相关论文: Efficient solution of Poisson's equation with free…
Accurate free-energy estimation is essential in molecular simulation, yet the periodic boundary conditions (PBC) commonly used in computer simulations have rarely been explicitly exploited. Equilibrium methods such as umbrella sampling,…
The boundary integral method is an efficient approach for solving time-harmonic obstacle scattering problems by a bounded scatterer. This paper presents the directional preconditioner for the iterative solution of linear systems of the…
In this paper we apply a scaling invariance analysis to reduce a class of parabolic moving boundary problems to free boundary problems governed by ordinary differential equations. As well known free boundary problems are always non-linear…
We apply boundary integral equations for the first time to the two-dimensional scattering of time-harmonic waves from a smooth obstacle embedded in a continuously-graded unbounded medium. In the case we solve the square of the wavenumber…
Flow-based generative models can face significant challenges when modeling scientific data with multiscale Fourier spectra, often producing large errors in fine-scale features. We address this problem within the framework of stochastic…
We consider a hyperbolic free boundary problem by means of minimizing time discretized functionals of Crank-Nicolson type. The feature of this functional is that it enjoys energy conservation in the absence of free boundaries, which is an…
We present an implementation of range separated functionals utilizing the Slater-function on grids in real space in the projector augmented waves method. The screened Poisson equation is solved to evaluate the necessary screened exchange…
High-dimensional Partial Differential Equations (PDEs) are a popular mathematical modelling tool, with applications ranging from finance to computational chemistry. However, standard numerical techniques for solving these PDEs are typically…
The problem of the one dimensional electro-diffusion of ions in a strong binary electrolyte is considered. In such a system the solute dissociates completely into two species of ions with unlike charges. The mathematical description…
Time-resolved electronic spectra can be obtained as the Fourier transform of a special type of time correlation function known as fidelity amplitude, which, in turn, can be evaluated approximately and efficiently with the dephasing…
This work considers charged systems described by the modified Poisson--Nernst--Planck (PNP) equations, which incorporate ionic steric effects and the Born solvation energy for dielectric inhomogeneity. Solving the steady-state modified PNP…
We propose a non grid-based interpolation scheme based on the information from the data collected from the vicinity of the query point. As a non-grid-based interpolation, the data points can be distributed randomly in a small region, and…
An efficient method is proposed for numerical solutions of nonlinear Schr\"{o}dinger equations in an unbounded domain. Through approximating the kinetic energy term by a one-way equation and uniting it with the potential energy equation,…
We study the transmission problem in bounded domains with dissipative boundary conditions. Under some natural assumptions, we prove uniform bounds of the corresponding resolvents on the real axis at high frequency, and as a consequence, we…
The semi-geostrophic system is widely used in the modelling of large-scale atmospheric flows. In this paper, we prove existence of solutions of the incompressible semi-geostrophic equations in a fully three-dimensional domain with a free…
We describe a new approach to compute the electron-phonon self-energy and carrier mobilities in semiconductors. Our implementation does not require a localized basis set to interpolate the electron-phonon matrix elements, with the advantage…
A simple technique is proposed for numerically determining equilibrium ion distribution functions belonging to free energies of the Poisson-Boltzmann type. The central idea is to perform a conventional Monte-Carlo simulation using the free…
We study the homogenization of a stochastic Schr\"odinger equation with a large periodic potential in solid state physics. Denoting by $\varepsilon$ the period, the potential is scaled as $\varepsilon^{-2}$. Under a generic assumption on…
A model for ionic and electronic grain boundary transport through thin films, scales or membranes with columnar grain structure is introduced. The grain structure is idealized as a lattice of identical hexagonal cells - a honeycomb pattern.…
We outline a remarkably efficient method for generating solutions to quantum anharmonic oscillators with an x^{2M} potential. We solve the Schroedinger equation in terms of a free parameter which is then tuned to give the correct boundary…