Science China Mathematics

, Volume 55, Issue 5, pp 1043-1051

First online:

A pedestrian introduction to fast multipole methods

  • Lexing YingAffiliated withDepartment of Mathematics and ICES, University of Texas at Austin Email author 

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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 method non-oscillatory kernels oscillatory kernels multiscale methods


65N38 65R20