A method is developed here for doing multiple calculations of lattice sums when the lattice structure is kept fixed, while the molecular orientations or the molecules within the unit cells are altered. The approach involves a two-step process. In the first step, a multipole expansion is factored in such a way as to separate the geometry from the multipole moments. This factorization produces a ...

Vortex particle methods, when combined with multipole-accelerated boundary element methods (BEM), become a complete tool for direct numerical simulation (DNS) of internal or external vortex-dominated flows. In previous work, we presented a method to accelerate the vorticity-velocity inversion at the heart of vortex particle methods by performing a multipole treecode N-body method on parallel gr...

The purpose of this study is to investigate the acoustic performance of mufflers. As a numerical scheme for analyzing an acoustic filter, the boundary element method is more suitable than are domain methods, such as the finite element method, which has to mesh the domain. However, the coefficient matrices established by the boundary element method are full and often non-symmetrical. In order to...

This paper presents a number of algorithms to run the fast multipole method (FMM) on NVIDIA CUDAcapable graphical processing units (GPUs) (Nvidia Corporation, Sta. Clara, CA, USA). The FMM is a class of methods to compute pairwise interactions between N particles for a given error tolerance and with computational cost of O.N /. The methods described in the paper are applicable to any FMMs in wh...

In this paper, we consider acoustic or electromagnetic scattering in two dimensions from an infinite three-layer medium with thousands of wavelength-size dielectric particles embedded in the middle layer. Such geometries are typical of microstructured composite materials, and the evaluation of the scattered field requires a suitable fast solver for either a single configuration or for a sequenc...