2023

• Lack of robustness and accuracy of many numerical schemes for phase-field simulations

• Greedy training algorithms for neural networks and applications to PDEs

• Characterization of the Variation Spaces Corresponding to Shallow Neural Networks

• An Interpretive Constrained Linear Model for ResNet and MgNet

• FV-MgNet: Fully Connected V-cycle MgNet for Interpretable Time Series Forecasting

• An efficient iterative method for dynamical Ginzburg-Landau equations

• Integral boundary conditions in phase field models

2022

• Sharp Bounds on the Approximation Rates, Metric Entropy, and n-widths of Shallow Neural Networks

• Block triangular preconditioning for stochastic Galerkin method

• Uniform Approximation Rates and Metric Entropy of Shallow Neural Networks

• Approximation Properties of Deep ReLU CNNs

• ReLU Deep Neural Networks from the Hierarchical Basis Perspective

• CNNs with Compact Activation Function

• Extensible Structure-Informed Prediction of Formation Energy with Improved Accuracy and Usability employing Neural Networks

• High-Order Approximation Rates for Neural Networks with ReLU^k Activation Functions

• Extended Galerkin analysis in finite element exterior calculus

• Meta-MgNet: Meta multigrid networks forsSolving parameterized partial differential equation

• Optimal convergence rates for the orthogonal greedy algorithm

2021

• New discontinuous Galerkin algorithms and analysis for linear elasticity with symmetric stress tensor

• Helicity-Conservative Finite Element Discretization for MHD Systems

• Multiscale and Monolithic Arbitrary Lagrangian-Eulerian Finite Element Method for a Hemodynamic Fluid-structure Interaction Problem Involving Aneurysms

• Uniform Stability and Error Analysis for Some Discontinuous Galerkin Methods

• An Extended Galerkin Analysis for Elliptic Problems

2020

• Finite Neuron Method and Convergence Analysis

• Approximation rates for neural networks with general activation functions

• Make $\ell_1$ regularization effective in training sparse CNN

• High-order extended finite element methods for solving interface problems

• A mixed discontinuous Galerkin method for linear elasticity with strongly imposed symmetry

• ReLU Deep Neural Networks and linear Finite Elements

• An Extended Galerkin Analysis for Linear Elasticity with Strongly Symmetric Stress Tensor

• Robust preconditioners for poroelasticity

• Simplex-Averaged Finite Element Methods for (grad), (curl), and (div) Convection-Diffusion Problems

2019

• MgNet: A unified framework of multigrid and convolutional neural network

• Randomized and Fault-Tolerant Method of Subspace Corrections

• On the Stability and Accuracy of Partially and Fully Implicit Schemes for Phase Field Modeling

• New Hybridized Mixed Methods for Linear Elasticity and Optimal Multilevel Solvers

• Numerical Simulation of An Immersed Rotating Structure in Fluid for Hemodynamic Applications

• A Unified Study of Continuous and Discontinuous Galerkin Methods

• Nonconforming Finite Element Spaces for 2m-th Order Partial Differential Equations on R^n Simplicial Grids When m=n+1

• Structure-preserving Finite Element Methods for Stationary MHD Models

2018

• Numerical Simulation of An Immersed Rotating Structure in Fluid for Hemodynamic Applications

• Newton Solvers for Drift-Diffusion and Electrokinetic Equations

• On the stability and accuracy of partially and fully implicit schemes for phase field modeling

• New hybridized mixed methods for linear elasticity and optimal multilevel solvers

• A Unified Study of Continuous and Discontinuous Galerkin Methods

• Nonconforming Finite Element Spaces for 2m-th Order Partial Differential Equations on R^n Simplicial Grids When m=n+1

• Structure-preserving Finite Element Methods for Stationary MHD Models

2017

• Interior Penalty Mixed Finite Element Methods of Any Order in Any Dimension for Linear Elasticity with Strongly Symmetric Stress Tensor

2016

• Toward Cost-Effective Reservoir Simulation Solvers on GPUs

• A Robust Multigrid Method for Discontinuous Galerkin Discretizations of Stokes and Linear Elasticity Equations

• A Nearly Optimal Multigrid Method for General Unstructured Grids

• Modeling and Simulations for Fluid and Rotating Structure Interactions

• A Two-grid SA-AMG Convergence Bound that Improves When Increasing the Polynomial Degree

• Robust Preconditioners for Incompressible MHD Models

• Fast Multilevel Solvers for a Class of Discrete Fourth Order Parabolic Problems

• Multilevel Preconditioners for Reaction-Diffusion Problems with Discontinuous Coefficients

• Energetically Stable Discretizations for Charge Transport and Electrokinetic Models

2015

• A Cascadic Multigrid Algorithm for Computing the Fiedler Vector of Graph Laplacians

• On Robust and Efficient Parallel Reservoir Simulation on Tianhe-2

• Modeling Low Salinity Waterflooding in Mineralogically Different Carbonates

• Mechanistic Modeling of Wettability Alteration by Chemically Tuned Water Flooding in Carbonate Reservoirs

• A Multigrid Solver based on Distributive Smoother and Residual Overweighting for Oseen Problems

• Optimal Finite Element Methods for Interface Problems

• A Scalable Consistent Second-order SPH Solver for Unsteady Low Reynolds Number Flows

• Well-posedness and Robust Preconditioners For Discretized Fluid-structure Interaction Systems

2014

• Compositional Modeling of Reaction-Induced Injectivity Alteration During CO2 Flooding in Carbonate Reservoirs

• The Study on Hemodynamic Effect of Varied Support Models of BJUT-II VAD on Coronary Artery: A Primary CFD Study

• Lower Bounds of the Discretization Error for Piecewise Polynomials

• Optimal Solvers for Fourth-Order PDEs Discretized on Unstructured Grids

• Full Eulerian Finite Element Method of a Phase Field Model for Fluid-structure Interaction Problem

• Spatial Heterogeneity and Co-occurrence Patterns of Human Mucosal-associated Intestinal Microbiota

• Numerical Study of Geometric Multigrid on CPU--GPU Heterogenous Computers

• A Simple Preconditioner for a Discontinuous Galerkin Method for the Stokes Problem

2013

• An Auxiliary Space Preconditioner for the Black Oil Model and Its OpenMP Implemetation

• Application of Auxiliary Space Preconditioning in Field-Scale Reservoir Simulation

• Multilevel Preconditioners for a New Generation Reservoir Simulator

• The Single-Grid Multilevel Method and Its Applications

• Combined Preconditioning with Applications in Reservoir Simulation

• On Adaptive Eulerian-Lagrangian Method for Linear Convection-Diffusion Problems

• A Parallel Auxiliary Grid Algebraic Multigrid Method for Graphic Processing Units

• Comparative Convergence Analysis of Nonlinear AMLI-cycle Multigrid

• Application of An Energy-minimizing Algebraic Multigrid Method for Subsurface Water Simulations

• Convergence and Optimality of the Adaptive Nonconforming Linear Element Method for the Stokes Problem

• Minimal Finite Element Spaces for 2m-th-order Partial Differential Equations in R^n

• Two-grid Methods for Time-harmonic Maxwell Equations,

• Analysis of a two-level method for anisotropic diffusion equations on aligned and nonaligned grids

2012

• Local Multilevel Preconditioners for Elliptic Equations with Jump Coefficients on Bisection Grids

• A Discontinuous Galerkin Method for the Fourth-order Curl Problem

• Convergence of Numerical Analysis of V-cycle Multigrid Methods for Anisotropic Elliptic Equations

• Optimal Multilevel Methods for Graded Bisection Grids

• Fully Discrete Semi-Lagrangian Methods for Advection of Differential Forms

• Convergence and Optimality of the Adaptive Morley Element Methods

• Convergence and optimality of adaptive edge finite element methods for time-harmonic Maxwell equations

2011

• Robust Preconditioner for H(curl) Interface Problems

• Stable Finite Element Discretizations for Viscoelastic Flow Models

• Global Existence, Uniqueness and Optimal Solvers of Discretized Viscoelastic Flow Models

• New Mixed Finite Elements for Plane Elasticity and Stokes Equations

• Development of a Fast Auxiliary Subspace Preconditioner for Numerical Reservoir Simulators

• A Nonconforming Finite Element Method for Fourth Order Curl Equations in $\Bbb{R}^{3}$

• Effects of Integrations and Adaptivity for the Eulerian--Lagrangian Method

• New mixed finite elements for plane elasticity and Stokes equations

• Books of Peking University Modern Mathematics

• Proceedings of the 20th International Conference on Domain Decomposition Methods

• Numerical Methods for Non-Newtonian Fluids

• A Eulerian-Lagrangian method for MHD equations

2010

• A Combined Finite Element-Upwind Finite Volume Method for Liquid-Feed Direct Methanol Fuel Cell Simulations

• Fast Poisson-Based Solvers for Linear and Nonlinear PDEs

• Numerical Studies of Adaptive Finite Element Methods for Two Dimensional Convection-Dominated Problems

• A Generalization of The Vertex-centered Finite Volume Scheme to Arbitrary High Order

• Convergence of Adaptive Edge Finite Element Methods for ${\bf H}({\bf curl})$-elliptic Problems

2009

• Phase Field Model of Thermo-induced Marangoni Effects in the Mixtures and Its Numerical Simulations with Mixed Finite Element Method

• Numerical Solution to A Mixed Navier-Stokes/Darcy Model by the Two-grid Approach

• Preconditioning Techniques for A Mixed Stokes/Darcy Model in Porous Media Applications

• Convergence and Optimality of Adaptive Mixed Finite Element Methods

• Preface: Special Issue on Adaptive and Multilevel Methods in Computational Electromagnetics

• New Numerical Techniques for A Three-dimensional Liquid-feed Direct Methanol Fuel Cell Model

• A Domain Decomposition Method for Two-phase Transport Model in the Cathode of a Polymer Electrolyte Fuel Cell

• Auxiliary Space Preconditoners for Mixed Finite Element Methods

• Optimal Multilevel Methods for $H({\rm grad})$, $H({\rm curl})$, and $H({\rm div})$ Systems on Graded and Unstructured Grids

• Analysis of linear and quadratic simplicial finite volume methods for elliptic equations

• Optimal algorithms for discretized partial differential equations

• Optimal error estimates for Nedelec edge elements for time-harmonic Maxwell's equations

• Fast numerical simulation of two-phase transport model in the cathode of a polymer electrolyte fuel cell

2008

• A Combined Finite Element-Upwind Finite Volume-Newton's Method for Liquid-Feed Direct Methanol Fuel Cell Simulations

• Multilevel Preconditioning Methods for Discrete Models of Lattice Block Materials

• Auxiliary space preconditioning for edge elements

• Stability and accuracy of adapted finite element methods for singularly perturbed problems

• New estimates for the rate of convergence of the method of subspace corrections

• Convergence and optimal complexity of adaptive finite element eigenvalue computations

• Local and parallel finite element algorithms for the {S}tokes problem

• Superconvergence of quadratic finite elements on mildly structured grids

• A sharp convergence estimate for the method of subspace corrections for singular systems of equations

• Convergence analysis on iterative methods for semidefinite systems

• Uniformly-stable finite element methods for Darcy-Stokes-Brinkman models

• Uniform convergent multigrid methods for elliptic problems with strongly discontinuous coefficients

• Convergence of adaptive conforming and nonconforming finite element methods for the perturbed Stokes equation

• New adaptive finite volume methods and convergence analysis

2007

• Optimal anisotropic simplicial meshes for minimizing interpolation errors in ${L}^p$-norm

• Superconvergent derivative recovery for Lagrange triangular elements of degree $p$ on unstructured grids

• The finite element approximation of the nonlinear Poisson-Boltzmann equation

• Nodal auxiliary space preconditioning in ${\bf H}({\bf curl})$ and ${\bf H}({\rm div})$ spaces

• Robust subspace correction methods for nearly singular systems

• A two-grid method of a mixed Stokes-Darcy model for coupling fluid flow with porous media flow

• A new adaptive local mesh refinement algorithm and its application on fourth order thin film flow problem

• A new class of Zienkiewicz-type non-conforming element in any dimensions

• Some $n$-rectangle nonconforming elements for fourth order elliptic equations

M. Wang and Z.-C. Shi and J. Xu
J. Comput. Math.  25  408--420  (2007)

• Adaptive Computations: Theory and Algorithm

• Consistent piecewise polynomial approximation of $H^m(\Omega)$ functions in $R^n$ for any $0\leq m\leq n$

2006

• Nonconforming tetrahedral finite elements for fourth order elliptic equations

• An application of multigrid methods for a discrete elastic model for epitaxial systems

• Local and parallel finite element algorithms for the Navier-Stokes problem

• A two-grid discretization method for decoupling systems of partial differential equations

• On the convergence of iterative methods for semidefinite linear systems

• New Formulations, Positivity Preserving Discretizations and Stability Analysis for Non-Newtonian Flow Models

• An algebraic multigrid method for higher-order finite element discretizations

• An algebraic multigrid method for finite element systems on criss-cross grids

• A toy model for testing finite element methods to simulate extreme-mass-ratio binary systems

• The Morley element for fourth order elliptic equations in any dimensions

• Modified Morley element method for a fourth elliptic singular perturbation problem

• On the well-posedness of a mathematical model for lithium-ion battery systems

• Extending the applicability of multigrid methods

• Algebraic Multigrid Methods and Preconditioned Conjugate Gradient Algorithm for Lattice Block Materials Models

2005

• Partition of unity method on nonmatching grids for the Stokes problem

• Asymptotically Optimal and Linear-time Algorithm for Polygonal Curve Simplification

• Measuring single cardiac myocyte contractile force via moving a magnetic bead

• Multilevel homotopic adaptive finite element methods for convection dominated problems

• An optimal streamline diffusion finite element method for a singularly perturbed problem

2004

• Uniformly convergent multigrid methods for convection-diffusion problems without any constraint on coarse grids

• Analysis of recovery type a posteriori error estimators for mildly structured grids

• Optimal Delaunay triangulations

• On an energy minimizing basis for algebraic multigrid methods

• Proceedings of the 15th International Conference on Domain Decomposition Methods

2003

• Regularity estimates for elliptic boundary value problems in Besov spaces

• Regularity estimates for elliptic boundary value problems with smooth data on polygonal domains

• Asymptotically exact a posteriori error estimators. I. Grids with superconvergence

• Asymptotically exact a posteriori error estimators. II. General unstructured grids

• A conforming finite element method for overlapping and nonmatching grids

• A multigrid method based on graph matching for convection-diffusion equations

• Successive subspace correction method for singular system of equations

• Some observations on Babuska and Brezzi theories

• Partition of Unity Method for Stokes Problem on Nonmatching Grids

• AMG and construction of coarse grids and related stuff

2002

• Algebraic multigrid method on lattice block materials

• Rate of convergence for parallel subspace correction methods for nonlinear variational inequalities

• Newton-Krylov-multigrid algorithms for battery simulation

• Local and parallel finite element algorithms for eigenvalue problems

• Some multiscale methods for partial differential equations

• The method of alternating projections and the method of subspace corrections in Hilbert space

• Recent Progress in Computational and Applied PDEs,

2001

• Global and uniform convergence of subspace correction methods for some convex optimization problems

• Local and parallel finite element algorithms based on two-grid discretizations for nonlinear problems

• Convergence of an explicit upwind finite element method to multi-dimensional conservation laws

2000

• The method of subspace corrections

• A finite element multigrid preconditioner for Chebyshev-collocation method

• Local and parallel finite element algorithms based on two-grid discretizations

1999

• A two-grid discretization scheme for eigenvalue problems

• A partition-of-unity finite element method for elliptic problems with highly oscillating coefficients

• On a Schur complement operator arisen from Navier-Stokes equations and its preconditioning

• Subspace correction methods for convex optimization problems

• A crosswind block iterative method for convection-dominated problems

• Some local and parallel properties of finite element discretizations

• A monotone finite element scheme for convection-diffusion equations

• A special volume on multilevel methods

1998

• An agglomeration multigrid method for unstructured grids

• A study of incorporating the multigrid method into the three-dimensional finite element discretization: a modular setting of grid generation and application

• Some nonoverlapping domain decomposition methods

1997

• The EAFE scheme and CWS method for Convection Dominated Problems

• Preconditioning the Poincaré-Steklov operator by using Green's function

• An Introdution to Multilevel Method

1996

• An Introdution to Multigrid Convergence Theory

• An algorithm for coarsening unstructured meshes

• The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grids

• Two-grid discretization techniques for linear and nonlinear PDEs

• Numerical Methods in Applied Sciences

1995

• A hierarchical basis multigrid method for unstructured grids

• Error estimates on a new nonlinear Galerkin method based on two-grid finite elements

1994

• The hierarchical basis multigrid method and incomplete LU decomposition

• Some remarks on a multigrid preconditioner

• A novel two-grid method for semilinear elliptic equations

• Some two-grid finite element methods

• Proceedings of Seventh International Conference on Domain Decomposition Methods

1992

• A New class of iterative methods for nonselfadjoint or indefinite problems

• A preconditioned GMRES method for nonsymmetric or indefinite problems

• Galerkin-wavelet methods for two-point boundary value problems

• Iterative methods by space decomposition and subspace correction

• Iterative methods by SPD and small subspace solvers for nonsymmetric or indefinite problems

• A multilevel preconditioner for domain decomposition boundary systems

1991

• Convergence estimates for multigrid algorithms without regularity assumptions

• Convergence estimates for product iterative methods with applications to domain decomposition

• The analysis of multigrid algorithms with nonnested spaces or noninherited quadratic forms

• Some estimates for a weighted $L^2$ projection

• Counterexamples concerning a weighted $L^2$ projection

1990

• Convergence estimates for some multigrid algorithms

• Parallel multilevel preconditioners

1989

• Superconvergence of the gradient in piecewise linear finite-element approximation to a parabolic problem

• Theory of multilevel methods

1988

• A local post-processing technique for improving the accuracy in mixed finite-element approximations

• The analysis of multigrid algorithms for nonsymmetric and indefinite elliptic problems

• The analysis and improvement on infinite element algorithms

• The error analysis and the improved algorithms for the infinite element method

1986

• Analysis and improvement of algorithms for the infinite element method

1985

• Linear finite elements with high accuracy

1984

• Some inequalities in Sobolev space and finite and infinite elements on polygonal domains

1982

• Estimate of the Convergence Rate of the Finite element Solutions to Elliptic Equation of Second Order with Discontinuous Coefficients