The present paper intends to couple the Fast Multipole Method (FMM) with the Boundary Element Method (BEM) in 2D acoustic problems. The evaluation of the integrals involved in the governing Boundary Integral Equations (BIEs) is fasten by the FMM contribution. The multipole expansion and some suitable moment translations make the procedure much faster if compared to the conventional approach. Th...

We introduce a method for obtaining atomic point-charges that yield accurate representations of the electrostatic potentials (ESP) of large systems. The method relies on a decomposition of the density and subsequent projection of the multipole moments of the density components onto neighbouring atomic sites. The resulting local multipole-derived charges (LMDCs) are well-defined, do not require ...

A new charge analysis is presented that gives an accurate description of the electrostatic potential from the charge distribution in molecules. This is achieved in three steps: first, the total density is written as a sum of atomic densities; next, from these atomic densities a set of atomic multipoles is defined; finally, these atomic multipoles are reconstructed exactly by distributing charge...

In this letter we describe the pseudoparticle multipole method (PM), a new method to express multipole expansion by a distribution of pseudoparticles. We can use this distribution of particles to calculate high order terms in both the Barnes-Hut treecode and FMM. The primary advantage of PM is that it works on GRAPE. GRAPE is a special-purpose hardware for the calculation of gravitational force...

An implementation of the multilevel Fast Multipole method for time harmonic electromagnetic computations is presented. The method is parallelized for shared memory machines. A new parallelization scheme which is a hybrid between previous methods is proposed. Several symmetries and other methods that reduce the storage requirement are proposed. The most important symmetry is for the translation ...

In this paper we discuss the development and implementation of volumetric integral equations for both dielectric and magnetically permeable materials using curvilinear hexahedral elements. Both piecewise constant and higher order basis functions will be examined in the context of volumetric multilevel fast multipole method implementation. Comparisons with corresponding finite element– boundary ...

This paper introduces two techniques for approximating the Biot–Savart integral for deforming elliptical Gaussian functions. The primary motivation is to develop a high spatial accuracy vortex method. The first technique is a regular perturbation of the streamfunction in the small parameter = a−1 a+1 , where a2 is the aspect ratio of the basis function. This perturbative technique is suitable f...

A method for the simulation of discontinuities in photonic crystal defect waveguides is presented. This frequency domain technique is based on the multiple multipole method. In contrast with other known techniques, spurious reflections (due to the impedance mismatch at the waveguide terminations) are avoided. The absence of spurious reflections allows one to characterize precisely the intrinsic...

In this paper, we propose a novel method to extend the fast multipole method (FMM) to calculate the electrostatic potential due to charges inside or outside a dielectric sphere. The key result which allows such an extension is the construction of a small number (two for a 10 2 relative error in reaction potentials inside the sphere) of image point charges for source point charges inside or outs...