A Finite Difference Method and Analysis for 2D Nonlinear Poisson-Boltzmann Equations. - Zhilin Li 002; C. V. Pao; Zhonghua Qiao (J. Sci. Comput., 2007)

A high order compact MAC finite difference scheme for the Stokes equations: Augmented variable approach. - Kazufumi Ito; Zhonghua Qiao (J. Comput. Phys., 2008)

A domain decomposition solver for acoustic scattering by elastic objects in layered media. - Kazufumi Ito; Zhonghua Qiao; Jari Toivanen (J. Comput. Phys., 2008)

Superconvergence and Extrapolation Analysis of a Nonconforming Mixed Finite Element Approximation for Time-Harmonic Maxwell's Equations. - Zhonghua Qiao; Changhui Yao; Shanghui Jia (J. Sci. Comput., 2011)

An Adaptive Time-Stepping Strategy for the Molecular Beam Epitaxy Models. - Zhonghua Qiao; Zhengru Zhang; Tao Tang 003 (SIAM J. Sci. Comput., 2011)

A Fast Preconditioned Iterative Algorithm for the Electromagnetic Scattering from a Large Cavity. - Chenliang Li; Zhonghua Qiao (J. Sci. Comput., 2012)

NRxx Simulation of Microflows with Shakhov Model. - Zhenning Cai; Ruo Li; Zhonghua Qiao (SIAM J. Sci. Comput., 2012)

An adaptive time-stepping strategy for solving the phase field crystal model. - Zhengru Zhang; Yuan Ma; Zhonghua Qiao (J. Comput. Phys., 2013)

C0-Nonconforming Triangular Prism Elements for the Three-Dimensional Fourth Order Elliptic Problem. - Hong-Ru Chen; Shao-Chun Chen; Zhonghua Qiao (J. Sci. Comput., 2013)

C0-nonconforming tetrahedral and cuboid elements for the three-dimensional fourth order elliptic problem. - Hong-Ru Chen; Shaochun Chen; Zhonghua Qiao (Numerische Mathematik, 2013)

Adaptive moving grid methods for two-phase flow in porous media. - Hao Dong; Zhonghua Qiao; Shuyu Sun 001; Tao Tang 003 (J. Comput. Appl. Math., 2014)

Two-Phase Fluid Simulation Using a Diffuse Interface Model with Peng-Robinson Equation of State. - Zhonghua Qiao; Shuyu Sun 001 (SIAM J. Sci. Comput., 2014)

Stability and convergence of second-order schemes for the nonlinear epitaxial growth model without slope selection. - Zhonghua Qiao; Zhi-Zhong Sun; Zhengru Zhang (Math. Comput., 2015)

Error Analysis of a Mixed Finite Element Method for the Molecular Beam Epitaxy Model. - Zhonghua Qiao; Tao Tang 003; Hehu Xie (SIAM J. Numer. Anal., 2015)

Modeling Pore-Scale Oil-Gas Systems Using Gradient Theory with Peng-Robinson Equation of State. - Xiaolin Fan; Jisheng Kou; Zhonghua Qiao; Shuyu Sun 001 (ICCS, 2016)

Acceleration for microflow simulations of high-order moment models by using lower-order model correction. - Zhicheng Hu; Ruo Li; Zhonghua Qiao (J. Comput. Phys., 2016)

Characterizing the Stabilization Size for Semi-Implicit Fourier-Spectral Method to Phase Field Equations. - Dong Li; Zhonghua Qiao; Tao Tang 003 (SIAM J. Numer. Anal., 2016)

On Second Order Semi-implicit Fourier Spectral Methods for 2D Cahn-Hilliard Equations. - Dong Li; Zhonghua Qiao (J. Sci. Comput., 2017)

Convergence of a Fast Explicit Operator Splitting Method for the Epitaxial Growth Model with Slope Selection. - Xiao Li; Zhonghua Qiao; Hui Zhang 021 (SIAM J. Numer. Anal., 2017)

A Componentwise Convex Splitting Scheme for Diffuse Interface Models with Van der Waals and Peng-Robinson Equations of State. - Xiaolin Fan; Jisheng Kou; Zhonghua Qiao; Shuyu Sun 001 (SIAM J. Sci. Comput., 2017)

Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation. - Qiang Du 001; Lili Ju; Xiao Li; Zhonghua Qiao (J. Comput. Phys., 2018)

Energy stability and error estimates of exponential time differencing schemes for the epitaxial growth model without slope selection. - Lili Ju; Xiao Li; Zhonghua Qiao; Hui Zhang 021 (Math. Comput., 2018)

A Third Order Exponential Time Differencing Numerical Scheme for No-Slope-Selection Epitaxial Thin Film Model with Energy Stability. - Kelong Cheng; Zhonghua Qiao; Cheng Wang 015 (J. Sci. Comput., 2019)

Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen-Cahn Equation. - Qiang Du 001; Lili Ju; Xiao Li; Zhonghua Qiao (SIAM J. Numer. Anal., 2019)

Unconditionally stable, efficient and robust numerical simulation of isothermal compositional grading by gravity. - Xiaolin Fan; Zhonghua Qiao; Shuyu Sun 001 (J. Comput. Sci., 2020)

Two-phase image segmentation by the Allen-Cahn equation and a nonlocal edge detection operator. - Zhonghua Qiao; Qian Zhang (CoRR, 2021)

Maximum bound principle preserving integrating factor Runge-Kutta methods for semilinear parabolic equations. - Lili Ju; Xiao Li; Zhonghua Qiao; Jiang Yang (J. Comput. Phys., 2021)

A Novel Lattice Boltzmann Model for Fourth Order Nonlinear Partial Differential Equations. - Zhonghua Qiao; Xuguang Yang; Yuze Zhang (J. Sci. Comput., 2021)

Convergence analysis for a stabilized linear semi-implicit numerical scheme for the nonlocal Cahn-Hilliard equation. - Xiao Li; Zhonghua Qiao; Cheng Wang 015 (Math. Comput., 2021)

Maximum Bound Principles for a Class of Semilinear Parabolic Equations and Exponential Time-Differencing Schemes. - Qiang Du 001; Lili Ju; Xiao Li; Zhonghua Qiao (SIAM Rev., 2021)

An Active Contour Model with Local Variance Force Term and Its Efficient Minimization Solver for Multi-phase Image Segmentation. - Chaoyu Liu; Zhonghua Qiao; Qian Zhang (CoRR, 2022)

Structure-preserving numerical method for Ampere-Nernst-Planck model. - Zhonghua Qiao; Zhenli Xu; Qian Yin; Shenggao Zhou (CoRR, 2022)

A linear adaptive BDF2 scheme for phase field crystal equation. - Dianming Hou; Zhonghua Qiao (CoRR, 2022)

Double stabilizations and convergence analysis of a second-order linear numerical scheme for the nonlocal Cahn-Hilliard equation. - Xiao Li; Zhonghua Qiao; Cheng Wang 015 (CoRR, 2022)

Energy stability and error estimates of a maximum bound principle preserving scheme for the dynamic Ginzburg-Landau equations of superconductivity. - Limin Ma; Zhonghua Qiao (CoRR, 2022)

Stabilized Exponential-SAV Schemes Preserving Energy Dissipation Law and Maximum Bound Principle for The Allen-Cahn Type Equations. - Lili Ju; Xiao Li; Zhonghua Qiao (J. Sci. Comput., 2022)

Two-Phase Segmentation for Intensity Inhomogeneous Images by the Allen-Cahn Local Binary Fitting Model. - Chaoyu Liu; Zhonghua Qiao; Qian Zhang (SIAM J. Sci. Comput., 2022)

Generalized SAV-Exponential Integrator Schemes for Allen-Cahn Type Gradient Flows. - Lili Ju; Xiao Li; Zhonghua Qiao (SIAM J. Numer. Anal., 2022)

Multi-phase image segmentation by the Allen-Cahn Chan-Vese model. - Chaoyu Liu; Zhonghua Qiao; Qian Zhang (Comput. Math. Appl., 2023)

Energy regularized models for logarithmic SPDEs and their numerical approximations. - Jianbo Cui; Dianming Hou; Zhonghua Qiao (CoRR, 2023)

Inverse Evolution Layers: Physics-informed Regularizers for Deep Neural Networks. - Chaoyu Liu; Zhonghua Qiao; Chao Li 031; Carola-Bibiane Schönlieb (CoRR, 2023)

Energy stable and maximum bound principle preserving schemes for the Q-tensor flow of liquid crystals. - Dianming Hou; Xiaoli Li 008; Zhonghua Qiao; Nan Zheng (CoRR, 2023)

Local Structure-Preserving Relaxation Method for Charged Systems on Unstructured Meshes. - Zhonghua Qiao; Zhenli Xu; Qian Yin; Shenggao Zhou (CoRR, 2023)

A linear doubly stabilized Crank-Nicolson scheme for the Allen-Cahn equation with a general mobility. - Dianming Hou; Zhonghua Qiao; Lili Ju (CoRR, 2023)

An Implicit-Explicit Second-Order BDF Numerical Scheme with Variable Steps for Gradient Flows. - Dianming Hou; Zhonghua Qiao (J. Sci. Comput., 2023)

Structure-preserving numerical method for Maxwell-Ampère Nernst-Planck model. - Zhonghua Qiao; Zhenli Xu; Qian Yin; Shenggao Zhou (J. Comput. Phys., 2023)

An Active Contour Model with Local Variance Force Term and Its Efficient Minimization Solver for Multiphase Image Segmentation. - Chaoyu Liu; Zhonghua Qiao; Qian Zhang (SIAM J. Imaging Sci., 2023)

An energy-stable Smoothed Particle Hydrodynamics discretization of the Navier-Stokes-Cahn-Hilliard model for incompressible two-phase flows. - Xiaoyu Feng; Zhonghua Qiao; Shuyu Sun 001; Xiuping Wang (J. Comput. Phys., 2023)

A Maxwell-Ampère Nernst-Planck Framework for Modeling Charge Dynamics. - Zhonghua Qiao; Zhenli Xu; Qian Yin; Shenggao Zhou (SIAM J. Appl. Math., 2023)

A linear second-order maximum bound principle-preserving BDF scheme for the Allen-Cahn equation with a general mobility. - Dianming Hou; Lili Ju; Zhonghua Qiao (Math. Comput., 2023)

An Energy Stable and Maximum Bound Principle Preserving Scheme for the Dynamic Ginzburg-Landau Equations under the Temporal Gauge. - Limin Ma; Zhonghua Qiao (SIAM J. Numer. Anal., 2023)

Global-in-time energy stability analysis for the exponential time differencing Runge-Kutta scheme for the phase field crystal equation. - Xiao Li; Zhonghua Qiao; Cheng Wang 015; Nan Zheng (CoRR, 2024)

Energy-Dissipative Spectral Renormalization Exponential Integrator Method for Gradient Flow Problems. - Dianming Hou; Lili Ju; Zhonghua Qiao (SIAM J. Sci. Comput., 2024)

Local Structure-Preserving Relaxation Method for Equilibrium of Charged Systems on Unstructured Meshes. - Zhonghua Qiao; Zhenli Xu; Qian Yin; Shenggao Zhou (SIAM J. Sci. Comput., 2024)

A Second-Order, Linear, ( boldsymbol{L^ infty} )-Convergent, and Energy Stable Scheme for the Phase Field Crystal Equation. - Xiao Li; Zhonghua Qiao (SIAM J. Sci. Comput., 2024)

An unconditionally energy stable linear scheme for Poisson-Nernst-Planck equations. - Tian Qiao; Zhonghua Qiao; Shuyu Sun 001; Shenggao Zhou (J. Comput. Appl. Math., 2024)

Curvature-Dependent Elastic Bending Total Variation Model for Image Inpainting with the SAV Algorithm. - Caixia Nan; Zhonghua Qiao; Qian Zhang (J. Sci. Comput., 2024)

Neural networks trained by weight permutation are universal approximators. - Yongqiang Cai; Gaohang Chen; Zhonghua Qiao (Neural Networks, 2025)

Energy Stable and Maximum Bound Principle Preserving Schemes for the ( boldsymbol {Q} )-Tensor Flow of Liquid Crystals. - Dianming Hou; Xiaoli Li 008; Zhonghua Qiao; Nan Zheng (SIAM J. Numer. Anal., 2025)

Inverse Evolution Layers: Physics-Informed Regularizers for Image Segmentation. - Chaoyu Liu; Zhonghua Qiao; Chao Li 031; Carola-Bibiane Schönlieb (SIAM J. Math. Data Sci., 2025)

Convergence analysis of SPH method on irregular particle distributions for the Poisson equation. - Zhonghua Qiao; Yifan Wei (CoRR, 2025)

Maximum Bound Principle and Bound Preserving ETD schemes for a Phase-Field Model of Tumor Growth with Extracellular Matrix Degradation. - Qiumei Huang; Zhonghua Qiao; Cheng Wang 015; Huiting Yang (CoRR, 2025)

Sidecar: A Structure-Preserving Framework for Solving Partial Differential Equations with Neural Networks. - Gaohang Chen; Zhonghua Qiao (CoRR, 2025)

Overcoming logarithmic singularities in the Cahn-Hilliard equation with Flory-Huggins potential: An unconditionally convergent ADMM approach. - Ruo Li; Shengtong Liang; Zhonghua Qiao (CoRR, 2025)

An Improved Shifted CholeskyQR Based on Columns. - Yuwei Fan; Haoran Guan; Zhonghua Qiao (J. Sci. Comput., 2025)