相关论文: An Explicitly Solvable Energy-Conserving Algorithm…

In this paper, we study the problem of computing the effective diffusivity for particles moving in chaotic flows. Instead of solving a convection-diffusion type cell problem in the Eulerian formulation (arising from homogenization theory…

This paper presents applications of weighted meshless scheme for conservation laws to the Euler equations and the equations of ideal magnetohydrodynamics. The divergence constraint of the latter is maintained to the truncation error by a…

Machine learning models are changing the paradigm of molecular modeling, which is a fundamental tool for material science, chemistry, and computational biology. Of particular interest is the inter-atomic potential energy surface (PES). Here…

This paper develops entropy stable (ES) adaptive moving mesh schemes for the 2D and 3D special relativistic hydrodynamic (RHD) equations. They are built on the ES finite volume approximation of the RHD equations in curvilinear coordinates,…

We are interested in the numerical approximation of non-linear stochastic differential equations (SDEs) with solution in a certain domain. Our goal is to construct explicit numerical schemes that preserve that structure. We generalize the…

In recent years, there has been a large increase in interest in numerical algorithms which preserve various qualitative features of the original continuous problem. Herein, we propose and investigate a numerical algorithm which preserves…

We have obtained the solutions of linearized Shr{\"o}dinger equation for spherically and axially symmetrical electrons density oscillations in plasma in the approximation of the self-consistent field. It was shown that in the center or on…

In this work, we derive particle schemes, based on micro-macro decomposition, for linear kinetic equations in the diffusion limit. Due to the particle approximation of the micro part, a splitting between the transport and the collision part…

The present paper is devoted to the convergence analysis of a class of asymptotic preserving particle schemes [Filbet \& Rodrigues, SIAM J. Numer. Anal., 54 (2) (2016)] for the Vlasov equation with a strong external magnetic field. In this…

Given a stochastic differential equation (SDE) in $\mathbb{R}^n$ whose solution is constrained to lie in some manifold $M \subset \mathbb{R}^n$, we propose a class of numerical schemes for the SDE whose iterates remain close to $M$ to high…

Maintaining conservation laws in the fully discrete setting is critical for accurate long-time behavior of numerical simulations and requires accounting for discrete conservation properties in both space and time. This paper derives…

The computation of the dominant eigenpair for symmetric positive semidefinite matrices is fundamental in numerical optimization. This work shifts the paradigm from the classical Rayleigh quotient to an unconstrained difference formulation,…

This paper presents an asymptotic preserving (AP) all Mach number finite volume shock capturing method for the numerical solution of compressible Euler equations of gas dynamics. Both isentropic and full Euler equations are considered. The…

To construct positivity-preserving numerical methods, a vast majority of existing works employ transformation techniques such as the Lamperti transformation or logarithmic transformation. However, using these techniques often leads to the…

We present a boundary integral formulation of electromagnetic scattering by homogeneous bodies that are characterized by linear constitutive equations in the frequency domain. By working with the Cartesian components of the electric, E and…

In this paper, we propose and analyze semi-implicit numerical schemes for the stochastic wave equation (SWE) with general nonlinearity and multiplicative noise. These numerical schemes, called stochastic scalar auxiliary variable (SAV)…

Astrophysical plasmas are subject to a tight connection between magnetic fields and the diffusion of particles, which leads to an anisotropic transport of energy. Under the fluid assumption, this effect can be reduced to an…

For Hamiltonian systems, simulation algorithms that exactly conserve numerical energy or pseudo-energy have seen extensive investigation. Most available methods either require the iterative solution of nonlinear algebraic equations at each…

In this work we consider a stochastic differential equation (SDEs) with jump. We prove the existence and the uniqueness of solution of this equation in the strong sense under global Lipschitz condition. Generally, exact solutions of SDEs…

In this paper we consider the spatial semi-discretization of conservative PDEs. Such finite dimensional approximations of infinite dimensional dynamical systems can be described as flows in suitable matrix spaces, which in turn leads to the…