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.
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. video
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.