- Pp. 69-90 (22)
Jun-Pu Li, Qing-Hua Qin
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Modified Dual-Level Fast Multipole Algorithm Based on the Burton-Miller Formulation for Large- Scale Sound Field Analysis

- Pp. 91-108 (18)
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Time-Dependent Singular Boundary Method for Scalar Wave Equation

- Pp. 109-120 (12)
Jun-Pu Li, Qing-Hua Qin
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Regularized Method of Moments for Time- Harmonic Electromagnetic Scattering

- Pp. 121-134 (14)
Jun-Pu Li, Qing-Hua Qin
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Recent Advances and Emerging Applications of the Radial Basis Function Method for Simulation of Large-Scale and High-Frequency Sound Wave Propagation

- Pp. 135-150 (16)
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Appendix A

- Pp. 151-155 (5)
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Appendix B

- Pp. 156-163 (8)
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Nomenclature

- Pp. 164

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Subject Index

- Pp. 165-170 (6)

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