Related papers: A fast simple algorithm for computing the potentia…
We present a novel numerical method for solving the elliptic partial differential equation problem for the electrostatic potential with piecewise constant conductivity. We employ an integral equation approach for which we derive a system of…
We study the computation of equilibrium points of electrostatic potentials: locations in space where the electrostatic force arising from a collection of charged particles vanishes. This is a novel scenario of optimization in which…
This letter describes a method for obtaining an explicit expression for the electrostatic energy of a charged elliptical infinitely thin disc. The charge distribution is assumed to be polynomial. Such explicit values for this energy are…
An efficient real space method is derived for the evaluation of the Madelung's potential of ionic crystals. The proposed method is an extension of the Evjen's method. It takes advantage of a general analysis for the potential convergence in…
We present new efficient (O(N log N)) methods for computing three quantities crucial to electronic structure calculations: the ionic potential, the electron-ion contribution to the Born-Oppenheimer forces, and the electron-ion contribution…
In computational molecular science, calculation of electrostatic interactions involving charged atoms - the strongest interactions in condensed phases, is a major bottleneck. We propose a quantum-classical algorithm for fast, yet, accurate…
The evaluation of electrostatic energy for a set of point charges in a periodic lattice is a computationally expensive part of molecular dynamics simulations (and other applications) because of the long-range nature of the Coulomb…
Statistically studied are the equilibrium characteristics of a subsystem of mobile charges of one sort, taking into account the subsystem of fixed charges of the opposite sign creating a compensating electric background. The distribution of…
This is a survey of the electrostatic potentials produced by charged straight-line segments, in various numbers of spatial dimensions, with comparisons between uniformly charged segments and those having non-uniform linear charge…
We propose a simple linear scaling expression in reciprocal space for evaluating the ion--electron potential of crystalline solids. The expression replaces the long-range ion--electron potential with an equivalent localized charge…
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…
An algorithm for fast calculation of the Coulombic forces and energies of point particles with free boundary conditions is proposed. Its calculation time scales as N log N for N particles. This novel method has lower crossover point with…
A matrix algorithm is said to be superfast (that is, runs at sublinear cost) if it involves much fewer scalars and flops than the input matrix has entries. Such algorithms have been extensively studied and widely applied in modern…
We develop a systematic approach to calculating the electrostatic force between point charges in an arbitrary geometry with arbitrary boundary conditions. When the boundary is present, the simple expression for the force acting on a charge…
We apply the Charge Simulation Method (CSM) in order to compute the logarithmic capacity of compact sets consisting of (infinitely) many "small" components. This application allows to use just a single charge point for each component. The…
In article the following tasks on computer modeling of electric fields are analyzed: 1) calculation of distribution of potential for the field created by two parallel plates and charged bodies in the non-uniform environment; 2) calculation…
An efficient real space method is derived for the evaluation of the Madelung's potential of ionic crystals. The proposed method is an extension of the Evjen's method. It takes advantage of a general analysis for the potential convergence in…
We calculate the electrostatic potential of a periodic lattice of arbitrary extended charges by using the Cartesian multipole formalism. This method allows the separation of the long-range potential from the contact potential (potential on…
Equations describing the complete series of image charges for a system of conducting spheres are presented. The method of image charges, originally described by J. C. Maxwell in 1873, has been and continues to be a useful method for solving…
We calculate electrostatic potential landscapes for an external probe charge in the presence of a set of metallic islands. Our numerical calculation in three dimensions (3D)uses an efficient grid relaxation technique. The well-known…