Related papers: Notes on the Fast Multipole Method
Molecular dynamics (MD) simulations of complex electrochemical systems, such as ionic liquid supercapacitors, are increasingly including the constant potential method (CPM) to model conductive electrodes at specified potential difference,…
A new scheme is presented for imposing periodic boundary conditions on unit cells with arbitrary source distributions. We restrict our attention here to the Poisson, modified Helmholtz, Stokes and modified Stokes equations. The approach…
This paper formalizes the use of integral and differential cumulants for measurements of multi-particle event-by-event transverse momentum fluctuations, rapidity fluctuations, as well as net charge fluctuations. This enables the…
A three-dimensional (3D) Poisson solver with longitudinal periodic and transverse open boundary conditions can have important applications in beam physics of particle accelerators. In this paper, we present a fast efficient method to solve…
The interaction of electrically charged particles in a dilute gas of point--like magnetic dipoles is studied. We show that the interaction potential at small distances has a linear piece due to overlap of the dipole clouds gathered near…
The fast multipole method (FMM) has received growing attention in the beam physics simulation. In this study, we formulate an interpolation-based FMM for the computation of the relativistic space-charge field. Different to the…
We present a technique to efficiently compute long-range interactions in systems with periodic boundary conditions. We extend the well-known Ewald method by using a linear combination of screening Gaussian charge distributions instead of…
It is shown that conserved charges associated with a specific subclass of gauge symmetries of Maxwell electrodynamics are proportional to the well known electric multipole moments. The symmetries are residual gauge transformations surviving…
The paper presents the algorithm of a code written for computing the cross section for a charge transfer process involving a neutral molecule and a monatomic ion. The entrance and exit potential energy surfaces, driving the collision…
This paper introduces a parallel directional fast multipole method (FMM) for solving N-body problems with highly oscillatory kernels, with a focus on the Helmholtz kernel in three dimensions. This class of oscillatory kernels requires a…
We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity, to counteract…
We present here a new algorithm for the fast computation of N-point correlation functions in large astronomical data sets. The algorithm is based on kdtrees which are decorated with cached sufficient statistics thus allowing for orders of…
We construct new algorithms from scratch, which use the fourth order cumulant of stochastic variables for the cost function. The multiplicative updating rule here constructed is natural from the homogeneous nature of the Lie group and has…
Calculating free energy differences is a topic of substantial interest and has many applications including molecular docking and hydration, solvation, and binding free energies which is used in computational drug discovery. However, in…
A field theoretic representation of the classical partition function is derived for a system composed of a mixture of anisotropic and isotropic mobile charges that interact {\sl via} long range Coulomb and short range nematic interactions.…
A formula for the corner charge in terms of the bulk quadrupole moment is derived for two-dimensional periodic systems. This is an analog of the formula for the surface charge density in terms of the bulk polarization. In the presence of an…
The use of effective local Coulomb interactions that are dynamical, that is, frequency-dependent, is an efficient tool to describe the effect of long-range Coulomb interactions and screening thereof in solids. The dynamical character of the…
The Barnes-Hut and Fast Multipole Methods are widely utilised methods applied in order to reduce the computational cost of evaluating long range forces in $N$-body simulations. Despite this, applying existing libraries to simple problems…
Pristine monolayer graphene exhibits very poor screening because the density of states vanishes at the Dirac point. As a result, charge relaxation is controlled by the effects of zero-point motion (rather than by the Coulomb interaction)…
This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some of the output variables are also input variables, linked by a linear dependency. Fundamental examples…