Yongyong Cai

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All published works
Action Title Year Authors
+ PDF Chat Positivity Preserving and Mass Conservative Projection Method for the Poisson–Nernst–Planck Equation 2024 Fenghua Tong
Yongyong Cai
+ PDF Chat A robust hybridizable discontinuous Galerkin scheme with harmonic averaging technique for steady state of real-world semiconductor devices 2024 Qingyuan Shi
Yongyong Cai
Chijie Zhuang
Bo Lin
Dan Wu
Rong Zeng
Weizhu Bao
+ PDF Chat Uniform and optimal error estimates of a nested Picard integrator for the nonlinear Schrödinger equation with wave operator 2024 Yongyong Cai
Yue Feng
Yichen Guo
Zhiguo Xu
+ PDF Chat Error estimates of a regularized finite difference method for the Logarithmic Schr\"{o}dinger equation with Dirac delta potential 2024 Xuanxuan Zhou
Tingchun Wang
Yong Wu
Yongyong Cai
+ PDF Chat Positivity preserving and mass conservative projection method for the Poisson-Nernst-Planck equation 2024 Fenghua Tong
Yongyong Cai
+ Revealing excited states of rotational Bose-Einstein condensates 2023 Jianyuan Yin
Zhen Huang
Yongyong Cai
Qiang Du
Lei Zhang
+ Accurate and efficient numerical methods for the nonlinear Schrödinger equation with Dirac delta potential 2023 Xuanxuan Zhou
Yongyong Cai
Xingdong Tang
Guixiang Xu
+ PDF Chat Error analysis of a linear numerical scheme for the Landau–Lifshitz equation with large damping parameters 2023 Yongyong Cai
Jingrun Chen
Cheng Wang
Changjian Xie
+ Second-Order Semi-Lagrangian Exponential Time Differencing Method with Enhanced Error Estimate for the Convective Allen–Cahn Equation 2023 Jingwei Li
Rihui Lan
Yongyong Cai
Lili Ju
Xiaoqiang Wang
+ PDF Chat Improved uniform error bounds on time-splitting methods for the long-time dynamics of the weakly nonlinear Dirac equation 2023 Weizhu Bao
Yongyong Cai
Yue Feng
+ A uniformly accurate method for the Klein-Gordon-Dirac system in the nonrelativistic regime 2023 Yongyong Cai
Wenfan Yi
+ Uniformly accurate nested Picard iterative integrators for the Klein-Gordon-Schrödinger equation in the nonrelativistic regime 2023 Yongyong Cai
Xuanxuan Zhou
+ Revealing Excited States of Rotational Bose-Einstein Condensates 2023 Jianyuan Yin
Zhen Huang
Yongyong Cai
Qiang Du
Lei Zhang
+ PDF Chat Stabilized exponential time differencing schemes for the convective Allen–Cahn equation 2022 Yongyong Cai
Lili Ju
Rihui Lan
Jingwei Li
+ Improved uniform error bounds of the time-splitting methods for the long-time (nonlinear) Schrödinger equation 2022 Weizhu Bao
Yongyong Cai
Yue Feng
+ PDF Chat Operator splitting based structure-preserving numerical schemes for the mass-conserving convective Allen-Cahn equation 2022 Rihui Lan
Jingwei Li
Yongyong Cai
Lili Ju
+ PDF Chat Improved Uniform Error Bounds on Time-Splitting Methods for Long-Time Dynamics of the Nonlinear Klein--Gordon Equation with Weak Nonlinearity 2022 Weizhu Bao
Yongyong Cai
Yue Feng
+ Uniformly Accurate Nested Picard Iterative Integrators for the Klein-Gordon Equation in the Nonrelativistic Regime 2022 Yongyong Cai
Xuanxuan Zhou
+ A fourth-order compact finite difference scheme for the quantum Zakharov system that perfectly inherits both mass and energy conservation 2022 Yongyong Cai
Jinxue Fu
Jianfeng Liu
Ting-Chun Wang
+ Uniformly Accurate Nested Picard Iterative Integrators for the Nonlinear Dirac Equation in the Nonrelativistic Regime 2022 Yongyong Cai
Yan Wang Yan Wang
+ Improved uniform error bounds on time-splitting methods for the long-time dynamics of the weakly nonlinear Dirac equation 2022 Weizhu Bao
Yongyong Cai
Yue Feng
+ Stabilized exponential time differencing schemes for the convective Allen-Cahn equation 2022 Yongyong Cai
Lili Ju
Rihui Lan
Jingwei Li
+ PDF Chat A second-order numerical method for Landau-Lifshitz-Gilbert equation with large damping parameters 2021 Yongyong Cai
Jingrun Chen
Cheng Wang
Changjian Xie
+ Improved uniform error bounds for the time-splitting methods for the long-time dynamics of the Schrödinger/nonlinear Schrödinger equation. 2021 Weizhu Bao
Yongyong Cai
Yue Feng
+ Unconditionally Maximum Bound Principle Preserving Linear Schemes for the Conservative Allen–Cahn Equation with Nonlocal Constraint 2021 Jingwei Li
Lili Ju
Yongyong Cai
Xinlong Feng
+ A second-order numerical method for Landau-Lifshitz-Gilbert equation with large damping parameters 2021 Yongyong Cai
Jingrun Chen
Cheng Wang
Changjian Xie
+ Uniformly accurate nested Picard integrators for a system of oscillatory ordinary differential equations 2021 Yongyong Cai
Yichen Guo
+ PDF Chat Uniform Error Bounds of Time-Splitting Methods for the Nonlinear Dirac Equation in the Nonrelativistic Regime without Magnetic Potential 2021 Weizhu Bao
Yongyong Cai
Jia Yin
+ Convergence Analysis of A Second-order Accurate, Linear Numerical Scheme for The Landau-Lifshitz Equation with Large Damping Parameters 2021 Yongyong Cai
Jingrun Chen
Cheng Wang
Changjian Xie
+ Improved uniform error bounds on time-splitting methods for long-time dynamics of the nonlinear Klein--Gordon equation with weak nonlinearity 2021 Weizhu Bao
Yongyong Cai
Yue Feng
+ Improved uniform error bounds of the time-splitting methods for the long-time (nonlinear) Schrödinger equation 2021 Weizhu Bao
Yongyong Cai
Yue Feng
+ Stationary state computation for nonlinear Dirac operators 2020 Yongyong Cai
Emmanuel Lorin
+ Super-resolution of time-splitting methods for the Dirac equation in the nonrelativistic regime 2020 Weizhu Bao
Yongyong Cai
Jia Yin
+ Operator-compensation methods with mass and energy conservation for solving the Gross-Pitaevskii equation 2020 Xiang‐Gui Li
Yongyong Cai
Pengde Wang
+ Uniform error bounds of time-splitting methods for the nonlinear Dirac equation in the nonrelativistic limit regime. 2019 Weizhu Bao
Yongyong Cai
Jia Yin
+ Zero extension for Poisson’s equation 2019 Yongyong Cai
Shulin Zhou
+ Ground states and their characterization of spin-$F$ Bose-Einstein condensates 2019 Tonghua Tian
Yongyong Cai
Xinming Wu
Zaiwen Wen
+ Uniformly Accurate Nested Picard Iterative Integrators for the Dirac Equation in the Nonrelativistic Limit Regime 2019 Yongyong Cai
Yan Wang
+ Super-resolution of time-splitting methods for the Dirac equation in the nonrelativistic regime. 2018 Weizhu Bao
Yongyong Cai
Jia Yin
+ Optimal error estimates of finite difference time domain methods for the Klein–Gordon–Dirac system 2018 Wenfan Yi
Yongyong Cai
+ PDF Chat Ground states of Bose–Einstein condensates with higher order interaction 2018 Weizhu Bao
Yongyong Cai
Xinran Ruan
+ PDF Chat Vortex patterns and the critical rotational frequency in rotating dipolar Bose-Einstein condensates 2018 Yongyong Cai
Yongjun Yuan
Matthias Rosenkranz
Han Pu
Weizhu Bao
+ PDF Chat A uniformly accurate (UA) multiscale time integrator pseudospectral method for the nonlinear Dirac equation in the nonrelativistic limit regime 2018 Yongyong Cai
Yan Wang
+ PDF Chat Review Article: Mathematical Models and Numerical Methods for Spinor Bose-Einstein Condensates 2018 Weizhu Bao
Yongyong Cai
+ Error estimates of finite difference time domain methods for the Klein–Gordon–Dirac system in the nonrelativistic limit regime 2018 Yongyong Cai
Wenfan Yi
+ Uniform error estimates of the conservative finite difference method for the Zakharov system in the subsonic limit regime 2017 Yongyong Cai
Yongjun Yuan
+ PDF Chat Numerical Methods and Comparison for the Dirac Equation in the Nonrelativistic Limit Regime 2017 Weizhu Bao
Yongyong Cai
Xiaowei Jia
Qinglin Tang
+ Ground states of Bose-Einstein condensates with higher order interaction 2017 Weizhu Bao
Yongyong Cai
Xinran Ruan
+ PDF Chat Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime 2016 Weizhu Bao
Yongyong Cai
Xiaowei Jia
Jia Yin
+ PDF Chat Mean-field regime and Thomas–Fermi approximations of trapped Bose–Einstein condensates with higher-order interactions in one and two dimensions 2016 Xinran Ruan
Yongyong Cai
Weizhu Bao
+ PDF Chat A uniformly accurate (UA) multiscale time integrator pseudospectral method for the Dirac equation in the nonrelativistic limit regime 2016 Weizhu Bao
Yongyong Cai
Xiaowei Jia
Qinglin Tang
+ PDF Chat A Uniformly Accurate Multiscale Time Integrator Pseudospectral Method for the Dirac Equation in the Nonrelativistic Limit Regime 2016 Weizhu Bao
Yongyong Cai
Xiaowei Jia
Qinglin Tang
+ PDF Chat Ground States and Dynamics of Spin-Orbit-Coupled Bose--Einstein Condensates 2015 Weizhu Bao
Yongyong Cai
+ PDF Chat Uniform and Optimal Error Estimates of an Exponential Wave Integrator Sine Pseudospectral Method for the Nonlinear Schrödinger Equation with Wave Operator 2014 Weizhu Bao
Yongyong Cai
+ Ground states and dynamics of spin-orbit-coupled Bose-Einstein condensates 2014 Weizhu Bao
Yongyong Cai
+ PDF Chat A Uniformly Accurate Multiscale Time Integrator Pseudospectral Method for the Klein--Gordon Equation in the Nonrelativistic Limit Regime 2014 Weizhu Bao
Yongyong Cai
Xiaofei Zhao
+ A uniformly accurate multiscale time integrator pseudospectral method for the Klein-Gordon equation in the nonrelativistic limit regime 2014 Weizhu Bao
Yongyong Cai
Xiaofei Zhao
+ PDF Chat Effective dipole-dipole interactions in multilayered dipolar Bose-Einstein condensates 2013 Matthias Rosenkranz
Yongyong Cai
Weizhu Bao
+ Uniform and optimal error estimates of an exponential wave integrator sine pseudospectral method for the nonlinear Schrodinger equation with wave operator 2013 Weizhu Bao
Yongyong Cai
+ PDF Chat Mathematical theory and numerical methods for Bose-Einstein condensation 2012 Weizhu Bao
Yongyong Cai
+ PDF Chat Optimal error estimates of finite difference methods for the Gross-Pitaevskii equation with angular momentum rotation 2012 Weizhu Bao
Yongyong Cai
+ PDF Chat Controlling phase separation of a two-component Bose-Einstein condensate by confinement 2012 Lin Wen
Weixi Liu
Yongyong Cai
J. M. Zhang
Jiangping Hu
+ PDF Chat Breathing oscillations of a trapped impurity in a Bose gas 2012 T. H. Johnson
M. Bruderer
Yongyong Cai
Stephen R. L. Clark
Weizhu Bao
Dieter Jaksch
+ Uniform Error Estimates of Finite Difference Methods for the Nonlinear Schrödinger Equation with Wave Operator 2012 Weizhu Bao
Yongyong Cai
+ PDF Chat Gross–Pitaevskii–Poisson Equations for Dipolar Bose–Einstein Condensate with Anisotropic Confinement 2012 Weizhu Bao
Naoufel Ben Abdallah
Yongyong Cai
+ Gross-Pitaevskii-Poisson equations for dipolar Bose-Einstein condensate with anisotropic confinement 2012 Weizhu Bao
Naoufel Ben Abdallah
Yongyong Cai
+ Second order averaging for the nonlinear Schrödinger equation with strongly anisotropic potential 2011 Naoufel Ben Abdallah
Yongyong Cai
François Castella
Florian MĂ©hats
+ PDF Chat Mean-field regime of trapped dipolar Bose-Einstein condensates in one and two dimensions 2010 Yongyong Cai
Matthias Rosenkranz
Zhen Lei
Weizhu Bao
+ Ground States of Two-component Bose-Einstein Condensates with an Internal Atomic Josephson Junction 2010 Weizhu Bao
Yongyong Cai
+ PDF Chat Efficient numerical methods for computing ground states and dynamics of dipolar Bose–Einstein condensates 2010 Weizhu Bao
Yongyong Cai
Hanquan Wang
+ Existence and uniqueness of weak solutions for a non-uniformly parabolic equation 2009 Yongyong Cai
Shulin Zhou
+ L q Interior Estimates of the Gradient for Weak Solutions of Quasilinear Elliptic Equations 2007 Feng Ping Yao
Yongyong Cai
Common Coauthors
Commonly Cited References
Action Title Year Authors # of times referenced
+ PDF Chat Numerical solution of the Gross–Pitaevskii equation for Bose–Einstein condensation 2003 Weizhu Bao
Dieter Jaksch
Peter A. Markowich
22
+ PDF Chat A Uniformly Accurate Multiscale Time Integrator Pseudospectral Method for the Dirac Equation in the Nonrelativistic Limit Regime 2016 Weizhu Bao
Yongyong Cai
Xiaowei Jia
Qinglin Tang
15
+ PDF Chat Uniform and Optimal Error Estimates of an Exponential Wave Integrator Sine Pseudospectral Method for the Nonlinear Schrödinger Equation with Wave Operator 2014 Weizhu Bao
Yongyong Cai
14
+ PDF Chat Mathematical theory and numerical methods for Bose-Einstein condensation 2012 Weizhu Bao
Yongyong Cai
14
+ PDF Chat On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations 2008 Christian Lubich
13
+ PDF Chat Computing the Ground State Solution of Bose--Einstein Condensates by a Normalized Gradient Flow 2004 Weizhu Bao
Qiang Du
13
+ PDF Chat Computational methods for the dynamics of the nonlinear Schrödinger/Gross–Pitaevskii equations 2013 Xavier Antoine
Weizhu Bao
Christophe Besse
13
+ PDF Chat Numerical Methods and Comparison for the Dirac Equation in the Nonrelativistic Limit Regime 2017 Weizhu Bao
Yongyong Cai
Xiaowei Jia
Qinglin Tang
12
+ PDF Chat Optimal error estimates of finite difference methods for the Gross-Pitaevskii equation with angular momentum rotation 2012 Weizhu Bao
Yongyong Cai
12
+ On the Construction and Comparison of Difference Schemes 1968 Gilbert Strang
12
+ Analysis and comparison of numerical methods for the Klein–Gordon equation in the nonrelativistic limit regime 2011 Weizhu Bao
Xuanchun Dong
12
+ (Semi)-Nonrelativistic Limits of the Dirac Equation with External Time-Dependent Electromagnetic Field 1998 Philippe Bechouche
Norbert J. Mauser
Philippe Bechouche
12
+ Numerical integration of ordinary differential equations based on trigonometric polynomials 1961 Walter Gautschi
11
+ On Time-Splitting Spectral Approximations for the Schrödinger Equation in the Semiclassical Regime 2002 Weizhu Bao
Shi Jin
Peter A. Markowich
11
+ On the nonrelativistic limits of the Klein-Gordon and Dirac equations 1979 Andrew Y. Schoene
10
+ The Nonlinear Schrödinger Equation with a Strongly Anisotropic Harmonic Potential 2005 Naoufel Ben Abdallah
Florian MĂ©hats
Christian Schmeiser
Rada M. WeishÀupl
10
+ Uniform Error Estimates of Finite Difference Methods for the Nonlinear Schrödinger Equation with Wave Operator 2012 Weizhu Bao
Yongyong Cai
10
+ Nonrelativistic limit in the energy space for nonlinear Klein-Gordon equations 2002 Shuji Machihara
Kenji Nakanishi
Tohru Ozawa
10
+ Uniformly Accurate Nested Picard Iterative Integrators for the Dirac Equation in the Nonrelativistic Limit Regime 2019 Yongyong Cai
Yan Wang
10
+ PDF Chat A Uniformly Accurate Multiscale Time Integrator Pseudospectral Method for the Klein--Gordon Equation in the Nonrelativistic Limit Regime 2014 Weizhu Bao
Yongyong Cai
Xiaofei Zhao
10
+ PDF Chat Exponential integrators 2010 Marlis Hochbruck
Alexander Ostermann
10
+ High-Order Exponential Operator Splitting Methods for Time-Dependent Schrödinger Equations 2008 Mechthild Thalhammer
10
+ PDF Chat Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime 2016 Weizhu Bao
Yongyong Cai
Xiaowei Jia
Jia Yin
9
+ Finite difference discretization of the cubic Schrödinger equation 1993 Georgios Akrivis
9
+ PDF Chat Numerical methods for nonlinear Dirac equation 2013 Xu Jian
Sihong Shao
Huazhong Tang
9
+ Honeycomb lattice potentials and Dirac points 2012 Charles Fefferman
Michael I. Weinstein
9
+ PDF Chat A time-splitting spectral scheme for the Maxwell–Dirac system 2005 Zhongyi Huang
Shi Jin
Peter A. Markowich
Christof Sparber
Chunxiong Zheng
9
+ PDF Chat Asymptotic preserving schemes for the Klein–Gordon equation in the non-relativistic limit regime 2013 Erwan Faou
Katharina Schratz
8
+ Uniformly accurate exponential-type integrators for Klein-Gordon equations with asymptotic convergence to the classical NLS splitting 2017 Simon Baumstark
Erwan Faou
Katharina Schratz
8
+ PDF Chat Uniformly accurate numerical schemes for highly oscillatory Klein–Gordon and nonlinear Schrödinger equations 2014 Philippe Chartier
Nicolas Crouseilles
Mohammed Lemou
Florian MĂ©hats
8
+ PDF Chat The nonrelativistic limit of the nonlinear Dirac equation 1992 Branko Najman
8
+ Numerical Study of Time-Splitting Spectral Discretizations of Nonlinear Schrödinger Equations in the Semiclassical Regimes 2003 Weizhu Bao
Shi Jin
Peter A. Markowich
8
+ Semilinear Schrödinger Equations 2003 Thierry Cazenave
8
+ PDF Chat A Fourth-Order Time-Splitting Laguerre--Hermite Pseudospectral Method for Bose--Einstein Condensates 2005 Weizhu Bao
Jie Shen
8
+ PDF Chat Ground States and Dynamics of Multicomponent Bose--Einstein Condensates 2004 Weizhu Bao
8
+ Ground States of Two-component Bose-Einstein Condensates with an Internal Atomic Josephson Junction 2010 Weizhu Bao
Yongyong Cai
8
+ PDF Chat On the Gross–Pitaevskii equation for trapped dipolar quantum gases 2008 RĂ©mi Carles
Peter A. Markowich
Christof Sparber
7
+ Soliton solutions for Dirac equations with homogeneous non-linearity in (1+1) dimensions 1985 Pierre Mathieu
7
+ Nonrelativistic approximation of nonlinear Klein-Gordon equations in two space dimensions 1984 Masayoshi Tsutsumi
7
+ PDF Chat Uniformly accurate numerical schemes for the nonlinear Dirac equation in the nonrelativistic limit regime 2017 Mohammed Lemou
Florian MĂ©hats
Xiaofei Zhao
7
+ PDF Chat Gaussian beam methods for the Dirac equation in the semi-classical regime 2012 Zhongyi Huang
Shi Jin
Hao Wu
Dongsheng Yin
7
+ PDF Chat Bose-Einstein Condensation of Chromium 2005 Axel Griesmaier
Jörg Werner
S. Hensler
J. StĂŒhler
Tilman Pfau
7
+ PDF Chat Modified Energy for Split-Step Methods Applied to the Linear Schrödinger Equation 2009 Arnaud Debussche
Erwan Faou
7
+ On the Numerical Solution of the Cubic Schrödinger Equation in One Space Variable 1993 Mark P. Robinson
Graeme Fairweather
B. M. Herbst
7
+ PDF Chat Uniformly Accurate Multiscale Time Integrators for Highly Oscillatory Second Order Differential Equations 2014 Weizhu Bao
Xuanchun Dong
Xiaofei Zhao
7
+ PDF Chat Convergence of an energy-preserving scheme for the Zakharov equations in one space dimension 1992 Robert T. Glassey
7
+ PDF Chat The nonlinear Dirac equation in Bose–Einstein condensates: Foundation and symmetries 2009 Laith H. Haddad
Lincoln D. Carr
7
+ PDF Chat On the nonrelativistic limit of the Dirac theory 1975 Walter Hunziker
7
+ PDF Chat Trapped atomic condensates with anisotropic interactions 2000 S. Yi
Li You
7
+ Solutions of nonlinear Dirac equations 2005 Thomas Bartsch
Yanheng Ding
7