Related papers: A Conservative Finite Difference Scheme for Poisso…
Over the last two decades, the field of geometric curve evolutions has attracted significant attention from scientific computing. One of the most popular numerical methods for solving geometric flows is the so-called BGN scheme, which was…
The model reduction of a mesoscopic kinetic dynamics to a macroscopic continuum dynamics has been one of the fundamental questions in mathematical physics since Hilbert's time. In this paper, we consider a diagram of the diffusion limit…
In this study, we present a finite element solver for a thermodynamically consistent electrolyte model that accurately captures multicomponent ionic transport by incorporating key physical phenomena such as steric effects, solvation, and…
The numerical solution of a nonlinear and space-fractional anti-diffusive equation used to model dune morphodynamics is considered. Spatial discretization is effected using a finite element method whereas the Crank-Nicolson scheme is used…
In this paper, an energy-consistent finite difference scheme for the compressible hydrodynamic and magnetohydrodynamic (MHD) equations is introduced. For the compressible magnetohydrodynamics, an energy-consistent finite difference…
This paper presents a finite element method that preserves (at the degrees of freedom) the eigenvalue range of the solution of tensor-valued time-dependent convection--diffusion equations. Starting from a high-order spatial baseline…
A new methodology is developed to integrate numerically the equations of motion for classical many-body systems in molecular dynamics simulations. Its distinguishable feature is the possibility to preserve, independently on the size of the…
This paper proposes a meshless deep learning algorithm, enriched physics-informed neural networks (EPINNs), to solve dynamic Poisson-Nernst-Planck (PNP) equations with strong coupling and nonlinear characteristics. The EPINNs takes the…
In this paper, we consider a finite difference grid-based semi-Lagrangian approach in solving the Vlasov-Poisson (VP) system. Many of existing methods are based on dimensional splitting, which decouples the problem into solving linear…
The transport of charged particles, which can be described by the Maxwell-Ampere Nernst-Planck (MANP) framework, is essential in various applications including ion channels and semiconductors. We propose a decoupled structure-preserving…
The current study extends previous analytical and numerical solutions of chronopotentiometric response of one-dimensional systems consisting of three layers to the more realistic two-dimensional heterogeneous ion-permselective medium. An…
At mesoscopic scales electrolyte solutions are modeled by the fluctuating generalized Poisson-Nernst-Planck (PNP) equations [J.-P. P\'eraud et al., Phys. Rev. F, 1(7):074103, 2016]. However, at length and time scales larger than the Debye…
This paper presents a numerical framework for the low-rank approximation of the solution to three-dimensional parabolic problems. The key contribution of this work is the tensorization process based on a tensor-train reformulation of the…
In this paper, we design and analyze third order positivity-preserving discontinuous Galerkin (DG) schemes for solving the time-dependent system of Poisson--Nernst--Planck (PNP) equations, which has found much use in diverse applications.…
An efficient numerical scheme for solving transport equations for tokamak plasmas within an integrated modelling framework is presented. The plasma transport equations are formulated as diffusion-advection equations in two coordinates (a…
We propose a new class of finite element approximations to ideal compressible magnetohydrodynamic equations in smooth regime. Following variational approximations developed for fluid models in the last decade, our discretizations are built…
Characterizing the local voltage distribution within nanophysiological domains, driven by ionic currents through membrane channels, is crucial for studying cellular activity in modern biophysics, yet it presents significant experimental and…
This paper deals with the numerical solution of conservation laws in the two dimensional case using a novel compact implicit time discretization that enables applications of fast algebraic solvers. We present details for the second order…
Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…
We propose a new numerical approach to compute nonclassical solutions to hyperbolic conservation laws. The class of finite difference schemes presented here is fully conservative and keep nonclassical shock waves as sharp interfaces,…