Short note: A kernel independent fast multipole algorithm for radial basis functions

Authors:
Lexing Ying
Affiliations:
Applied and Computational Mathematics, California Institute of Technology, MC 217-50, Caltech, Pasadena, CA 91125, United States
Venue:
Journal of Computational Physics
Year:
2006

Citing 4
Cited 6

A fast algorithm for particle simulations

Journal of Computational Physics
The fast Gauss transform

SIAM Journal on Scientific and Statistical Computing
Fast Evaluation of Radial Basis Functions: Methods for Generalized Multiquadrics in $\RR^\protectn$

SIAM Journal on Scientific Computing
Coulomb Interactions on Planar Structures: Inverting the Square Root of the Laplacian

SIAM Journal on Scientific Computing

Scattered data interpolation and approximation for computer graphics

ACM SIGGRAPH ASIA 2010 Courses
Second kind integral equations for the first kind Dirichlet problem of the biharmonic equation in three dimensions

Journal of Computational Physics
Fast Evaluation of Multiquadric RBF Sums by a Cartesian Treecode

SIAM Journal on Scientific Computing
An automatic learning system to derive multipole and local expansions for the fast multipole method

ICSI'12 Proceedings of the Third international conference on Advances in Swarm Intelligence - Volume Part II
Second kind integral equation formulation for the modified biharmonic equation and its applications

Journal of Computational Physics
A genetic programming based learning system to derive multipole and local expansions for the fast multipole method

AI Communications

Quantified Score

Hi-index	31.46

Visualization

Abstract

We present a fast multipole algorithm for the evaluation of pairwise interaction through the radial basis functions such as 1/r^a, r^2+a^2 and 1/r^2+a^2 (with a0) 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.