Jinchao Xu

Found. Comput. Math., April, 2024

Convergence Analysis and Trajectory Comparison of Gradient Descent for Overparameterized Deep Linear Networks.

[BibT_eX]

[DOI]

Hongru Zhao

Trans. Mach. Learn. Res., 2024

A unified-field monolithic fictitious domain-finite element method for fluid-structure-contact interactions and applications to deterministic lateral displacement problems.

[BibT_eX]

[DOI]

J. Comput. Phys., 2024

Service capability aware big data workflow scheduling approach in cloud datacentre.

[BibT_eX]

[DOI]

Jie Cao

Bo Wang

Int. J. Intell. Syst. Technol. Appl., 2024

Approximation Rates for Shallow ReLUk Neural Networks on Sobolev Spaces via the Radon Transform.

[BibT_eX]

[DOI]

Tong Mao

CoRR, 2024

Randomized greedy algorithms for neural network optimization.

[BibT_eX]

[DOI]

Jongho Park

Xiaofeng Xu

CoRR, 2024

AceGPT, Localizing Large Language Models in Arabic.

[BibT_eX]

[DOI]

Proceedings of the 2024 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long Papers), 2024

MgNO: Efficient Parameterization of Linear Operators via Multigrid.

[BibT_eX]

[DOI]

Xinliang Liu

Proceedings of the Twelfth International Conference on Learning Representations, 2024

2023

Fabrication and optimization of passive flexible ammonia sensor for aquatic supply chain monitoring based on adaptive parameter adjustment artificial neural network (APA-ANN).

[BibT_eX]

[DOI]

Comput. Electron. Agric., September, 2023

Greedy training algorithms for neural networks and applications to PDEs.

[BibT_eX]

[DOI]

J. Comput. Phys., July, 2023

Robust BPX preconditioner for fractional Laplacians on bounded Lipschitz domains.

[BibT_eX]

[DOI]

Juan Pablo Borthagaray

Ricardo H. Nochetto

Math. Comput., June, 2023

An interpretive constrained linear model for ResNet and MgNet.

[BibT_eX]

[DOI]

Neural Networks, May, 2023

FV-MgNet: Fully connected V-cycle MgNet for interpretable time series forecasting.

[BibT_eX]

[DOI]

J. Comput. Sci., May, 2023

Integral boundary conditions in phase field models.

[BibT_eX]

[DOI]

Comput. Math. Appl., April, 2023

An efficient iterative method for dynamical Ginzburg-Landau equations.

[BibT_eX]

[DOI]

J. Comput. Phys., February, 2023

Expressivity and Approximation Properties of Deep Neural Networks with ReLUk Activation.

[BibT_eX]

[DOI]

Tong Mao

CoRR, 2023

Deep Neural Networks and Finite Elements of Any Order on Arbitrary Dimensions.

[BibT_eX]

[DOI]

CoRR, 2023

AceGPT, Localizing Large Language Models in Arabic.

[BibT_eX]

[DOI]

CoRR, 2023

DualFL: A Duality-based Federated Learning Algorithm with Communication Acceleration in the General Convex Regime.

[BibT_eX]

[DOI]

Jongho Park

CoRR, 2023

2022

Optimal Convergence Rates for the Orthogonal Greedy Algorithm.

[BibT_eX]

[DOI]

IEEE Trans. Inf. Theory, 2022

An extended Galerkin analysis in finite element exterior calculus.

[BibT_eX]

[DOI]

Yuwen Li

Math. Comput., 2022

Meta-MgNet: Meta multigrid networks for solving parameterized partial differential equations.

[BibT_eX]

[DOI]

Yuyan Chen

Bin Dong

J. Comput. Phys., 2022

Block triangular preconditioning for stochastic Galerkin method.

[BibT_eX]

[DOI]

J. Comput. Appl. Math., 2022

A neuron-wise subspace correction method for the finite neuron method.

[BibT_eX]

[DOI]

Jongho Park

Xiaofeng Xu

CoRR, 2022

On the Activation Function Dependence of the Spectral Bias of Neural Networks.

[BibT_eX]

[DOI]

CoRR, 2022

A sharp Korn's inequality for piecewise H1 space and its application.

[BibT_eX]

[DOI]

YounJu Lee

CoRR, 2022

An efficient iterative method for dynamical Ginzburg-Landau equations.

[BibT_eX]

[DOI]

Limin Ma

CoRR, 2022

ReLU deep neural networks from the hierarchical basis perspective.

[BibT_eX]

[DOI]

Lin Li

Comput. Math. Appl., 2022

CNNs with Compact Activation Function.

[BibT_eX]

[DOI]

Jindong Wang

Jianqing Zhu

Proceedings of the Computational Science - ICCS 2022, 2022

2021

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

[BibT_eX]

[DOI]

Numerische Mathematik, 2021

Helicity-conservative finite element discretization for incompressible MHD systems.

[BibT_eX]

[DOI]

Young-Ju Lee

J. Comput. Phys., 2021

Multiscale and monolithic arbitrary Lagrangian-Eulerian finite element method for a hemodynamic fluid-structure interaction problem involving aneurysms.

[BibT_eX]

[DOI]

J. Comput. Phys., 2021

A reliability-aware scheduling algorithm for parallel task executing on cloud computing system.

[BibT_eX]

[DOI]

Int. J. Intell. Syst. Technol. Appl., 2021

Approximation Properties of Deep ReLU CNNs.

[BibT_eX]

[DOI]

Lin Li

CoRR, 2021

An efficient greedy training algorithm for neural networks and applications in PDEs.

[BibT_eX]

[DOI]

CoRR, 2021

Characterization of the Variation Spaces Corresponding to Shallow Neural Networks.

[BibT_eX]

[DOI]

CoRR, 2021

Improved Convergence Rates for the Orthogonal Greedy Algorithm.

[BibT_eX]

[DOI]

CoRR, 2021

Robust BPX preconditioner for the integral fractional Laplacian on bounded domains.

[BibT_eX]

[DOI]

Juan Pablo Borthagaray

Ricardo H. Nochetto

CoRR, 2021

Optimal Approximation Rates and Metric Entropy of ReLU$^k$ and Cosine Networks.

[BibT_eX]

[DOI]

CoRR, 2021

2020

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

[BibT_eX]

[DOI]

SIAM J. Numer. Anal., 2020

Approximation rates for neural networks with general activation functions.

[BibT_eX]

[DOI]

Neural Networks, 2020

A Mixed Discontinuous Galerkin Method for Linear Elasticity with Strongly Imposed Symmetry.

[BibT_eX]

[DOI]

Fei Wang

J. Sci. Comput., 2020

High-Order Approximation Rates for Neural Networks with ReLUk Activation Functions.

[BibT_eX]

[DOI]

CoRR, 2020

The Finite Neuron Method and Convergence Analysis.

[BibT_eX]

[DOI]

CoRR, 2020

Training Sparse Neural Networks using Compressed Sensing.

[BibT_eX]

[DOI]

Jianhong Chen

CoRR, 2020

Helicity-conservative finite element discretization for MHD systems.

[BibT_eX]

[DOI]

Young-Ju Lee

CoRR, 2020

An Abstract Stabilization Method with Applications to Nonlinear Incompressible Elasticity.

[BibT_eX]

[DOI]

Chunmei Liu

CoRR, 2020

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

[BibT_eX]

[DOI]

CoRR, 2020

Robust block preconditioners for poroelasticity.

[BibT_eX]

[DOI]

CoRR, 2020

Make ℓ 1 regularization effective in training sparse CNN.

[BibT_eX]

[DOI]

Comput. Optim. Appl., 2020

2019

Generalized Gaffney inequality and discrete compactness for discrete differential forms.

[BibT_eX]

[DOI]

Numerische Mathematik, 2019

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

[BibT_eX]

[DOI]

Shihua Gong

Numerische Mathematik, 2019

Nonconforming finite element spaces for 2mth order partial differential equations on ℝn simplicial grids when m=n+1.

[BibT_eX]

[DOI]

Math. Comput., 2019

Structure-preserving finite element methods for stationary MHD models.

[BibT_eX]

[DOI]

Math. Comput., 2019

Numerical simulation of an immersed rotating structure in fluid for hemodynamic applications.

[BibT_eX]

[DOI]

J. Comput. Sci., 2019

Constrained Linear Data-feature Mapping for Image Classification.

[BibT_eX]

[DOI]

Yuyan Chen

CoRR, 2019

A machine learning method correlating pulse pressure wave data with pregnancy.

[BibT_eX]

[DOI]

CoRR, 2019

Extended Galerkin Method.

[BibT_eX]

[DOI]

CoRR, 2019

On the Approximation Properties of Neural Networks.

[BibT_eX]

[DOI]

CoRR, 2019

MgNet: A Unified Framework of Multigrid and Convolutional Neural Network.

[BibT_eX]

[DOI]

CoRR, 2019

2018

Newton Solvers for Drift-Diffusion and Electrokinetic Equations.

[BibT_eX]

[DOI]

SIAM J. Sci. Comput., 2018

Modified Regularized Dual Averaging Method for Training Sparse Convolutional Neural Networks.

[BibT_eX]

[DOI]

CoRR, 2018

ALE Method for a Rotating Structure Immersed in the Fluid and Its Application to the Artificial Heart Pump in Hemodynamics.

[BibT_eX]

[DOI]

Proceedings of the Computational Science - ICCS 2018, 2018

2017

Stable finite element methods preserving $\nabla \cdot \varvec{B}=0$ exactly for MHD models.

[BibT_eX]

[DOI]

Yicong Ma

Numerische Mathematik, 2017

Multiphase Allen-Cahn and Cahn-Hilliard models and their discretizations with the effect of pairwise surface tensions.

[BibT_eX]

[DOI]

J. Comput. Phys., 2017

Analytical decoupling techniques for fully implicit reservoir simulation.

[BibT_eX]

[DOI]

J. Comput. Phys., 2017

Numerical studies of a class of linear solvers for fine-scale petroleum reservoir simulation.

[BibT_eX]

[DOI]

Comput. Vis. Sci., 2017

An error-resilient redundant subspace correction method.

[BibT_eX]

[DOI]

Tao Cui

Chen-Song Zhang

Comput. Vis. Sci., 2017

Algebraic multigrid methods.

[BibT_eX]

[DOI]

Acta Numer., 2017

2016

A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations.

[BibT_eX]

[DOI]

Numerische Mathematik, 2016

A nearly optimal multigrid method for general unstructured grids.

[BibT_eX]

[DOI]

Lars Grasedyck

Lu Wang

Numerische Mathematik, 2016

A two-grid SA-AMG convergence bound that improves when increasing the polynomial degree.

[BibT_eX]

[DOI]

Xiaozhe Hu

Panayot S. Vassilevski

Numer. Linear Algebra Appl., 2016

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

[BibT_eX]

[DOI]

J. Sci. Comput., 2016

Multilevel Preconditioners for Reaction-Diffusion Problems with Discontinuous Coefficients.

[BibT_eX]

[DOI]

Tzanio V. Kolev

Yunrong Zhu

J. Sci. Comput., 2016

Energetically stable discretizations for charge transport and electrokinetic models.

[BibT_eX]

[DOI]

Maximilian S. Metti

Chun Liu

J. Comput. Phys., 2016

Robust preconditioners for incompressible MHD models.

[BibT_eX]

[DOI]

J. Comput. Phys., 2016

2014

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

[BibT_eX]

[DOI]

Shuo Zhang

SIAM J. Numer. Anal., 2014

Lower bounds of the discretization error for piecewise polynomials.

[BibT_eX]

[DOI]

Qun Lin

Hehu Xie

Math. Comput., 2014

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

[BibT_eX]

[DOI]

J. Sci. Comput., 2014

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

[BibT_eX]

[DOI]

J. Sci. Comput., 2014

2013

Equidistribution and Optimal Approximation Class.

[BibT_eX]

[DOI]

Constantin Bacuta

Proceedings of the Domain Decomposition Methods in Science and Engineering XX, 2013

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

[BibT_eX]

[DOI]

SIAM J. Sci. Comput., 2013

Comparative Convergence Analysis of Nonlinear AMLI-Cycle Multigrid.

[BibT_eX]

[DOI]

Xiaozhe Hu

Panayot S. Vassilevski

SIAM J. Numer. Anal., 2013

Two-grid methods for time-harmonic Maxwell equations.

[BibT_eX]

[DOI]

Numer. Linear Algebra Appl., 2013

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

[BibT_eX]

[DOI]

Guozhu Yu

Numer. Linear Algebra Appl., 2013

Minimal finite element spaces for 2m-th-order partial differential equations in Rn.

[BibT_eX]

[DOI]

Ming Wang

Math. Comput., 2013

Combined Preconditioning with Applications in Reservoir Simulation.

[BibT_eX]

[DOI]

Multiscale Model. Simul., 2013

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

[BibT_eX]

[DOI]

Jun Hu

J. Sci. Comput., 2013

The online monitoring system software design and the SOC estimation algorithm research for power battery.

[BibT_eX]

[DOI]

Zhiping Wang

Tun Wang

Proceedings of the IEEE International Conference on Vehicular Electronics and Safety, 2013

2012

Convergence and optimality of the adaptive Morley element method.

[BibT_eX]

[DOI]

Jun Hu

Zhongci Shi

Numerische Mathematik, 2012

Optimal multilevel methods for graded bisection grids.

[BibT_eX]

[DOI]

Ricardo H. Nochetto

Numerische Mathematik, 2012

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

[BibT_eX]

[DOI]

Math. Comput., 2012

Numerical Study of Geometric Multigrid Methods on CPU--GPU Heterogeneous Computers

[BibT_eX]

[DOI]

CoRR, 2012

Local multilevel preconditioners for elliptic equations with jump coefficients on bisection grids.

[BibT_eX]

[DOI]

Comput. Vis. Sci., 2012

Norms of Discrete Trace Functions of H¹(Ω) and H2(Ω).

[BibT_eX]

[DOI]

Shuo Zhang

Comput. Methods Appl. Math., 2012

2011

A nonconforming finite element method for fourth order curl equations in R3.

[BibT_eX]

[DOI]

Bin Zheng

Qiya Hu

Math. Comput., 2011

2010

Convergence of adaptive edge finite element methods for H(curl)-elliptic problems.

[BibT_eX]

[DOI]

Numer. Linear Algebra Appl., 2010

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

[BibT_eX]

[DOI]

Pengtao Sun

J. Sci. Comput., 2010

A generalization of the vertex-centered finite volume scheme to arbitrary high order.

[BibT_eX]

[DOI]

Andreas Vogel

Gabriel Wittum

Comput. Vis. Sci., 2010

A Software Watermarking Algorithm Based on Stack-State Transition Graph.

[BibT_eX]

[DOI]

Guosun Zeng

Proceedings of the Fourth International Conference on Network and System Security, 2010

2009

Numerical Solution to a Mixed Navier-Stokes/Darcy Model by the Two-Grid Approach.

[BibT_eX]

[DOI]

Mingchao Cai

Mo Mu

SIAM J. Numer. Anal., 2009

New Numerical Techniques for a Three-Dimensional Liquid-Feed Direct Methanol Fuel Cell Model.

[BibT_eX]

[DOI]

SIAM J. Appl. Math., 2009

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

[BibT_eX]

[DOI]

Qingsong Zou

Numerische Mathematik, 2009

Convergence and optimality of adaptive mixed finite element methods.

[BibT_eX]

[DOI]

Michael J. Holst

Math. Comput., 2009

A domain decomposition method for two-phase transport model in the cathode of a polymer electrolyte fuel cell.

[BibT_eX]

[DOI]

J. Comput. Phys., 2009

Preconditioning techniques for a mixed Stokes/Darcy model in porous media applications.

[BibT_eX]

[DOI]

Mingchao Cai

Mo Mu

J. Comput. Appl. Math., 2009

2008

Multilevel Preconditioning Methods for Discrete Models of Lattice Block Materials.

[BibT_eX]

[DOI]

SIAM J. Sci. Comput., 2008

Local and parallel finite element algorithms for the stokes problem.

[BibT_eX]

[DOI]

Numerische Mathematik, 2008

Convergence and optimal complexity of adaptive finite element eigenvalue computations.

[BibT_eX]

[DOI]

Xiaoying Dai

Numerische Mathematik, 2008

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

[BibT_eX]

[DOI]

Numerische Mathematik, 2008

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

[BibT_eX]

[DOI]

Math. Comput., 2008

Superconvergence of quadratic finite elements on mildly structured grids.

[BibT_eX]

[DOI]

Yunqing Huang

Math. Comput., 2008

2007

A Two-Grid Method of a Mixed Stokes-Darcy Model for Coupling Fluid Flow with Porous Media Flow.

[BibT_eX]

[DOI]

Mo Mu

SIAM J. Numer. Anal., 2007

Nodal Auxiliary Space Preconditioning in H(curl) and H(div) Spaces.

[BibT_eX]

[DOI]

Ralf Hiptmair

SIAM J. Numer. Anal., 2007

The Finite Element Approximation of the Nonlinear Poisson-Boltzmann Equation.

[BibT_eX]

[DOI]

Michael J. Holst

SIAM J. Numer. Anal., 2007

Superconvergent Derivative Recovery for Lagrange Triangular Elements of Degree p on Unstructured Grids.

[BibT_eX]

[DOI]

Randolph E. Bank

Bin Zheng

SIAM J. Numer. Anal., 2007

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

[BibT_eX]

[DOI]

Ming Wang

Zhongci Shi

Numerische Mathematik, 2007

Nonconforming tetrahedral finite elements for fourth order elliptic equations.

[BibT_eX]

[DOI]

Wang Ming

Math. Comput., 2007

Optimal anisotropic meshes for minimizing interpolation errors in Lp-norm.

[BibT_eX]

[DOI]

Pengtao Sun

Math. Comput., 2007

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

[BibT_eX]

[DOI]

Pengtao Sun

Robert D. Russell

J. Comput. Phys., 2007

2006

On the Convergence of Iterative Methods for Semidefinite Linear Systems.

[BibT_eX]

[DOI]

SIAM J. Matrix Anal. Appl., 2006

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

[BibT_eX]

[DOI]

Wang Ming

Numerische Mathematik, 2006

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

[BibT_eX]

[DOI]

Jicheng Jin

Shi Shu

Math. Comput., 2006

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

[BibT_eX]

[DOI]

J. Comput. Phys., 2006

An Algebraic Multigrid Method for Higher-order Finite Element Discretizations.

[BibT_eX]

[DOI]

Shi Shu

Dudu Sun

Computing, 2006

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

[BibT_eX]

[DOI]

Adv. Comput. Math., 2006

2005

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

[BibT_eX]

[DOI]

J. Num. Math., 2005

2004

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

[BibT_eX]

[DOI]

Zhimin Zhang

Math. Comput., 2004

Uniformly Convergent Multigrid Methods for Convection-Diffusion Problems without Any Constraint on Coarse Grids.

[BibT_eX]

[DOI]

Hwanho Kim

Adv. Comput. Math., 2004

2003

Asymptotically Exact A Posteriori Error Estimators, Part II: General Unstructured Grids.

[BibT_eX]

[DOI]

Randolph E. Bank

SIAM J. Numer. Anal., 2003

Asymptotically Exact A Posteriori Error Estimators, Part I: Grids with Superconvergence.

[BibT_eX]

[DOI]

Randolph E. Bank

SIAM J. Numer. Anal., 2003

Some observations on Babu\vs}ka and Brezzi theories.

[BibT_eX]

[DOI]

Numerische Mathematik, 2003

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

[BibT_eX]

[DOI]

Hwanho Kim

Numer. Linear Algebra Appl., 2003

A conforming finite element method for overlapping and nonmatching grids.

[BibT_eX]

[DOI]

Yunqing Huang

Math. Comput., 2003

Regularity estimates for elliptic boundary value problems in Besov spaces.

[BibT_eX]

[DOI]

Constantin Bacuta

James H. Bramble

Math. Comput., 2003

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

[BibT_eX]

[DOI]

Constantin Bacuta

James H. Bramble

J. Num. Math., 2003

2002

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

[BibT_eX]

[DOI]

Xue-Cheng Tai

Math. Comput., 2002

2001

A two-grid discretization scheme for eigenvalue problems.

[BibT_eX]

[DOI]

Math. Comput., 2001

Local and Parallel Finite Element Algorithms Based on Two-Grid Discretizations for Nonlinear Problems.

[BibT_eX]

[DOI]

Adv. Comput. Math., 2001

2000

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

[BibT_eX]

[DOI]

Math. Comput., 2000

1999

A Crosswind Block Iterative Method for Convection-Dominated Problems.

[BibT_eX]

[DOI]

Feng Wang

SIAM J. Sci. Comput., 1999

A monotone finite element scheme for convection-diffusion equations.

[BibT_eX]

[DOI]

Math. Comput., 1999

1998

Some Nonoverlapping Domain Decomposition Methods.

[BibT_eX]

[DOI]

Jun Zou

SIAM Rev., 1998

1997

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

[BibT_eX]

[DOI]

Sheng Zhang

Math. Comput., 1997

1996

Multigrid Methods for Process Simulation (W. Joppich and S. Mijalkovic).

[BibT_eX]

[DOI]

SIAM Rev., 1996

Multigrid Methods for Finite Elements (V. V. Shaidurov).

[BibT_eX]

[DOI]

SIAM Rev., 1996

The Auxiliary Space Method and Optimal Multigrid Preconditioning Techniques for Unstructured Grids.

[BibT_eX]

[DOI]

Computing, 1996

1994

Some Remarks on a Multigrid Preconditioner.

[BibT_eX]

[DOI]

Jinshui Qin

SIAM J. Sci. Comput., 1994

A Novel Two-Grid Method for Semilinear Elliptic Equations.

[BibT_eX]

[DOI]

SIAM J. Sci. Comput., 1994

1992

Iterative Methods by Space Decomposition and Subspace Correction.

[BibT_eX]

[DOI]