This book surveys the latest advances in radial basis function (RBF) meshless collocation methods which emphasis on recent novel kernel RBFs and new numerical schemes for solving partial differential equations. The RBF collocation methods are inherently free of integration and mesh, and avoid tedious mesh generation involved in standard finite element and boundary element methods. This book focuses primarily on the numerical algorithms, engineering applications, and highlights a large class of novel boundary-type RBF meshless collocation methods. These methods have shown a clear edge over the traditional numerical techniques especially for problems involving infinite domain, moving boundary, thin-walled structures, and inverse problems.

Due to the rapid development in RBF meshless collocation methods, there is a need to summarize all these new materials so that they are available to scientists, engineers, and graduate students who are interest to apply these newly developed methods for solving real world's problems. This book is intended to meet this need.

Prof. Wen Chen and Dr. Zhuo-Jia Fu work at Hohai University. Pr of. C.S. Chen works at the University of Southern Mississippi.

Systematically introduces various RBF collocation methods for domain and boundary-only discretization, including some very recent techniques not covered elsewhere Introduces new approaches to constructing characteristic kernel RBFs Provides illustrative benchmark examples Includes open-source codes

Autorentext

Dr. Wen Chen is a Distinguished Professor and former Dean of the College of Mechanics and Materials at Hohai University, China. His research covers computational mechanics, hydrodynamics, and acoustics. His research interests include RBF-based numerical simulation, anomalous diffusion, and non-local statistics of soft matter mechanics. He also serves as Associate Director of the Chinese Society of Environmental Mechanics and the TC member on Linear Control Systems of the International Federation of Automatic Control. He is former TC Chair of the sector in computational mechanics software, China Mechanics Society. Dr. Hongguang Sun works as a Professor in the College of Mechanics and Materials, Director of Sino-US Joint Research Center of Groundwater and Environmental Fluid Mechanics, and Deputy Director of the Institute of Hydraulics and Fluid Mechanics, Hohai University, China. His main research interests include simulation and remediation of groundwater and soil pollution,sediment transport, and high-precision computational mechanics. Dr. Xicheng Li works as an Associate Professor at the School of Mathematical Sciences, the University of Jinan, China. He has been engaged in theoretical and applied research of fractional calculus, especially fractional derivative modeling of anomalous diffusion. He is also done much exploration in modeling heat and mass transfer and solving fractional differential equations.

Inhalt

Introduction.- Radial basis functions.- Different formulations of the Kansa method domain discretization.- Boundary-type RBF collocation methods.- Open issues and Perspectives.