Related papers: Notes on the Fast Multipole Method
A novel implementation of a charge based quantum computer is proposed. There is no charge transfer during calculation, therefore, uncontrollable entanglement between qubits due to long-range Coulomb forces is suppressed. High-speed…
We consider the two-dimensional two-component plasma, or Coulomb gas, consisting of $N$ positive and $N$ negative charges with logarithmic interaction. We introduce a suitable regularization of the interaction by smearing the charges over a…
The Fast Multipole Method (FMM) offers an acceleration for pairwise interaction calculation, known as $N$-body problems, from $\mathcal{O}(N^2)$ to $\mathcal{O}(N)$ with $N$ particles. This has brought dramatic increase in the capability of…
In an effort to increase spatial and temporal resolution of ultrafast electron diffraction and microscopy, ultra-high brightness photocathodes are actively sought to improve electron beam quality. Beam dynamics codes often approximate the…
We describe a technique to analytically compute the multipole moments of a charge distribution confined to a planar triangle, which may be useful in solving the Laplace equation using the fast multipole boundary element method (FMBEM) and…
The meshless/meshfree radial basis function (RBF) method is a powerful technique for interpolating scattered data. But, solving large RBF interpolation problems without fast summation methods is computationally expensive. For RBF…
Integral equation methods for solving the Laplace-Beltrami equation on the unit sphere in the presence of multiple "islands" are presented. The surface of the sphere is first mapped to a multiply-connected region in the complex plane via a…
We present a fast and accurate algorithm for the evaluation of nonlocal (long-range) Coulomb and dipole-dipole interactions in free space. The governing potential is simply the convolution of an interaction kernel $U(\bx)$ and a density…
The Fast Multipole Method (FMM) provides a highly efficient computational tool for solving constant coefficient partial differential equations (e.g. the Poisson equation) on infinite domains. The solution to such an equation is given as the…
Simulating charged many-body systems has been a computational demanding task due to the long-range nature of electrostatic interaction. For the multi-scale model of electrolytes which combines the strengths of atomistic/continuum…
We present a new, for plasma physics, highly efficient multilevel Monte Carlo numerical method for simulating Coulomb collisions. The method separates and optimally minimizes the finite-timestep and finite-sampling errors inherent in the…
We consider dynamically constrained Monte-Carlo dynamics and show that this leads to the generation of long ranged effective interactions. This allows us to construct a local algorithm for the simulation of charged systems without ever…
We present a new reciprocal space analytical method to cutoff the long range interactions in supercell calculations for systems that are infinite and periodic in 1 or 2 dimensions, extending previous works for finite systems. The proposed…
We consider two point charges in electrostatic interaction between them within the framework of a nonlinear model, associated with QED, that provides finiteness of their field energy. We argue that if the two charges are equal to each other…
Point multipole expansions are widely used to gain physical insight into complex distributions of charges and to reduce the cost of computing interactions between such distributions. However, practical applications that typically retain…
Density functional theory (DFT) calculations of charged molecules and surfaces are critical to applications in electro-catalysis, energy materials and related fields of materials science. DFT implementations such as the Vienna ab-initio…
Using the specific model of a system of like charged ions confined between two planar like charged surfaces, we compare the predictions for the energy and density profile of four simulation methods available to treat the long range Coulomb…
We investigate the coupling of the electromagnetic sources (charge and current densities) to the scalar and vector potentials in classical electrodynamics, using Green function techniques. As is well known, the scalar potential shows an…
We demonstrate a new, hybrid symbolic-numerical method for the automatic synthesis of all families of translation operators required for the execution of the Fast Multipole Method (FMM). Our method is applicable in any dimensionality and to…
Multipole representation is proposed for the anisotropic Coulomb interactions in solids. Any local interactions can be expressed as the product of two multipole operators, and the interaction parameters are systematically classified based…