Introduction to Radial Basis Function Method

Abstract

This chapter presents an overview of the radial basis function (RBF) method and its application in wave propagation problems. First, the historical background development of the radial basis function method is reviewed. Then, applications of RBF to problems of large scale high-frequency wave propagation are described. Strategies are presented for reducing sampling frequency and computational and storage complexity while maintaining high stability, accuracy, and efficiency. This is followed by a list of methods using the RBF in simulating wave propagation problems, including the boundary element method, method of fundamental solutions, singular boundary method, boundary knot method, method of moments, and fast multipole method.

Keywords: Fundamental solution, Radial basis function, Wave propagation.

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