The book "Radial Basis Function Methods For Large-Scale Wave Propagation", 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.
About the Editors:
Dr. Jun-Pu Li received his Bachelor of Engineering degree in mechanical engineering from Hohai University, China in 2014, earning his Doctoral degree in 2019 from Hohai University in China. He joined the school of mechanics and safety engineering of Zhengzhou University as a lecturer in 2020 and was promoted to associate professor in mechanics in 2021. His main research interests focus on computational mechanics and virtual simulations of wave propagation. He has over 20 articles in referred international journals, with more than 460 SCI citations. His H index is 12 and 6 articles are selected as ESI highly cited papers.
Dr Qing-Hua Qin is a Professor at Shenzhen MSU-BIT University. He has worked in several leading Australian and Chinese institutions and was awarded a Queen Elizabeth II fellow and a professorial fellowship at University of Sydney and Australian National University. His research interests include meshless methods, hybrid finite element methods, piezoelectric materials, metamaterials, and composite materials. He has published more than 300 journal papers and 8 English monographs in the field of applied mechanics.
Keywords:
Fundamental solution, Radial basis function, Wave propagation. Radial basis functions, Singular boundary method, Origin intensity factor, Modified dual-level algorithm, Three-dimensional potential model.
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