相关论文: Efficient solution of Poisson's equation with free…
In this paper, He's frequency-amplitude formulation with some choice of location points that improve accuracy is applied to determine the periodic solution for the nonlinear oscillations of a punctual charge in the electric field of charged…
We solve Poisson's equation using new multigrid algorithms that converge rapidly. The novel feature of the 2D and 3D algorithms are the use of extra diagonal grids in the multigrid hierarchy for a much richer and effective communication…
Noise in initial conditions from measurement errors can create unwanted oscillations which propagate in numerical solutions. We present a technique of prohibiting such oscillation errors when solving initial-boundary-value problems of…
We present a novel efficient implementation of the flexible boundary condition (FBC) method, initially proposed by Sinclair et al., for large single-periodic problems. Efficiency is primarily achieved by constructing a hierarchical matrix…
We are interested in numerical algorithms for computing the electrical field generated by a charge distribution localized on scale $\ell$ in an infinite heterogeneous medium, in a situation where the medium is only known in a box of…
Over the last two decades, several fast, robust, and high-order accurate methods have been developed for solving the Poisson equation in complicated geometry using potential theory. In this approach, rather than discretizing the partial…
The density matrix renormalization group method for ladders works much more efficiently with open boundary conditions. One consequence of these boundary conditions is groundstate charge density oscillations that often appear to be nearly…
A collection of algorithms is described for numerically computing with smooth functions defined on the unit sphere. Functions are approximated to essentially machine precision by using a structure-preserving iterative variant of Gaussian…
We present a method for calculating the kinetic energy of localised functions represented on a regular real space grid. This method uses fast Fourier transforms applied to restricted regions commensurate with the simulation cell and is…
This paper is devoted to the efficient numerical solution of the Helmholtz equation in a two- or three-dimensional rectangular domain with an absorbing boundary condition (ABC). The Helmholtz problem is discretized by standard bilinear and…
In this paper, we propose a trigonometric-interpolation approach for solutions of second order nonlinear ODEs with mixed boundary conditions. The method interpolates secondary derivative $y''$ of a target solution $y$ by a trigonometric…
We present a fast algorithm for evaluating the (non-smooth) solution of the free-space two-dimensional (2D) scalar wave equation with many point sources, each with a high-frequency band-limited time signature. Such an algorithm is key to an…
We develop an efficient algorithm for a spatially inhomogeneous matrix-valued quantum Boltzmann equation derived from the Hubbard model. The distribution functions are $2 \times 2$ matrix-valued to accommodate the spin degree of freedom,…
The path-following scheme in [Loisel and Maxwell, SIAM J. Matrix Anal. Appl., 39-4 (2018), pp. 1726-1749] is adapted to efficiently calculate the dispersion relation curve for linear surface waves on an arbitrary vertical shear current.…
Poisson-Nernst-Planck equations are widely used to describe the electrodiffusion of ions in a solvated biomolecular system. Two kinds of two-grid finite element algorithms are proposed to decouple the steady-state Poisson-Nernst-Planck…
Vico et al. (2016) suggest a fast algorithm for computing volume potentials, beneficial to fields with problems requiring the solution of the free-space Poisson's equation, such as beam and plasma physics. Currently, the standard is the…
A method to compute the bound state eigenvalues and eigenfunctions of a Schr\"{o}dinger equation or a spinless Salpeter equation with central interaction is presented. This method is the generalization to the three-dimensional case of the…
We apply a type of background independent "polymer" quantization to a free scalar field in a flat spacetime. Using semi-classical states, we find an effective wave equation that is both nonlinear and Lorentz invariance violating. We solve…
We implement a well-established concept to consider dispersion effects within a Poisson-Boltzmann approach of continuum solvation of proteins. The theoretical framework is particularly suited for boundary element methods. Free parameters…
An accurate force calculation with the Poisson-Boltzmann equation is challenging, as it requires the electric field on the molecular surface. Here, we present a calculation of the electric field on the solute-solvent interface that is exact…