On maximum-principle-satisfying high order schemes for scalar conservation laws. - Xiangxiong Zhang; Chi-Wang Shu (J. Comput. Phys., 2010)

On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes. - Xiangxiong Zhang; Chi-Wang Shu (J. Comput. Phys., 2010)

A Genuinely High Order Total Variation Diminishing Scheme for One-Dimensional Scalar Conservation Laws. - Xiangxiong Zhang; Chi-Wang Shu (SIAM J. Numer. Anal., 2010)

Positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations with source terms. - Xiangxiong Zhang; Chi-Wang Shu (J. Comput. Phys., 2011)

Robust high order discontinuous Galerkin schemes for two-dimensional gaseous detonations. - Cheng Wang; Xiangxiong Zhang; Chi-Wang Shu; Jianguo Ning (J. Comput. Phys., 2012)

Positivity-preserving high order finite difference WENO schemes for compressible Euler equations. - Xiangxiong Zhang; Chi-Wang Shu (J. Comput. Phys., 2012)

Maximum-Principle-Satisfying and Positivity-Preserving High Order Discontinuous Galerkin Schemes for Conservation Laws on Triangular Meshes. - Xiangxiong Zhang; Yinhua Xia; Chi-Wang Shu (J. Sci. Comput., 2012)

A minimum entropy principle of high order schemes for gas dynamics equations. - Xiangxiong Zhang; Chi-Wang Shu (Numerische Mathematik, 2012)

Maximum-principle-satisfying High Order Finite Volume Weighted Essentially Nonoscillatory Schemes for Convection-diffusion Equations. - Xiangxiong Zhang; Yuanyuan Liu; Chi-Wang Shu (SIAM J. Sci. Comput., 2012)

Maximum-principle-satisfying second order discontinuous Galerkin schemes for convection-diffusion equations on triangular meshes. - Yifan Zhang; Xiangxiong Zhang; Chi-Wang Shu (J. Comput. Phys., 2013)

Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for the Shallow Water Equations on Unstructured Triangular Meshes. - Yulong Xing; Xiangxiong Zhang (J. Sci. Comput., 2013)

Solving PhaseLift by Low-rank Riemannian Optimization Methods. - Wen Huang 001; Kyle A. Gallivan; Xiangxiong Zhang (ICCS, 2016)

A curved boundary treatment for discontinuous Galerkin schemes solving time dependent problems. - Xiangxiong Zhang (J. Comput. Phys., 2016)

Positivity-Preserving High Order Finite Volume HWENO Schemes for Compressible Euler Equations. - Xiaofeng Cai; Xiangxiong Zhang; Jianxian Qiu (J. Sci. Comput., 2016)

Eventual linear convergence of the Douglas-Rachford iteration for basis pursuit. - Laurent Demanet; Xiangxiong Zhang (Math. Comput., 2016)

On positivity-preserving high order discontinuous Galerkin schemes for compressible Navier-Stokes equations. - Xiangxiong Zhang (J. Comput. Phys., 2017)

On a Class of Implicit-Explicit Runge-Kutta Schemes for Stiff Kinetic Equations Preserving the Navier-Stokes Limit. - Jingwei Hu; Xiangxiong Zhang (J. Sci. Comput., 2017)

Solving PhaseLift by Low-Rank Riemannian Optimization Methods for Complex Semidefinite Constraints. - Wen Huang 001; Kyle A. Gallivan; Xiangxiong Zhang (SIAM J. Sci. Comput., 2017)

A positivity-preserving high order discontinuous Galerkin scheme for convection-diffusion equations. - Sashank Srinivasan; Jonathan Poggie; Xiangxiong Zhang (J. Comput. Phys., 2018)

Asymptotic-Preserving and Positivity-Preserving Implicit-Explicit Schemes for the Stiff BGK Equation. - Jingwei Hu; Ruiwen Shu; Xiangxiong Zhang (SIAM J. Numer. Anal., 2018)

A High Order Accurate Bound-Preserving Compact Finite Difference Scheme for Scalar Convection Diffusion Equations. - Hao Li; Shusen Xie; Xiangxiong Zhang (SIAM J. Numer. Anal., 2018)

On the monotonicity of high order discrete Laplacian. - Logan J. Cross; Xiangxiong Zhang (CoRR, 2020)

Superconvergence of C0-Qk Finite Element Method for Elliptic Equations with Approximated Coefficients. - Hao Li; Xiangxiong Zhang (J. Sci. Comput., 2020)

Superconvergence of High Order Finite Difference Schemes Based on Variational Formulation for Elliptic Equations. - Hao Li; Xiangxiong Zhang (J. Sci. Comput., 2020)

On the monotonicity and discrete maximum principle of the finite difference implementation of (C^0 ) - (Q^2 ) finite element method. - Hao Li; Xiangxiong Zhang (Numerische Mathematik, 2020)

Positivity-preserving and energy-dissipative finite difference schemes for the Fokker-Planck and Keller-Segel equations. - Jingwei Hu; Xiangxiong Zhang (CoRR, 2021)

Discrete Maximum principle of a high order finite difference scheme for a generalized Allen-Cahn equation. - Jie Shen 001; Xiangxiong Zhang (CoRR, 2021)

Positivity-preserving high order finite volume hybrid Hermite WENO schemes for compressible Navier-Stokes equations. - Chuan Fan; Xiangxiong Zhang; Jianxian Qiu (J. Comput. Phys., 2021)

A bound-preserving high order scheme for variable density incompressible Navier-Stokes equations. - Maojun Li; Yongping Cheng; Jie Shen 001; Xiangxiong Zhang (J. Comput. Phys., 2021)

Riemannian optimization using three different metrics for Hermitian PSD fixed-rank constraints: an extended version. - Shixin Zheng; Wen Huang; Bart Vandereycken; Xiangxiong Zhang (CoRR, 2022)

Positivity-preserving high order finite difference WENO schemes for compressible Navier-Stokes equations. - Chuan Fan; Xiangxiong Zhang; Jianxian Qiu (J. Comput. Phys., 2022)

Accuracy of Spectral Element Method for Wave, Parabolic, and Schrödinger Equations. - Hao Li; Daniel Appelö; Xiangxiong Zhang (SIAM J. Numer. Anal., 2022)

An efficient and robust SAV based algorithm for discrete gradient systems arising from optimizations. - Xinyu Liu; Jie Shen 001; Xiangxiong Zhang (CoRR, 2023)

Riemannian Langevin Monte Carlo schemes for sampling PSD matrices with fixed rank. - Tianmin Yu; Shixin Zheng; Jianfeng Lu 001; Govind Menon; Xiangxiong Zhang (CoRR, 2023)

A simple GPU implementation of spectral-element methods for solving 3D Poisson type equations on cartesian meshes. - Xinyu Liu; Jie Shen 001; Xiangxiong Zhang (CoRR, 2023)

On the monotonicity of Q2 spectral element method for Laplacian on quasi-uniform rectangular meshes. - Logan J. Cross; Xiangxiong Zhang (CoRR, 2023)

A high order accurate bound-preserving compact finite difference scheme for two-dimensional incompressible flow. - Hao Li; Xiangxiong Zhang (CoRR, 2023)

A monotone Q1 finite element method for anisotropic elliptic equations. - Hao Li; Xiangxiong Zhang (CoRR, 2023)

1D Model for the 3D Magnetohydrodynamics. - Mimi Dai; Bhakti Vyas; Xiangxiong Zhang (J. Nonlinear Sci., 2023)

An Efficient and Robust Scalar Auxialiary Variable Based Algorithm for Discrete Gradient Systems Arising from Optimizations. - Xinyu Liu; Jie Shen 001; Xiangxiong Zhang (SIAM J. Sci. Comput., 2023)

A positivity-preserving implicit-explicit scheme with high order polynomial basis for compressible Navier-Stokes equations. - Chen Liu 015; Xiangxiong Zhang (J. Comput. Phys., 2023)

Positivity and bound preserving well-balanced high order compact finite difference scheme for Ripa and pollutant transport model. - Baifen Ren; Bao-Shan Wang; Xiangxiong Zhang; Zhen Gao (Comput. Math. Appl., 2024)

On enforcing non-negativity in polynomial approximations in high dimensions. - Yuan Chen; Dongbin Xiu; Xiangxiong Zhang (CoRR, 2024)

An optimization based limiter for enforcing positivity in a semi-implicit discontinuous Galerkin scheme for compressible Navier-Stokes equations. - Chen Liu 015; Xiangxiong Zhang (CoRR, 2024)

Fully discretized Sobolev gradient flow for the Gross-Pitaevskii eigenvalue problem. - Ziang Chen; Jianfeng Lu 001; Yulong Lu; Xiangxiong Zhang (CoRR, 2024)

On the convergence of orthogonalization-free conjugate gradient method for extreme eigenvalues of Hermitian matrices: A Riemannian optimization interpretation. - Shixin Zheng; Haizhao Yang; Xiangxiong Zhang (J. Comput. Appl. Math., 2024)

An optimization based limiter for enforcing positivity in a semi-implicit discontinuous Galerkin scheme for compressible Navier-Stokes equations. - Chen Liu 015; Gregery T. Buzzard; Xiangxiong Zhang (J. Comput. Phys., 2024)

On the Convergence of Sobolev Gradient Flow for the Gross-Pitaevskii Eigenvalue Problem. - Ziang Chen; Jianfeng Lu 001; Yulong Lu; Xiangxiong Zhang (SIAM J. Numer. Anal., 2024)

A Simple and Efficient Convex Optimization Based Bound-Preserving High Order Accurate Limiter for Cahn-Hilliard-Navier-Stokes System. - Chen Liu 015; Beatrice Riviere; Jie Shen 001; Xiangxiong Zhang (SIAM J. Sci. Comput., 2024)

Structure Preserving Schemes for Fokker-Planck Equations of Irreversible Processes. - Chen Liu 015; Yuan Gao 004; Xiangxiong Zhang (J. Sci. Comput., 2024)

An optimization-based positivity-preserving limiter in semi-implicit discontinuous Galerkin schemes solving Fokker-Planck equations. - Chen Liu 015; Jingwei Hu; William T. Taitano; Xiangxiong Zhang (Comput. Math. Appl., 2025)

A bound-preserving Runge-Kutta discontinuous Galerkin method with compact stencils for hyperbolic conservation laws. - Chen Liu 015; Zheng Sun 004; Xiangxiong Zhang (J. Comput. Phys., 2025)

On Enforcing Nonnegativity in Polynomial Approximations in High Dimensions. - Yuan Chen; Dongbin Xiu; Xiangxiong Zhang (SIAM J. Sci. Comput., 2025)

Asymptotic Linear Convergence of ADMM for Isotropic TV Norm Compressed Sensing. - Emmanuel Gil Torres; Matt Jacobs; Xiangxiong Zhang (CoRR, 2025)

An Efficient Quasi-Newton Method with Tensor Product Implementation for Solving Quasi-Linear Elliptic Equations and Systems. - Wenrui Hao; Sun Lee; Xiangxiong Zhang (J. Sci. Comput., 2025)

Riemannian optimization using three different metrics for Hermitian PSD fixed-rank constraints. - Shixin Zheng; Wen Huang; Bart Vandereycken; Xiangxiong Zhang (Comput. Optim. Appl., 2025)