We present an implementation of the fast multipole method for computing Coulombic electrostatic and polarization forces from polarizable force-fields based on induced point dipole moments. We demonstrate the expected O(N) scaling of that approach by performing single energy point calculations on hexamer protein subunits of the mature HIV-1 capsid. We also show the long time energy conservation ...

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...

An Θ(n) parallel multigrid summation method for the N -body problem is presented. The method works with vacuum or periodic boundary conditions. It is based on a hierarchical decomposition of computational kernels on multiple grids. For low accuracy calculations, appropriate for molecular dynamics, a sequential implementation is faster than both Fast Multipole and Particle Mesh Ewald (PME). Its ...

In this paper, we present a fast multipole method (FMM) for the half-space Green’s function in a homogeneous elastic half-space subject to zero normal stress, for which an explicit solution was given by Mindlin (1936). The image structure of this Green’s function is unbounded, so that standard outgoing representations are not easily available. We introduce two such representations here, one inv...

This paper presents an empirical study of the accuracy of multipole expansions of Helmholtz-like kernels with complex wavenumbers of the form k = (α + iβ )θ , with α = 0,±1 and β > 0, which, the paucity of available studies notwithstanding, arise for a wealth of different physical problems. It is suggested that a simple point-wise error indicator can provide an a-priori indication on the number...

A rigorous three-dimensional (3-D) electromagnetic model is developed to analyze the scattering from anti-personnel (AP) nonmetallic mine-like target when it is buried near a clutter object under two-dimensional (2-D) random rough surfaces. The steepest descent fast multipole method (SDFMM) is implemented to solve for the unknown electric and magnetic surface currents on the ground surface, on ...

Many models in natural and social sciences are comprised of sets of interacting entities whose intensity of interaction decreases with distance. This often leads to structures of interest in these models composed of dense packs of entities. Fast Multipole Methods are a family of methods developed to help with the calculation of a number of computable models such as described above. We propose a...

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