吴开亮｜南方科技大学｜学者主页

2026

COS(DG): A convex oscillation-suppressing framework for high-order discontinuous Galerkin methods

Hui-Hui Cao, Yun-Qing Huang, Zhuo-Yun Li, Kailiang Wu

Journal of Computational Physics

DOI

2026

Structure of ENO Entropy Dissipation: Parity Dichotomy for the ENO--TV Conjecture and Shift Cohomology

Zhuo-Yun Li, Kailiang Wu

2026

High-order positivity-preserving and globally divergence-free discontinuous Galerkin methods for ideal magnetohydrodynamics with conditional energy conservation

Mengqing Liu, Kailiang Wu, Cai-You Yuan

Journal of Computational Physics

DOI

2026

Learning missing physics from legacy simulators with alternating neural integrators

Hao Wang, Qinghua Wang, Cai-You Yuan, Kailiang Wu

Nature Communications

DOI

2026

Robust and provably convergent primitive variable recovery for relativistic hydrodynamics with Synge-type equations of state

Jiahe Yue, Fangyue Du, Kailiang Wu

Journal of Computational Physics

DOI

2025

Positivity-preserving new low-dissipation central-upwind schemes for compressible Euler equations

Shu-Mo Cui, Yaguang Gu, A. Kurganov, Kailiang Wu, Ruixiao Xin

Journal of Computational Physics

DOI

2025

Spectral Volume from a Discontinuous Galerkin Perspective: Oscillation Elimination, Stability, and Optimal Error Estimates

Zhuo-Yun Li, Kailiang Wu

SIAM Journal on Scientific Computing

DOI

2025

Structure-preserving oscillation-eliminating discontinuous Galerkin schemes for ideal MHD equations: Locally divergence-free and positivity-preserving

Mengqing Liu, Kailiang Wu

Journal of Computational Physics

DOI

2025

Physical-Constraint-Preserving High-Order Finite Volume WENO Method Via Geometric Quasilinearization for Chaplygin Gas Dynamics

Lae Yin Win, Ya-Ping Chen, Yu-Feng Nie, Li Cai, Kailiang Wu

Journal of Scientific Computing

DOI

2025

DUE: A Deep Learning Framework and Library for Modeling Unknown Equations

Junfeng Chen, Kailiang Wu, Dong-Bin Xiu

SIAM Review

DOI

2024

High-order accurate positivity-preserving and well-balanced discontinuous Galerkin schemes for ten-moment Gaussian closure equations with source terms

Jiangfu Wang, Huazhong Tang, Kailiang Wu

Journal of Computational Physics

DOI

2024

Positional Knowledge is All You Need: Position-induced Transformer (PiT) for Operator Learning

Junfeng Chen, Kailiang Wu

International Conference on Machine Learning

DOI

2023

Critical Sampling for Robust Evolution Operator Learning of Unknown Dynamical Systems

Ce Zhang, Kailiang Wu, Zhi-Hai He

IEEE Transactions on Artificial Intelligence

DOI

2023

A new discretely divergence-free positivity-preserving high-order finite volume method for ideal MHD equations

Sheng-Rong Ding, Kailiang Wu

SIAM Journal on Scientific Computing

DOI

2023

Provably convergent Newton-Raphson methods for recovering primitive variables with applications to physical-constraint-preserving Hermite WENO schemes for relativistic hydrodynamics

Chao-Yi Cai, Jian-Xian Qiu, Kailiang Wu

Journal of Computational Physics

DOI

2023

Deep-OSG: Deep learning of operators in semigroup

Junfeng Chen, Kailiang Wu

Journal of Computational Physics

DOI

2023

On high order positivity-preserving well-balanced finite volume methods for the Euler equations with gravitation

Yupeng Ren, Kailiang Wu, Jian-Xian Qiu, Y. Xing

Journal of Computational Physics

DOI

2023

Provably Positive Central Discontinuous Galerkin Schemes via Geometric Quasilinearization for Ideal MHD Equations

Kailiang Wu, Haili Jiang, Chi-Wang Shu

SIAM Journal on Numerical Analysis

DOI

2022

On Energy Laws and Stability of Runge-Kutta Methods for Linear Seminegative Problems

Zheng Sun, Yuanzhen Wei, Kailiang Wu

SIAM Journal on Numerical Analysis

DOI

2022

High order asymptotic preserving finite difference WENO schemes with constrained transport for MHD equations in all sonic Mach numbers

Wei Chen, Kailiang Wu, Tao Xiong

Journal of Computational Physics

DOI

2022

Is the Classic Convex Decomposition Optimal for Bound-Preserving Schemes in Multiple Dimensions?

S. Cui, Sheng-Rong Ding, Kailiang Wu

Journal of Computational Physics

DOI

2022

A New Locally Divergence-Free Path-Conservative Central-Upwind Scheme for Ideal and Shallow Water Magnetohydrodynamics

Alina Chertock, A. Kurganov, Michael Redle, Kailiang Wu

SIAM Journal on Scientific Computing

DOI

2022

Positivity-preserving well-balanced central discontinuous Galerkin schemes for the Euler equations under gravitational fields

Haili Jiang, Hua-Zhong Tang, Kailiang Wu

Journal of Computational Physics

DOI

2022

On Optimal Cell Average Decomposition for High-Order Bound-Preserving Schemes of Hyperbolic Conservation Laws

S. Cui, Sheng-Rong Ding, Kailiang Wu

arXiv.org

DOI

2022

A Physical-Constraint-Preserving Finite Volume WENO Method for Special Relativistic Hydrodynamics on Unstructured Meshes

Ya-Ping Chen, Kailiang Wu

Journal of Computational Physics

DOI

2021

Minimum Principle on Specific Entropy and High-Order Accurate Invariant Region Preserving Numerical Methods for Relativistic Hydrodynamics

Kailiang Wu

SIAM Journal on Scientific Computing

DOI

2021

Geometric Quasilinearization Framework for Analysis and Design of Bound-Preserving Schemes

Kailiang Wu, Chi-Wang Shu

SIAM Review

DOI

2021

Deep Neural Network Modeling of Unknown Partial Differential Equations in Nodal Space

Zhen Chen, Victor Churchill, Kailiang Wu, Dong-Bin Xiu

Journal of Computational Physics

DOI

2021

A WENO-Based Stochastic Galerkin Scheme for Ideal MHD Equations with Random Inputs

Kailiang Wu

Communications in Computational Physics

DOI

2020

Uniformly High-Order Structure-Preserving Discontinuous Galerkin Methods for Euler Equations with Gravitation: Positivity and Well-Balancedness

Kailiang Wu, Y. Xing

SIAM Journal on Scientific Computing

DOI

2020

Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations

Kailiang Wu, Chi-Wang Shu

Numerische Mathematik

DOI

2020

Methods to Recover Unknown Processes in Partial Differential Equations Using Data

Zhen Chen, Kailiang Wu, Dong-Bin Xiu

Journal of Scientific Computing

DOI

2019

Sequential Approximation of Functions in Sobolev Spaces Using Random Samples

Kailiang Wu, Dong-Bin Xiu

Communication on Applied Mathematics and Computation

DOI

2019

Structure-preserving Method for Reconstructing Unknown Hamiltonian Systems from Trajectory Data

Kailiang Wu, Tong Qin, Dong-Bin Xiu

SIAM Journal on Scientific Computing

DOI

2019

Entropy Symmetrization and High-Order Accurate Entropy Stable Numerical Schemes for Relativistic MHD Equations

Kailiang Wu, Chi-Wang Shu

SIAM Journal on Scientific Computing

DOI

2019

Data-Driven Deep Learning of Partial Differential Equations in Modal Space

Kailiang Wu, Dong-Bin Xiu

Journal of Computational Physics

DOI

2018

Sequential function approximation with noisy data

Yeonjong Shin, Kailiang Wu, Dong-Bin Xiu

Journal of Computational Physics

DOI

2018

Provably positive high-order schemes for ideal magnetohydrodynamics: analysis on general meshes

Kailiang Wu, Chi-Wang Shu

Numerische Mathematik

DOI

2018

A Provably Positive Discontinuous Galerkin Method for Multidimensional Ideal Magnetohydrodynamics

Kailiang Wu, Chi-Wang Shu

SIAM Journal on Scientific Computing

DOI

2018

An Explicit Neural Network Construction for Piecewise Constant Function Approximation

Kailiang Wu, Dong-Bin Xiu

arXiv.org

2018

Numerical Aspects for Approximating Governing Equations Using Data

Kailiang Wu, Dong-Bin Xiu

Journal of Computational Physics

DOI

2018

Positivity-Preserving Analysis of Numerical Schemes for Ideal Magnetohydrodynamics

Kailiang Wu

SIAM Journal on Numerical Analysis

DOI

2018

Data Driven Governing Equations Approximation Using Deep Neural Networks

Tong Qin, Kailiang Wu, Dong-Bin Xiu

Journal of Computational Physics

DOI

2018

Sequential function approximation on arbitrarily distributed point sets

Kailiang Wu, Dong-Bin Xiu

Journal of Computational Physics

DOI

2017

A Randomized Tensor Quadrature Method for High Dimensional Polynomial Approximation

Kailiang Wu, Yeonjong Shin, Dong-Bin Xiu

SIAM Journal on Scientific Computing

DOI

2017

On physical-constraints-preserving schemes for special relativistic magnetohydrodynamics with a general equation of state

Kailiang Wu, Hua-Zhong Tang

Zeitschrift für Angewandte Mathematik und Physik

DOI

2016

A Direct Eulerian GRP Scheme for Spherically Symmetric General Relativistic Hydrodynamics

Kailiang Wu, Hua-Zhong Tang

SIAM Journal on Scientific Computing

DOI

2016

PHYSICAL-CONSTRAINT-PRESERVING CENTRAL DISCONTINUOUS GALERKIN METHODS FOR SPECIAL RELATIVISTIC HYDRODYNAMICS WITH A GENERAL EQUATION OF STATE

Kailiang Wu, Hua-Zhong Tang

DOI

2016

Admissible states and physical-constraints-preserving schemes for relativistic magnetohydrodynamic equations

Kailiang Wu, Hua-Zhong Tang

DOI

2016

トポグラフィーと乾燥地域を伴う定常浅水方程式のためのNewton多重格子法【Powered by NICT】

Kailiang Wu, Hua-Zhong Tang

2016

A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty

Kailiang Wu, Hua-Zhong Tang, Dong-Bin Xiu

Journal of Computational Physics

DOI

2016

Design of provably physical-constraint-preserving methods for general relativistic hydrodynamics

Kailiang Wu

DOI

2016

Physical-Constraints-Preserving Methods for General Relativistic Hydrodynamics: Theoretical Analysis

Kailiang Wu

2016

A Newton multigrid method for steady-state shallow water equations with topography and dry areas

Kailiang Wu, Hua-Zhong Tang

Applied Mathematics and Mechanics

DOI

2016

Runge-Kutta Discontinuous Local Evolution Galerkin Methods for the Shallow Water Equations on the Cubed-Sphere Grid

Yang-Yu Kuang, Kailiang Wu, Hua-Zhong Tang

DOI

2015

High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics

Kailiang Wu, Hua-Zhong Tang

Journal of Computational Physics

DOI

2014

Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics

Kailiang Wu, Hua-Zhong Tang

Journal of Computational Physics

DOI

2014

A Third-Order Accurate Direct Eulerian GRP Scheme for One-Dimensional Relativistic Hydrodynamics

Kailiang Wu, Zhicheng Yang, Hua-Zhong Tang

DOI

2014

A third-order accurate direct Eulerian GRP scheme for the Euler equations in gas dynamics

Kailiang Wu, Zhicheng Yang, Hua-Zhong Tang

Journal of Computational Physics

DOI

精选作品

期刊论文

COS(DG): A convex oscillation-suppressing framework for high-order discontinuous Galerkin methods

Structure of ENO Entropy Dissipation: Parity Dichotomy for the ENO--TV Conjecture and Shift Cohomology

High-order positivity-preserving and globally divergence-free discontinuous Galerkin methods for ideal magnetohydrodynamics with conditional energy conservation

Learning missing physics from legacy simulators with alternating neural integrators

Robust and provably convergent primitive variable recovery for relativistic hydrodynamics with Synge-type equations of state

Positivity-preserving new low-dissipation central-upwind schemes for compressible Euler equations

Spectral Volume from a Discontinuous Galerkin Perspective: Oscillation Elimination, Stability, and Optimal Error Estimates

Structure-preserving oscillation-eliminating discontinuous Galerkin schemes for ideal MHD equations: Locally divergence-free and positivity-preserving

Physical-Constraint-Preserving High-Order Finite Volume WENO Method Via Geometric Quasilinearization for Chaplygin Gas Dynamics

DUE: A Deep Learning Framework and Library for Modeling Unknown Equations

High-order accurate positivity-preserving and well-balanced discontinuous Galerkin schemes for ten-moment Gaussian closure equations with source terms

Positional Knowledge is All You Need: Position-induced Transformer (PiT) for Operator Learning

Critical Sampling for Robust Evolution Operator Learning of Unknown Dynamical Systems

A new discretely divergence-free positivity-preserving high-order finite volume method for ideal MHD equations

Provably convergent Newton-Raphson methods for recovering primitive variables with applications to physical-constraint-preserving Hermite WENO schemes for relativistic hydrodynamics

Deep-OSG: Deep learning of operators in semigroup

On high order positivity-preserving well-balanced finite volume methods for the Euler equations with gravitation

Provably Positive Central Discontinuous Galerkin Schemes via Geometric Quasilinearization for Ideal MHD Equations

On Energy Laws and Stability of Runge-Kutta Methods for Linear Seminegative Problems

High order asymptotic preserving finite difference WENO schemes with constrained transport for MHD equations in all sonic Mach numbers

Is the Classic Convex Decomposition Optimal for Bound-Preserving Schemes in Multiple Dimensions?

A New Locally Divergence-Free Path-Conservative Central-Upwind Scheme for Ideal and Shallow Water Magnetohydrodynamics

Positivity-preserving well-balanced central discontinuous Galerkin schemes for the Euler equations under gravitational fields

On Optimal Cell Average Decomposition for High-Order Bound-Preserving Schemes of Hyperbolic Conservation Laws

A Physical-Constraint-Preserving Finite Volume WENO Method for Special Relativistic Hydrodynamics on Unstructured Meshes

Minimum Principle on Specific Entropy and High-Order Accurate Invariant Region Preserving Numerical Methods for Relativistic Hydrodynamics

Geometric Quasilinearization Framework for Analysis and Design of Bound-Preserving Schemes

Deep Neural Network Modeling of Unknown Partial Differential Equations in Nodal Space

A WENO-Based Stochastic Galerkin Scheme for Ideal MHD Equations with Random Inputs

Uniformly High-Order Structure-Preserving Discontinuous Galerkin Methods for Euler Equations with Gravitation: Positivity and Well-Balancedness

Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations

Methods to Recover Unknown Processes in Partial Differential Equations Using Data

Sequential Approximation of Functions in Sobolev Spaces Using Random Samples

Structure-preserving Method for Reconstructing Unknown Hamiltonian Systems from Trajectory Data

Entropy Symmetrization and High-Order Accurate Entropy Stable Numerical Schemes for Relativistic MHD Equations

Data-Driven Deep Learning of Partial Differential Equations in Modal Space

Sequential function approximation with noisy data

Provably positive high-order schemes for ideal magnetohydrodynamics: analysis on general meshes

A Provably Positive Discontinuous Galerkin Method for Multidimensional Ideal Magnetohydrodynamics

An Explicit Neural Network Construction for Piecewise Constant Function Approximation

Numerical Aspects for Approximating Governing Equations Using Data

Positivity-Preserving Analysis of Numerical Schemes for Ideal Magnetohydrodynamics

Data Driven Governing Equations Approximation Using Deep Neural Networks

Sequential function approximation on arbitrarily distributed point sets

A Randomized Tensor Quadrature Method for High Dimensional Polynomial Approximation

On physical-constraints-preserving schemes for special relativistic magnetohydrodynamics with a general equation of state

A Direct Eulerian GRP Scheme for Spherically Symmetric General Relativistic Hydrodynamics

PHYSICAL-CONSTRAINT-PRESERVING CENTRAL DISCONTINUOUS GALERKIN METHODS FOR SPECIAL RELATIVISTIC HYDRODYNAMICS WITH A GENERAL EQUATION OF STATE

Admissible states and physical-constraints-preserving schemes for relativistic magnetohydrodynamic equations

トポグラフィーと乾燥地域を伴う定常浅水方程式のためのNewton多重格子法【Powered by NICT】

A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty

Design of provably physical-constraint-preserving methods for general relativistic hydrodynamics

Physical-Constraints-Preserving Methods for General Relativistic Hydrodynamics: Theoretical Analysis

A Newton multigrid method for steady-state shallow water equations with topography and dry areas

Runge-Kutta Discontinuous Local Evolution Galerkin Methods for the Shallow Water Equations on the Cubed-Sphere Grid

High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics

Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics

A Third-Order Accurate Direct Eulerian GRP Scheme for One-Dimensional Relativistic Hydrodynamics

A third-order accurate direct Eulerian GRP scheme for the Euler equations in gas dynamics