Publications

Yingjie Liu, Lixin Liu and Tao Tang, ``The Numerical Computation of Connecting Orbits in Dynamical Systems: A Rational Spectral Approach''. J. Comput. Phys., v. 111, no.2, pp373--380, 1994.
Yingjie Liu, "Tangential Wheel Suspension System" . US patent No.6260871, published on July 17, 2001.
James Glimm, Xiaolin Li and Yingjie Liu, "Conservative Front Tracking in Higher Space Dimensions". Transactions of Nanjing University of Aeronautics and Astronautics, 18, Suppl., pp1-15, 2001. Proceedings of International Workshop on Computational Methods for Continuum Physics and Their Applications (IWCCPA), Nanjing, China.
James Glimm, Xiao Lin Li, Yingjie Liu and Ning Zhao, "Conservative Front Tracking and Level Set Algorithms". Proc. Natl. Acad. Sci. USA, 98, no. 25, pp14198-14201, 2001. ( pdf ).
Yingjie Liu, "The Fully Polynomial Approximation Algorithm for the 0-1 Knapsack Problem". Theory Comput. Syst., 35 (2002), no. 5, pp559-564. ( pdf ).
James Glimm, Xiaolin Li and Yingjie Liu, "Conservative Front Tracking in One Space Dimension". Fluid flow and transport in porous media: mathematical and numerical treatment (South Hadley, MA, 2001), pp253--264, Contemp. Math., 295, Amer Math Soc, Providence, RI, 2002.
Yingjie Liu, "A Backward Point Shifted Levelset Method for Highly Accurate Interface Computation". CDSNS2002-388, School of Mathematics, Georgia Institute of Technology., Oct., 02.
Todd F. Dupont and Yingjie Liu, "Symmetric Error Estimates for Moving Mesh Galerkin Methods for Advection Diffusion Equations". SIAM J. Numer. Anal., v 40, no. 3, pp914 - 927, 2002. ( pdf ).
James Glimm, Xiaolin Li, Yingjie Liu and Zhiliang Xu, "Unstructured grids in 3D and 4D for time-dependent interface in front tracking with improved accuracy". Proc. 8th Int. Conf. Num. Grid Generation in Comp. Field Simulations, edited by B. K. Soni et al, pp179-188, 2002.
E. George, J. Glimm, J. W. Grove, X. L. Li, Y. J. Liu, Z. L. Xu, and N. Zhao, "Simplification. Conservation and Adaptivity in the Front Tracking Method", Hyperbolic Problems: Theory, Numerics, Applications, edited by T. Y. Hou and E. Tadmor, pp 175-184, 2003.
Yingjie Liu, Randolph E. Bank, Todd F. Dupont, Sonia Garcia and Rafael F. Santos, "Symmetric Error Estimates for Moving Mesh Mixed Methods for Advection-Diffusion Equations". SIAM J. Numer. Anal., v 40, no. 6, pp2270 - 2291, 2003. ( pdf ).
James Glimm, Xiaolin Li, Yingjie Liu, Zhiliang Xu and Ning Zhao, "Conservative Front Tracking with Improved Accuracy". SIAM J. Numer. Anal., v 41, no. 5, pp1926-1947 2003.
Todd F. Dupont and Yingjie Liu, "Back and Forth Error Compensation and Correction Methods for Removing Errors Induced by Uneven Gradients of The Level Set Function", J. Comput. Phys., v 190/1, pp311-324, 2003.
Todd F. Dupont and Yingjie Liu, "An Explanation to the Phenomenon of Coupled First Order Shift of Conservative Quantities During the Interaction of Captured Discontinuities". CDSNS2003-391, School of Mathematics, Georgia Institute of Technology, Mar., 2003.
Todd F. Dupont and Yingjie Liu, "Back and Forth Error Compensation and Correction Methods for Semi-Lagrangian Schemes with Application to Interface Computation Using Level Set Method". CDSNS2004-399, School of Mathematics, Georgia Institute of Technology, Mar., 2004.
Yingjie Liu, "Central Schemes and Central Discontinuous Galerkin Methods on Overlapping Cells", Conference on Analysis, Modeling and Computation of PDE and Multiphase Flow, Stony Brook, NY, August 3-5, 2004. CDSNS2005-404, School of Mathematics, Georgia Institute of Technology.
Yingjie Liu, "Central Schemes on Overlapping Cells", J. Comput. Phys. 209 (2005), 82-104.
Byungmoon Kim, Yingjie Liu, Ignacio Llamas, Jarek Rossignac, "FlowFixer: Using BFECC for Fluid Simulation", Eurographics Workshop on Natural Phenomena 2005. video(DivX)
Byungmoon Kim, Yingjie Liu, Ignacio Llamas, Jarek Rossignac, "Advections with Significantly Reduced Dissipation and Diffusion", IEEE Transactions on Visualization and Computer Graphics, 13 (2007), pp135--144.
Todd F. Dupont and Yingjie Liu, "Back and Forth Error Compensation and Correction Methods for Semi-Lagrangian Schemes with Application to Level Set Interface Computations". Math. Comp., 76 (2007), pp 647--668.
Yingjie Liu, Chi-Wang Shu, Eitan Tadmor and Mengping Zhang, "Central Discontinuous Galerkin Methods on Overlapping Cells with a Non-Oscillatory Hierarchical Reconstruction", SIAM J. Numer. Anal., 45 (2007), pp2442-2467.
Yingjie Liu, Chi-Wang Shu, Eitan Tadmor and Mengping Zhang, "Non-Oscillatory Hierarchical Reconstruction for Central and Finite Volume Schemes", Communications in Computational Physics, 2 (2007), pp. 933-963.
David S. Mebane, Yingjie Liu and Meilin Liu, "A Two-Dimensional Model and Numerical Treatment for Mixed-Conducting Thin Films: The Effect of Sheet Resistance", Journal of the Electrochemical Society, 154 (2007), A421.
Byungmoon Kim, Yingjie Liu, Ignacio Llamas, Xiangmin Jiao, Jarek Rossignac, "Simulation of Bubbles in Foam by Volume Control", ACM SIGGRAPH 2007.
Andrew Selle, Ron Fedkiw, Byungmoon Kim, Yingjie Liu and Jarek Rossignac, "An Unconditionally Stable MacCormack Method", J. Sci. Comput., 35(2008), 350-371.
Yingjie Liu, Chi-Wang Shu, Eitan Tadmor and Mengping Zhang, "L2 stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods ", ESAIM: Mathematical Modelling and Numerical Analysis, 42 (2008), 593--607.
David S. Mebane, Yingjie Liu and Meilin Liu, "Refinement of the Bulk Defect Model for La_xSr_1-xMnO_3+-d.", Solid State Ionics, 178(39-40), (2008), 1950--1957.
Matthew E. Lynch, David S. Mebane, Yingjie Liu and Meilin Liu, "Triple Phase Boundary and Surface Transport in Mixed Conducting Patterned Electrodes", Journal of the Electrochemical Society, 155(6), B635-B643, 2008.
Zhiliang Xu, Yingjie Liu and Chi-Wang Shu, "Hierarchical reconstruction for discontinuous Galerkin methods on unstructured grids with a WENO type linear reconstruction and partial neighboring cells", J. Comput. Phys., 228 (2009), 2194-2212.
Zhiliang Xu, Yingjie Liu and Chi-Wang Shu, "Hierarchical Reconstruction for Spectral Volume Method on Unstructured Grids", J. Comput. Phys., 228 (2009), 5787--5802.
L. O. Baksmaty, Y.-J. Liu, U. Landman, N. P. Bigelow and H. Pu, "Numerical exploration of vortex matter in Bose-Einstein condensates", Mathematics and Computers in Simulation, 80 (2009), 131--138.
Yingjie Liu, Chi-Wang Shu and Zhiliang Xu, "Hierarchical Reconstruction with up to Second Degree Remainder for Solving Nonlinear Conservation Laws", Nonlinearity, 22 (2009), 2799--2812.
Yingjie Liu, Chi-Wang Shu, Eitan Tadmor and Mengping Zhang, "Central local discontinuous Galerkin methods on overlapping cells for diffusion equations", ESAIM: Mathematical Modelling and Numerical Analysis, 45 (2011), 1009--1032.
Yingjie Liu, "Simplified Physics behind a Powerful Forehand Loop in Table Tennis", Table Tennis Magazines, February, 2011, Page 60 (in Chinese).
Zhiliang Xu, Yingjie Liu, Huijing Du, Guang Lin and Chi-Wang Shu, "Point-wise Hierarchical Reconstruction for Discontinuous Galerkin and Finite Volume Methods for Solving Conservation Laws", J. Comput. Phys., 230 (2011), 6843—6865.
Zhiliang Xu, Xu-Yan Chen and Yingjie Liu, "A New Runge-Kutta Discontinuous Galerkin Method with Conservation Constraint to Improve CFL Condition for Solving Conservation Laws", J. Comput. Phys., 278 (2014), 348-377.
Suo Yang, Alexander Kurganov and Yingjie Liu, "Well-Balanced Central Schemes on Overlapping Cells with Constant Subtraction Techniques for the Saint-Venant Shallow Water System", J. Sci Comput., 63 (2015), pp 678-698.
Lili Hu, Yao Li and Yingjie Liu, "A limiting strategy for the back and forth error compensation and correction method for solving advection equations", Math. Comp., 85 (2016), 1263--1280.
Zhiliang Xu, and Yingjie Liu, "New Central and Central Discontinuous Galerkin Schemes on Overlapping Cells of Unstructured Grids for Solving Ideal Magnetohydrodynamic Equations with Globally Divergence-Free Magnetic Field", J. Comput. Phys., 327 (2016), pp 203-224
S. Ashwin Renganathan, Yingjie Liu, and Dimitri N. Mavris, "A Koopman-POD-DEIM based approach to non-intrusive projection based reduced order modeling with black-box high-fidelity models", AIAA Journal, v56, No. 10, (2018), 4087-4111.
Xin Wang and Yingjie Liu, "Back and Forth Error Compensation and Correction Method for Linear Hyperbolic Systems with Application to the Maxwell’s Equations", Journal of Computational Physics: X, 1 (2019), 100014.
Huijing Du, Yingjie Liu, Yuan Liu and Zhiliang Xu, "Well-balanced discontinuous Galerkin method for shallow water equations with constant subtraction techniques on unstructured meshes", J. Sci Comput., 81 (2019), 2115-2131.
Sung Ha Kang, Wenjing Liao and Yingjie Liu, "IDENT: Identifying differential equations with numerical time evolution", J. Sci Comput., 87,1 (2021).
Haoxiang Huang, Yingjie Liu and Vigor Yang, "Neural Networks with Inputs Based on Domain of Dependence and A Converging Sequence for Solving Conservation Laws, Part I: 1D Riemann Problems", arXiv:2109.09316, 20 Sep., 2021.
Yuchen He, Sung Ha Kang, Wenjing Liao, Hao Liu and Yingjie Liu, "Robust Identification of Differential Equations by Numerical Techniques from a Single Set of Noisy Data", SIAM J. Sci. Comput., 44 (2022). arXiv:2006.06557, 11 June, 2020.
Yuchen He, Sung-Ha Kang, Wenjing Liao, Hao Liu and Yingjie Liu, "Numerical Identification of Nonlocal Potentials in Aggregation", Communications in Computational Physics, 32 (2022), 638-670.
Haiyu Zou and Yingjie Liu, "A Finite Difference Method on Irregular Grids with Local Second Order Ghost Point Extension for Solving Maxwell's Equations Around Curved PEC Objects", J. Comput. Phys., 463 (2022), 111273.
Wenbin Dong, Yingjie Liu and Hansong Tang, "Accuracy Enhancing Interface Treatment Algorithm: the Back and Forth Error Compensation and Correction method", J. Sci. Comput., 93, 29 (2022). arXiv:2112.08595, 16 Dec 2021.
Haoxiang Huang, Yingjie Liu and Vigor Yang, "Neural Networks with Local Converging Inputs (NNLCI) for Solving Conservation Laws, Part II: 2D Problems", arXiv:2204.10424, 21 Apr 2022.
Harris Cobb, Hwi Lee and Yingjie Liu, "Solving Maxwell's Equation in 2D with Neural Networks with Local Converging Inputs", arXiv:2302.02860, 6 Feb 2023.
Hwi Lee and Yingjie Liu, "A ghost-point based second order accurate finite difference method on uniform orthogonal grids for electromagnetic scattering around curved perfect electric conductors with corners", J. Comput. Phys., 490 (2023), 112314. https://doi.org/10.1016/j.jcp.2023.112314
Haoxiang Huang, Vigor Yang and Yingjie Liu, "Neural Networks with Local Converging Inputs (NNLCI) for Solving Conservation Laws, Part I: 1D Problems", Commun. Comput. Phys., 34(2), 2023, pp. 290-317. (DOI:10.4208/cicp.OA-2022-0285)
Haoxiang Huang, Vigor Yang and Yingjie Liu, "Neural Networks with Local Converging Inputs (NNLCI) for Solving Conservation Laws, Part II: 2D Problems", Commun. Comput. Phys., 34(4), 2023, pp. 907-933.
Yuchen He, Sung Ha Kang, Wenjing Liao, Hao Liu and Yingjie Liu, "Group Projected subspace pursuit for IDENTification of variable coefficient differential equations (GP-IDENT)", J. Comput. Phys., 494 (2023), pp. 112526.
Weiming Ding, Haoxiang Huang, Tzu Jung Lee, Yingjie Liu and Vigor Yang, "Neural Network with Local Converging Input for Unstructured-Grid Computational Fluid Dynamics", AIAA Journal, 62(8), 2024, pp. 3155-3166. arXiv:2310.15299.
Hwi Lee, Zhen Chao, Harris Cobb, Yingjie Liu and Dexuan Xie, "A PNP ion channel deep learning solver with local neural network and finite element input data", Mach. Learn.: Sci. Technol. 5 (2024), pp. 045001.