~assuming the simulation box is cubic!, where qi and ri are the charge and position of particle i, L is the size of the simulation box, n5(n1 ,n2 ,n3), and the prime indicates that the i5 j terms are omitted when n50. The Ewald summation method has been widely used to handle the lattice sum in Eq. ~1!. In the method, the above-mentioned conditionally convergent series is written as a sum of a c...

The evaluation of sums (matrix-vector products) of the solutions of the three-dimensional biharmonic equation can be accelerated using the fast multipole method, while memory requirements can also be significantly reduced. We develop a complete translation theory for these equations. It is shown that translations of elementary solutions of the biharmonic equation can be achieved by considering ...

In this paper we present an implementation of the well known “fast multipole” method for the efficient calculation of dipole fields, that uses polynomials in the Cartesian coordinates rather than spherical harmonics. This has considerable efficiency and simplicity advantages. We have implemented it in the context of an arbitrary hierarchical system of cells – no periodic mesh is required. The i...

Despite its wide applicability in scientific computing, the linear time fast multipole method (FMM) with provable error bounds has not been used extensively in computer graphics. This paper presents – to our knowledge – the first application of FMM to the problem of global illumination. The light transport kernel is broken into multipole and local expansions and required transformations for the...

The transferability of atomic and functional group properties is an implicit concept in chemistry. The work presented here describes the use of Transferable Atom Equivalents (TAE) to represent molecular electrostatic potential fields through the use of integrated atomic multipole moments that are associated with each TAE atom type used in the reconstruction. TAE molecular surface distributions ...

A fast multipole formulation for 2D linear viscoelastic problems is presented in this paper by incorporating the elastic–viscoelastic correspondence principle. Systems of multipole expansion equations are formed and solved analytically in Laplace transform domain. Three commonly used viscoelastic models are introduced to characterize the time-dependent behavior of the materials. Since the trans...

In this work, we propose a novel and efficient solution for the generalized multipole technique (GMT): the localized iterative generalized multipole technique (LIGMT). In LIGMT, an analytic constraint is imposed on the power radiated by the set of multipole sources sharing the same origin, rendering it minimum over a given angular sector. In this way, the power radiated by each set of multipole...

Rapid evaluation of potentials in particle systems is an important, time-consuming step in many physical simulations. Over the past decade, the development of treecodes, such as the fast multipole method and Barnes–Hut method, has enabled large scale simulations in astrophysics, molecular dynamics, material science, etc. These methods use fixed-degree polynomial approximations of the potential ...

As graphics processors become powerful, ubiquitous and easier to program, they have also become more amenable to general purpose high-performance computing, including the computationally expensive task of drawing large graphs. This paper describes a new parallel analysis of the multipole method of graph drawing to support its efficient GPU implementation. We use a variation of the Fast Multipol...