Some recent results and proposals for the use of radial basis functions inthe BEM

We survey some recent applications of radial basis functions (rbfs) for the BEM and related algorithms such as the method of fundamental solutions, Am ong these are the use of alternatives to the traditional 1 + r function in the dual reciprocity method such as thin plate splines, multquadrics and th e recently discovered compactly supported positive definite rbfs, and conve rgence proofs of the DRM for Poisson's equation. Newly discovered particula r solutions for Helmholtz-type operators are discussed and applied to give efficient mesh free algorithms for the diffusion equation. In addition, a n umber of proposals are given for future applications of rbfs such as the us e of surface rbfs for interpolation and the solution of boundary integral e quations and the application of Kansa's method to develop new rbf based cou pled domain-boundary approximation methods. (C) 1999 Elsevier Science Ltd. All rights reserved.