Jie Shen

Orcid: 0000-0002-4885-5732

Affiliations:
  • Purdue University, Department of Mathematics, West Lafayette, IN, USA
  • Xiamen University, School of Mathematical Sciences, China
  • Université Paris-Sud, Orsay, France (PhD 1987)


According to our database1, Jie Shen authored at least 158 papers between 1994 and 2024.

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Bibliography

2024
Eigenvalue analysis and applications of the Legendre dual-Petrov-Galerkin methods for initial value problems.
Adv. Comput. Math., October, 2024

A Simple and Efficient Convex Optimization Based Bound-Preserving High Order Accurate Limiter for Cahn-Hilliard-Navier-Stokes System.
SIAM J. Sci. Comput., 2024

On a New Class of BDF and IMEX Schemes for Parabolic Type Equations.
SIAM J. Numer. Anal., 2024

Efficient and stable SAV-based methods for gradient flows arising from deep learning.
J. Comput. Phys., 2024

Efficient energy stable numerical schemes for Cahn-Hilliard equations with dynamical boundary conditions.
J. Comput. Phys., 2024

On a class of higher-order length preserving and energy decreasing IMEX schemes for the Landau-Lifshitz equation.
CoRR, 2024

Higher-Order Energy-Decreasing Exponential Time Differencing Runge-Kutta methods for Gradient Flows.
CoRR, 2024

2023
An Efficient and Robust Scalar Auxialiary Variable Based Algorithm for Discrete Gradient Systems Arising from Optimizations.
SIAM J. Sci. Comput., October, 2023

Stability and Error Analysis of a Second-Order Consistent Splitting Scheme for the Navier-Stokes Equations.
SIAM J. Numer. Anal., October, 2023

A Ginzburg-Landau-H<sup>-1</sup> Model and Its SAV Algorithm for Image Inpainting.
J. Sci. Comput., August, 2023

Bound/positivity preserving SAV schemes for the Patlak-Keller-Segel-Navier-Stokes system.
J. Comput. Phys., May, 2023

Length Preserving Numerical Schemes for Landau-Lifshitz Equation Based on Lagrange Multiplier Approaches.
SIAM J. Sci. Comput., April, 2023

Log Orthogonal Functions in Semi-Infinite Intervals: Approximation Results and Applications.
SIAM J. Numer. Anal., February, 2023

A Fictitious Domain Spectral Method for Solving the Helmholtz Equation in Exterior Domains.
J. Sci. Comput., February, 2023

Error analysis of a fully discrete consistent splitting MAC scheme for time dependent Stokes equations.
J. Comput. Appl. Math., 2023

A positivity preserving scheme for Poisson-Nernst-Planck Navier-Stokes equations and its error analysis.
CoRR, 2023

Global error estimates of high-order fully decoupled schemes for the Cahn-Hilliard-Navier-Stokes model of Two-Phase Incompressible Flows.
CoRR, 2023

A simple GPU implementation of spectral-element methods for solving 3D Poisson type equations on cartesian meshes.
CoRR, 2023

An efficient and robust SAV based algorithm for discrete gradient systems arising from optimizations.
CoRR, 2023

Error estimate of a consistent splitting GSAV scheme for the Navier-Stokes equations.
CoRR, 2023

2022
A Fast Petrov-Galerkin Spectral Method for the Multidimensional Boltzmann Equation Using Mapped Chebyshev Functions.
SIAM J. Sci. Comput., 2022

Stability and Error Analysis of IMEX SAV Schemes for the Magneto-Hydrodynamic Equations.
SIAM J. Numer. Anal., 2022

A New Lagrange Multiplier Approach for Constructing Structure Preserving Schemes, II. Bound Preserving.
SIAM J. Numer. Anal., 2022

New SAV-pressure correction methods for the Navier-Stokes equations: stability and error analysis.
Math. Comput., 2022

A generalized SAV approach with relaxation for dissipative systems.
J. Comput. Phys., 2022

A new class of higher-order decoupled schemes for the incompressible Navier-Stokes equations and applications to rotating dynamics.
J. Comput. Phys., 2022

Bound/positivity preserving and unconditionally stable schemes for a class of fourth order nonlinear equations.
J. Comput. Phys., 2022

Modeling and simulation of cell nuclear architecture reorganization process.
J. Comput. Phys., 2022

2021
Bound/Positivity Preserving and Energy Stable Scalar auxiliary Variable Schemes for Dissipative Systems: Applications to Keller-Segel and Poisson-Nernst-Planck Equations.
SIAM J. Sci. Comput., 2021

An Efficient Spectral Method for Elliptic PDEs in Complex Domains with Circular Embedding.
SIAM J. Sci. Comput., 2021

Stability and Error Analysis of a Class of High-Order IMEX Schemes for Navier-Stokes Equations with Periodic Boundary Conditions.
SIAM J. Numer. Anal., 2021

Unconditionally positivity preserving and energy dissipative schemes for Poisson-Nernst-Planck equations.
Numerische Mathematik, 2021

Efficient Structure Preserving Schemes for the Klein-Gordon-Schrödinger Equations.
J. Sci. Comput., 2021

Efficient Spectral Methods for PDEs with Spectral Fractional Laplacian.
J. Sci. Comput., 2021

Second-Order SAV Schemes for the Nonlinear Schrödinger Equation and Their Error Analysis.
J. Sci. Comput., 2021

A bound-preserving high order scheme for variable density incompressible Navier-Stokes equations.
J. Comput. Phys., 2021

Computing interface with quasiperiodicity.
J. Comput. Phys., 2021

Scalar Auxiliary Variable/Lagrange multiplier based pseudospectral schemes for the dynamics of nonlinear Schrödinger/Gross-Pitaevskii equations.
J. Comput. Phys., 2021

Generalized SAV approaches for gradient systems.
J. Comput. Appl. Math., 2021

A new Lagrange multiplier approach for constructing positivity preserving schemes.
CoRR, 2021

A fast Petrov-Galerkin spectral method for the multi-dimensional Boltzmann equation using mapped Chebyshev functions.
CoRR, 2021

Discrete Maximum principle of a high order finite difference scheme for a generalized Allen-Cahn equation.
CoRR, 2021

Modeling and simulation of nuclear architecture reorganization process using a phase field approach.
CoRR, 2021

Implicit-explicit BDF k SAV schemes for general dissipative systems and their error analysis.
CoRR, 2021

2020
A Highly Efficient and Accurate New Scalar Auxiliary Variable Approach for Gradient Flows.
SIAM J. Sci. Comput., 2020

Global Constraints Preserving Scalar Auxiliary Variable Schemes for Gradient Flows.
SIAM J. Sci. Comput., 2020

A Spectrally Accurate Approximation to Subdiffusion Equations Using the Log Orthogonal Functions.
SIAM J. Sci. Comput., 2020

Fast Fourier-like Mapped Chebyshev Spectral-Galerkin Methods for PDEs with Integral Fractional Laplacian in Unbounded Domains.
SIAM J. Numer. Anal., 2020

Unconditionally Bound Preserving and Energy Dissipative Schemes for a Class of Keller-Segel Equations.
SIAM J. Numer. Anal., 2020

Error Analysis of the SAV-MAC Scheme for the Navier-Stokes Equations.
SIAM J. Numer. Anal., 2020

Optimal error estimates for the scalar auxiliary variable finite-element schemes for gradient flows.
Numerische Mathematik, 2020

A Total Fractional-Order Variation Model for Image Super-Resolution and Its SAV Algorithm.
J. Sci. Comput., 2020

Accurate and Efficient Spectral Methods for Elliptic PDEs in Complex Domains.
J. Sci. Comput., 2020

An Efficient and Accurate Numerical Method for the Spectral Fractional Laplacian Equation.
J. Sci. Comput., 2020

Bound preserving and energy dissipative schemes for porous medium equation.
J. Comput. Phys., 2020

A new interface capturing method for Allen-Cahn type equations based on a flow dynamic approach in Lagrangian coordinates, I. One-dimensional case<sup>☆</sup>.
J. Comput. Phys., 2020

Two classes of linearly implicit local energy-preserving approach for general multi-symplectic Hamiltonian PDEs.
J. Comput. Phys., 2020

An efficient numerical scheme for a 3D spherical dynamo equation.
J. Comput. Appl. Math., 2020

Error estimate of Gauge-Uzawa methods for incompressible flows with variable density.
J. Comput. Appl. Math., 2020

On fully decoupled MSAV schemes for the Cahn-Hilliard-Navier-Stokes model of Two-Phase Incompressible Flows.
CoRR, 2020

Efficient Linear and Unconditionally Energy Stable Schemes for the Modified Phase Field Crystal Equation.
CoRR, 2020

Log orthogonal functions: approximation properties and applications.
CoRR, 2020

Stability and error estimates of the SAV Fourier-spectral method for the phase field crystal equation.
Adv. Comput. Math., 2020

2019
A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows.
SIAM Rev., 2019

Fast structured Jacobi-Jacobi transforms.
Math. Comput., 2019

Energy stability and convergence of SAV block-centered finite difference method for gradient flows.
Math. Comput., 2019

An Efficient Space-Time Method for Time Fractional Diffusion Equation.
J. Sci. Comput., 2019

Highly Efficient and Accurate Numerical Schemes for the Epitaxial Thin Film Growth Models by Using the SAV Approach.
J. Sci. Comput., 2019

Efficient SAV approach for imaginary time gradient flows with applications to one- and multi-component Bose-Einstein Condensates.
J. Comput. Phys., 2019

Global constraints preserving SAV schemes for gradient flows.
CoRR, 2019

A new Lagrange Multiplier approach for gradient flows.
CoRR, 2019

Stability and convergence analysis of rotational velocity correction methods for the Navier-Stokes equations.
Adv. Comput. Math., 2019

2018
Multiple Scalar Auxiliary Variable (MSAV) Approach and its Application to the Phase-Field Vesicle Membrane Model.
SIAM J. Sci. Comput., 2018

Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows.
SIAM J. Numer. Anal., 2018

Error estimates for a fully discretized scheme to a Cahn-Hilliard phase-field model for two-phase incompressible flows.
Math. Comput., 2018

Approximations on SO(3) by Wigner D-matrix and Applications.
J. Sci. Comput., 2018

Laguerre Functions and Their Applications to Tempered Fractional Differential Equations on Infinite Intervals.
J. Sci. Comput., 2018

Enriched Spectral Methods and Applications to Problems with Weakly Singular Solutions.
J. Sci. Comput., 2018

The scalar auxiliary variable (SAV) approach for gradient flows.
J. Comput. Phys., 2018

Efficient energy stable schemes for isotropic and strongly anisotropic Cahn-Hilliard systems with the Willmore regularization.
J. Comput. Phys., 2018

Spectral element method with geometric mesh for two-sided fractional differential equations.
Adv. Comput. Math., 2018

2017
Hermite Spectral Methods for Fractional PDEs in Unbounded Domains.
SIAM J. Sci. Comput., 2017

Error estimates for time discretizations of Cahn-Hilliard and Allen-Cahn phase-field models for two-phase incompressible flows.
Numerische Mathematik, 2017

Highly Accurate Pseudospectral Approximations of the Prolate Spheroidal Wave Equation for Any Bandwidth Parameter and Zonal Wavenumber.
J. Sci. Comput., 2017

Unconditionally stable Gauge-Uzawa finite element schemes for incompressible natural convection problems with variable density.
J. Comput. Phys., 2017

Efficient and accurate numerical schemes for a hydro-dynamically coupled phase field diblock copolymer model.
J. Comput. Phys., 2017

2016
Fast Structured Direct Spectral Methods for Differential Equations with Variable Coefficients, I. The One-Dimensional Case.
SIAM J. Sci. Comput., 2016

Müntz-Galerkin Methods and Applications to Mixed Dirichlet-Neumann Boundary Value Problems.
SIAM J. Sci. Comput., 2016

Generalized Jacobi functions and their applications to fractional differential equations.
Math. Comput., 2016

Efficient Spectral-Galerkin Method and Analysis for Elliptic PDEs with Non-local Boundary Conditions.
J. Sci. Comput., 2016

A decoupled energy stable scheme for a hydrodynamic phase-field model of mixtures of nematic liquid crystals and viscous fluids.
J. Comput. Phys., 2016

Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients.
J. Comput. Phys., 2016

Efficient, adaptive energy stable schemes for the incompressible Cahn-Hilliard Navier-Stokes phase-field models.
J. Comput. Phys., 2016

2015
Decoupled, Energy Stable Schemes for Phase-Field Models of Two-Phase Incompressible Flows.
SIAM J. Numer. Anal., 2015

Dynamic Transitions of Quasi-geostrophic Channel Flow.
SIAM J. Appl. Math., 2015

Decoupled Energy Stable Schemes for a Phase-Field Model of Two-Phase Incompressible Flows with Variable Density.
J. Sci. Comput., 2015

Efficient energy stable numerical schemes for a phase field moving contact line model.
J. Comput. Phys., 2015

A pressure correction scheme for generalized form of energy-stable open boundary conditions for incompressible flows.
J. Comput. Phys., 2015

Spectral approximation to a transmission eigenvalue problem and its applications to an inverse problem.
Comput. Math. Appl., 2015

2014
Decoupled Energy Stable Schemes for Phase-Field Models of Two-Phase Complex Fluids.
SIAM J. Sci. Comput., 2014

A new spectral method for numerical solution of the unbounded rough surface scattering problem.
J. Comput. Phys., 2014

Approximations by orthonormal mapped Chebyshev functions for higher-dimensional problems in unbounded domains.
J. Comput. Appl. Math., 2014

2013
A Spectral-Element Method for Transmission Eigenvalue Problems.
J. Sci. Comput., 2013

Modeling and simulations of drop pinch-off from liquid crystal filaments and the leaky liquid crystal faucet immersed in viscous fluids.
J. Comput. Phys., 2013

A GPU parallelized spectral method for elliptic equations in rectangular domains.
J. Comput. Phys., 2013

Error Analysis of the Strang Time-Splitting Laguerre-Hermite/Hermite Collocation Methods for the Gross-Pitaevskii Equation.
Found. Comput. Math., 2013

2012
Efficient Spectral Sparse Grid Methods and Applications to High-Dimensional Elliptic Equations II. Unbounded Domains.
SIAM J. Sci. Comput., 2012

On the Approximation of the Fokker-Planck Equation of the Finitely Extensible Nonlinear Elastic Dumbbell Model I: A New Weighted Formulation and an Optimal Spectral-Galerkin Algorithm in Two Dimensions.
SIAM J. Numer. Anal., 2012

Second-order Convex Splitting Schemes for Gradient Flows with Ehrlich-Schwoebel Type Energy: Application to Thin Film Epitaxy.
SIAM J. Numer. Anal., 2012

A New Spectral Element Method for Pricing European Options Under the Black-Scholes and Merton Jump Diffusion Models.
J. Sci. Comput., 2012

An efficient and stable spectral method for electromagnetic scattering from a layered periodic structure.
J. Comput. Phys., 2012

A time-stepping scheme involving constant coefficient matrices for phase-field simulations of two-phase incompressible flows with large density ratios.
J. Comput. Phys., 2012

Efficient spectral-Galerkin methods for systems of coupled second-order equations and their applications.
J. Comput. Phys., 2012

2010
Efficient Spectral Sparse Grid Methods and Applications to High-Dimensional Elliptic Problems.
SIAM J. Sci. Comput., 2010

A Phase-Field Model and Its Numerical Approximation for Two-Phase Incompressible Flows with Different Densities and Viscosities.
SIAM J. Sci. Comput., 2010

Sparse Spectral Approximations of High-Dimensional Problems Based on Hyperbolic Cross.
SIAM J. Numer. Anal., 2010

Optimal error estimates in Jacobi-weighted Sobolev spaces for polynomial approximations on the triangle.
Math. Comput., 2010

A Coupled Legendre-Laguerre Spectral-Element Method for the Navier-Stokes Equations in Unbounded Domains.
J. Sci. Comput., 2010

An unconditionally stable rotational velocity-correction scheme for incompressible flows.
J. Comput. Phys., 2010

2009
A Generalized-Laguerre--Fourier--Hermite Pseudospectral Method for Computing the Dynamics of Rotating Bose--Einstein Condensates.
SIAM J. Sci. Comput., 2009

A Triangular Spectral Element Method Using Fully Tensorial Rational Basis Functions.
SIAM J. Numer. Anal., 2009

A Rigorous Numerical Analysis of the Transformed Field Expansion Method.
SIAM J. Numer. Anal., 2009

On spectral approximations in elliptical geometries using Mathieu functions.
Math. Comput., 2009

Efficient stochastic Galerkin methods for random diffusion equations.
J. Comput. Phys., 2009

An efficient moving mesh spectral method for the phase-field model of two-phase flows.
J. Comput. Phys., 2009

2008
On Numerical Approximations of Forward-Backward Stochastic Differential Equations.
SIAM J. Numer. Anal., 2008

A Laguerre-Legendre Spectral Method for the Stokes Problem in a Semi-Infinite Channel.
SIAM J. Numer. Anal., 2008

Error analysis of fully discrete velocity-correction methods for incompressible flows.
Math. Comput., 2008

Dimensional Robustness and Instability of Sheared, Semidilute, Nanorod Dispersions.
Multiscale Model. Simul., 2008

A Dual-Petrov-Galerkin Method for the Kawahara-Type Equations.
J. Sci. Comput., 2008

A generalized-Laguerre-Hermite pseudospectral method for computing symmetric and central vortex states in Bose-Einstein condensates.
J. Comput. Phys., 2008

Irrational approximations and their applications to partial differential equations in exterior domains<sup>, </sup>.
Adv. Comput. Math., 2008

2007
Analysis of a Spectral-Galerkin Approximation to the Helmholtz Equation in Exterior Domains.
SIAM J. Numer. Anal., 2007

Gauge-Uzawa methods for incompressible flows with variable density.
J. Comput. Phys., 2007

An efficient direct parallel spectral-element solver for separable elliptic problems.
J. Comput. Phys., 2007

A stable, high-order method for three-dimensional, bounded-obstacle, acoustic scattering.
J. Comput. Phys., 2007

2006
A Stable High-Order Method for Two-Dimensional Bounded-Obstacle Scattering.
SIAM J. Sci. Comput., 2006

Optimal Spectral-Galerkin Methods Using Generalized Jacobi Polynomials.
J. Sci. Comput., 2006

Numerical simulations of jet pinching-off and drop formation using an energetic variational phase-field method.
J. Comput. Phys., 2006

2005
A Fourth-Order Time-Splitting Laguerre-Hermite Pseudospectral Method for Bose-Einstein Condensates.
SIAM J. Sci. Comput., 2005

Spectral Approximation of the Helmholtz Equation with High Wave Numbers.
SIAM J. Numer. Anal., 2005

Error Analysis of Pressure-Correction Schemes for the Time-Dependent Stokes Equations with Open Boundary Conditions.
SIAM J. Numer. Anal., 2005

Error Analysis for Mapped Jacobi Spectral Methods.
J. Sci. Comput., 2005

2004
Error Analysis for Mapped Legendre Spectral and Pseudospectral Methods.
SIAM J. Numer. Anal., 2004

On the error estimates for the rotational pressure-correction projection methods.
Math. Comput., 2004

2003
A New Dual-Petrov-Galerkin Method for Third and Higher Odd-Order Differential Equations: Application to the KDV Equation.
SIAM J. Numer. Anal., 2003

Velocity-Correction Projection Methods for Incompressible Flows.
SIAM J. Numer. Anal., 2003

Corrigendum: Fourier Spectral Approximation to a Dissipative System Modeling the Flow of Liquid Crystals.
SIAM J. Numer. Anal., 2003

Spectral and Pseudospectral Approximations Using Hermite Functions: Application to the Dirac Equation.
Adv. Comput. Math., 2003

2001
Fourier Spectral Approximation to a Dissipative System Modeling the Flow of Liquid Crystals.
SIAM J. Numer. Anal., 2001

2000
Stable and Efficient Spectral Methods in Unbounded Domains Using Laguerre Functions.
SIAM J. Numer. Anal., 2000

Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval.
Numerische Mathematik, 2000

A Rational Approximation and Its Applications to Differential Equations on the Half Line.
J. Sci. Comput., 2000

1999
Efficient Spectral-Galerkin Methods IV. Spherical Geometries.
SIAM J. Sci. Comput., 1999

1997
Efficient Spectral-Galerkin Methods III: Polar and Cylindrical Geometries.
SIAM J. Sci. Comput., 1997

1996
On error estimates of the projection methods for the Navier-Stokes equations: Second-order schemes.
Math. Comput., 1996

1995
Efficient Spectral-Galerkin Method II. Direct Solvers of Second- and Fourth-Order Equations Using Chebyshev Polynomials.
SIAM J. Sci. Comput., 1995

1994
Efficient Spectral-Galerkin Method I. Direct Solvers of Second- and Fourth-Order Equations Using Legendre Polynomials.
SIAM J. Sci. Comput., 1994


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