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

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 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...

The multilevel fast multipole method (MLFMM) is an algorithm that has had great success in reducing the computational time required to find the solution to the Galerkin boundary integral form of the Helmholtz equation. We present a new formulation of the MLFMM using Fourier basis functions rather than spherical harmonics in order to accelerate and simplify the time-critical stages of the algori...

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 Laplace equation is presented. through the multipole expansion and local expansion for the basic solution of the kernel function of the Laplace equati...

Because of its practical significance, many different methods have been developed for the solution of the time-harmonic Maxwell equations in an exterior domain at higher frequency. Often methods with complimentary strengths can be combined to obtain an even better method. In this paper we provide a numerical study of a method for coupling of the Ultra-Weak Variational Formulation (UWVF) of Maxw...

Article history: Received 27 January 2012 Received in revised form 3 October 2012 Accepted 16 January 2013 Available online 1 February 2013

A new two-dimensional panel technique has been developed to solve Laplacian flows, which eliminates the edge effect present in traditional panel methods. Such a method is very useful for applications where the velocity induced by the panels is required at arbitrary locations. Particle based flow solvers are a prime example. The method, however, requires considerably more computational effort. I...