相关论文: Locally Order-Preserving Mapping for WENO Methods
Object proposal is essential for current state-of-the-art object detection pipelines. However, the existing proposal methods generally fail in producing results with satisfying localization accuracy. The case is even worse for small objects…
High-order gas-kinetic scheme (HGKS) has been well-developed in the past years. Abundant numerical tests including hypersonic flow, turbulence, and aeroacoustic problems, have been used to validate its accuracy, efficiency, and robustness.…
This paper establishes the minimum entropy principle (MEP) for the relativistic Euler equations with a broad class of equations of state (EOSs) and addresses the challenge of preserving the local version of the discovered MEP in high-order…
High order reconstruction in the finite volume (FV) approach is achieved by a more fundamental form of the fifth order WENO reconstruction in the framework of orthogonally-curvilinear coordinates, for solving the hyperbolic conservation…
Higher order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes for conservation laws are extremely popular because, for multidimensional problems, they offer high order accuracy at a fraction of the cost of finite volume…
In this paper, we combine the nonlinear HWENO reconstruction in \cite{newhwenozq} and the fixed-point iteration with Gauss-Seidel fast sweeping strategy, to solve the static Hamilton-Jacobi equations in a novel HWENO framework recently…
ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes are widely used high-order schemes for solving partial differential equations (PDEs), especially hyperbolic conservation laws with piecewise smooth…
This paper is devoted to the convergence and stability analysis of a class of nonlinear subdivision schemes and associated multi-resolution transforms. These schemes are defined as a perturbation of a linear subdivision scheme. Assuming a…
Finite element based simulation of phenomena governed by partial differential equations is a standard tool in many engineering workflows today. However, the simulation of complex geometries is computationally expensive. Many engineering…
Third order WENO and CWENO reconstruction are widespread high order reconstruction techniques for numerical schemes for hyperbolic conservation and balance laws. In their definition, there appears a small positive parameter, usually called…
A new, high-order slope-limiting procedure for the Piecewise Parabolic Method (PPM) and the Piecewise Quartic Method (PQM) is described. Following a Weighted Essentially Non-Oscillatory (WENO)-type paradigm, the proposed slope-limiter seeks…
This paper is concerned with high-order numerical methods for hyperbolic systems of balance laws. Such methods are typically based on high-order piecewise polynomial reconstructions (interpolations) of the computed discrete quantities.…
The aim of the present paper is to provide a comparison between several finite-volume methods of different numerical accuracy: second-order Godunov method with PPM interpolation and high-order finite-volume WENO method. The results show…
In this paper, we propose a well-balanced fifth-order finite difference Hermite WENO (HWENO) scheme for the shallow water equations with non-flat bottom topography in pre-balanced form. For achieving the well-balance property, we adopt the…
Context. Several numerical problems require the interpolation of discrete data that present various types of discontinuities. The radiative transfer is a typical example of such a problem. This calls for high-order well-behaved techniques…
In this paper, we propose a novel approximation strategy for time-dependent hyperbolic systems of conservation laws for the Euler system of gas dynamics that aims to represent the dynamics of strong interacting discontinuities. The goal of…
Deep learning models excel in stationary data but struggle in non-stationary environments due to a phenomenon known as loss of plasticity (LoP), the degradation of their ability to learn in the future. This work presents a first-principles…
In this paper, a high-order moment-based multi-resolution Hermite weighted essentially non-oscillatory (HWENO) scheme is designed for hyperbolic conservation laws. The main idea of this scheme is derived from our previous work [J. Comput.…
Change detection, i.e., anomaly detection from local maps built by a mobile robot at multiple different times, is a challenging problem to solve in practice. Most previous work either cannot be applied to scenarios where the size of the map…
We present a new perspective on the use of weighted essentially nonoscillatory (WENO) reconstructions in high-order methods for scalar hyperbolic conservation laws. The main focus of this work is on nonlinear stabilization of continuous…