相关论文: An asymptotic preserving scheme for kinetic models…

We prove convergence of a class of space-time discontinuous Galerkin schemes for scalar hyperbolic conservation laws. Convergence to the unique entropy solution is shown for all orders of polynomial approximation, provided strictly monotone…

Non-reciprocal interactions are a generic feature of non-equilibrium systems. We define a non-reciprocal generalization of the kinetic Ising model in one spatial dimension. We solve the model exactly using two different approaches for…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

Curvilinear, multiblock summation-by-parts finite difference operators with the simultaneous approximation term method provide a stable and accurate framework for solving the wave equation in second order form. That said, the standard…

In this work, we present a modification of explicit Runge-Kutta temporal integration schemes that guarantees the preservation of any locally-defined quasiconvex set of bounds for the solution. These schemes operate on the basis of a…

In this paper, we develop a numerical method for the L\'evy-Fokker-Planck equation with the fractional diffusive scaling. There are two main challenges. One comes from a two-fold nonlocality, that is, the need to apply the fractional…

We present a method for solving a class of initial valued, coupled, non-linear differential equations with `moving singularities' subject to some subsidiary conditions. We show that this type of singularities can be adequately treated by…

The question is studied whether weak solutions of linear partial integrodifferential equations approach a constant spatial profile after rescaling, as time goes to infinity. The possible limits and corresponding scaling functions are…

The present work concerns the derivation of a numerical scheme to approximate weak solutions of the Euler equations with a gravitational source term. The designed scheme is proved to be fully well-balanced since it is able to exactly…

Time scale separation is a natural property of many control systems that can be ex- ploited, theoretically and numerically. We present a numerical scheme to solve optimal control problems with considerable time scale separation that is…

We investigate time complexities of finite difference methods for solving the multiscale transport equation with quantum algorithms. We find that the time complexities of both the classical treatment and quantum treatment for a standard…

We extend our two-scale neural-network method for scalar singularly perturbed problems with one small parameter to dynamical systems with multiple small parameters. To accommodate multiple small parameters, we use a single effective scale…

A new linear relaxation system for nonconservative hyperbolic systems is introduced, in which a nonlocal source term accounts for the nonconservative product of the original system. Using an asymptotic analysis the relaxation limit and its…

New asymptotic models are formulated to capture the thermal transfer across falling films. These models enable to simulate a wide range of Biot and Peclet number values, without displaying nonphysical behaviors. The models correctly capture…

We are interested in this work in the numerical resolution of the Quantum Liouville-BGK equation, which arises in the derivation of quantum hydrodynamical models from first principles. Such models are often obtained in some asymptotic…

A series of third- and fifth-order hybrid compact least-squares central weighted essentially non-oscillatory schemes are proposed and applied to curvilinear structured grids for the finite volume method. In smooth regions, compact…

In this paper, we study a time discrete scheme for the initial value problem of the ES-BGK kinetic equation. Numerically solving these equations are challenging due to the nonlinear stiff collision (source) terms induced by small mean free…

This paper deals with the numerical study of a nonlinear, strongly anisotropic heat equation. The use of standard schemes in this situation leads to poor results, due to the high anisotropy. An Asymptotic-Preserving method is introduced in…

In this work, we introduce a novel approach to formulating an artificial viscosity for shock capturing in nonlinear hyperbolic systems by utilizing the property that the solutions of hyperbolic conservation laws are not reversible in time…

In this paper we study structure-preserving numerical methods for low Mach number barotropic Euler equations. Besides their asymptotic preserving properties that are crucial in order to obtain uniformly consistent and stable approximations…