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.