相关论文: Sparse grid implementation of a fixed-point fast s…

Finite-difference WENO schemes are capable of approximating accurately and efficiently weak solutions of hyperbolic conservation laws. In this context high order numerical boundary conditions have been proven to increase significantly the…

In this paper, we develop high-order, conservative, non-splitting Eulerian-Lagrangian (EL) Runge-Kutta (RK) finite volume (FV) weighted essentially non-oscillatory (WENO) schemes for convection-diffusion equations. The proposed…

As computational astrophysics comes under pressure to become a precision science, there is an increasing need to move to high accuracy schemes for computational astrophysics. Hence the need for a specialized review on higher order schemes…

A novel scheme, based on third-order Weighted Essentially Non-Oscillatory (WENO) reconstructions, is presented. It attains unconditionally optimal accuracy when the data is smooth enough, even in presence of critical points, and…

We propose a sparse grid stochastic collocation method for long-time simulations of stochastic differential equations (SDEs) driven by white noise. The method uses pre-determined sparse quadrature rules for the forcing term and constructs…

In \cite{christlieb2019kernel}, the authors developed a class of high-order numerical schemes for the Hamilton-Jacobi (H-J) equations, which are unconditionally stable, yet take the form of an explicit scheme. This paper extends such…

The present paper introduces a class of finite volume schemes of increasing order of accuracy in space and time for hyperbolic systems that are in conservation form. This paper specifically focuses on Euler system that is used for modeling…

This paper presents a fully multidimensional kernel-based reconstruction scheme for finite volume methods applied to systems of hyperbolic conservation laws, with a particular emphasis on the compressible Euler equations. Non-oscillatory…

In this article, we propose a modified convex combination of the polynomial reconstructions of odd-order WENO schemes to maintain the central substencil prevalence over the lateral ones in all parts of the solution. New "centered" versions…

We consider new implicit-explicit (IMEX) Runge-Kutta methods for hyperbolic systems of conservation laws with stiff relaxation terms. The explicit part is treated by a strong-stability-preserving (SSP) scheme, and the implicit part is…

In this paper, high order semi-implicit well-balanced and asymptotic preserving finite difference WENO schemes are proposed for the shallow water equations with a non-flat bottom topography. We consider the Froude number ranging from O(1)…

A novel central weighted essentially non-oscillatory (central WENO; CWENO)-type scheme for the construction of high-resolution approximations to discontinuous solutions to hyperbolic systems of conservation laws is presented. This procedure…

In this paper, we introduce an improved version of the fifth-order weighted essentially non-oscillatory (WENO) shock-capturing scheme by incorporating deep learning techniques. The established WENO algorithm is improved by training a…

In this paper, a maximum-principle-satisfying finite volume compact scheme is proposed for solving scalar hyperbolic conservation laws. The scheme combines WENO schemes (Weighted Essentially Non-Oscillatory) with a class of compact schemes…

Based on the understandings regarding linear upwind schemes with flux splitting to achieve free-stream preservation (Q. Li, etc. Commun. Comput. Phys., 22 (2017) 64-94), a series of WENO interpolation-based and upwind-biased nonlinear…

In this paper, we study the finite element operator network (FEONet), an operator-learning method for parametric problems, originally introduced in J. Y. Lee, S. Ko, and Y. Hong, Finite Element Operator Network for Solving Elliptic-Type…

We develop new adaptive alternative weighted essentially non-oscillatory (A-WENO) schemes for hyperbolic systems of conservation laws. The new schemes employ the recently proposed local characteristic decomposition based central-upwind…

Large sparse symmetric linear systems appear in several branches of science and engineering thanks to the widespread use of the finite element method (FEM). The fastest sparse linear solvers available implement hybrid iterative methods.…

The recently proposed high-order TENO scheme [Fu et al., Journal of Computational Physics, 305, pp.333-359] has shown great potential in predicting complex fluids owing to the novel weighting strategy, which ensures the high-order accuracy,…

We describe a newly developed cosmological hydrodynamics code based on the weighted essentially non-oscillatory (WENO) schemes for hyperbolic conservation laws. High order finite difference WENO schemes are designed for problems with…