Science China Mathematics

, Volume 55, Issue 5, pp 1043–1051

A pedestrian introduction to fast multipole methods


DOI: 10.1007/s11425-012-4392-0

Cite this article as:
Ying, L. Sci. China Math. (2012) 55: 1043. doi:10.1007/s11425-012-4392-0


This paper provides a conceptual and non-rigorous description of the fast multipole methods for evaluating convolution kernel functions with source distributions. Both the non-oscillatory and the oscillatory kernels are considered. For non-oscillatory kernel, we outline the main ideas of the classical fast multipole method proposed by Greengard and Rokhlin. In the oscillatory case, the directional fast multipole method developed recently by Engquist and Ying is presented.


fast multipole methodnon-oscillatory kernelsoscillatory kernelsmultiscale methods



Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of Mathematics and ICESUniversity of Texas at AustinAustinUSA