A kernel independent fast multipole algorithm for radial basis functions

We present a fast multipole algorithm for the evaluation of pairwise interaction through the radial basis functions such as 1/r, ffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2 þ a2 p and 1= ffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2 þ a2 p (with a > 0) in both two and three dimensions. Our algorithm is an extension of the kernel independent fast multipole method presented in Ying et al. [L. Ying, G. Biros, D. Zorin, A kernel-independent adaptive fast multipole algorithm in two and three dimensions, J. Comput. Phys. 196(2) (2004) 591–626]. Numerical results are provided to illustrate the accuracy and complexity properties of the algorithm. 2005 Elsevier Inc. All rights reserved.