Solving differential equations with radial basis functions: multilevel methods and smoothing

Some of the meshless radial basis function methods used for the numerical solution of partial diierential equations are reviewed. In particular, the diierences between globally and locally supported methods are discussed, and for locally supported methods the important role of smoothing within a multilevel framework is demonstrated. A possible connection between multigrid nite elements and multilevel radial basis function methods with smoothing is explored. Various numerical examples are also provided throughout the paper.