Article history: Received 8 March 2010 Received in revised form 1 September 2010 Accepted 15 September 2010

Article history: Received 30 April 2009 Received in revised form 25 June 2009 Accepted 29 June 2009 Available online 2 July 2009 PACS: 02.30.Em 02.30.Rz 02.60.Dc 24.10.Cn

The fast multipole method (FMM) is a technique allowing the fast calculation of long-range interactions between N points in O(N) or O(N lnN) steps with some prescribed error tolerance. The FMM has found many applications in the field of integral equations and boundary element methods, in particular by accelerating the solution of dense linear systems arising from such formulations. Original FMM...

In order to overcome the difficulties of low computational efficiency and high memory requirement in the conventional boundary element method for solving large-scale potential problems, a fast multipole boundary element method for the problems of Poisson equation is presented. First of all, through the multipole expansion and local expansion for the basic solution of the kernel function of the ...

Many different simulation methods for Stokes flow problems involve a common computationally intense task -- the summation of kernel function over $O(N^2)$ pairs points. One popular technique is Kernel Independent Fast Multipole Method (KIFMM), which constructs spatial adaptive octree all points and places small number equivalent multipole local around each box, completes sum with $O(N)$ cost, u...

The Fast Multipole Method (FMM) is well known to possess a bottleneck arising from decreasing workload on higher levels of the FMM tree [Greengard and Gropp, Comp. Math. Appl., 20(7), 1990]. We show that this potential bottleneck can be eliminated by overlapping multipole and local expansion computations with direct kernel evaluations on the finest level grid.

We present a matrix interpretation of the three-dimensional fast multipole method (FMM). The FMM is for efficient computation of gravitational/electrostatic potentials and fields. It has found various applications and inspired the design of many efficient algorithms. The one-dimensional FMM is well interpreted in terms of matrix computations. The threedimensional matrix version reveals the unde...

Article history: Received 31 March 2009 Received in revised form 17 August 2009 Accepted 26 August 2009 Available online 6 September 2009

This article introduces a new fast direct solver for linear systems arising out of wide range of applications, integral equations, multivariate statistics, radial basis interpolation, etc., to name a few. The highlight of this new fast direct solver is that the solver scales linearly in the number of unknowns in all dimensions. The solver, termed as Inverse Fast Multipole Method (abbreviated as...