23-01 High Order Conservative Lagrangian Scheme for Three-Temperature Radiation Hydrodynamics.. Juan Cheng and Chi-Wang Shu.
23-02 The high order local discontinuous Galerkin Schemes with variable-coefficient explicit-implicit-null time-marching for diffusion and dispersion equations . Meiqi Tan, Juan Cheng, and Chi-Wang Shu.
23-03 A high order positivity-preserving discontinuous Galerkin remapping method based on a moving mesh solver for ALE simulation of the compressible fluid flow. Xiaolu Gu, Juan Cheng, and Chi-Wang Shu.
2022A high order positivity-preserving discontinuous
22-01 A high order positivity-preserving conservative WENO remapping methoon 3D tetrahedral meshes. Nuo Lei, Juan Cheng and Chi-Wang Shu.
22-02 Local Discontinuous Galerkin Method for the carpet cloak model Xinyue Yu, Lichun Li, and Chi-Wang Shu.
22-03 Moment-based multi-resolution HWENO scheme for hyperbolic conservation laws Jiayin Li , Chi-Wang Shu and Jianxian Qiu.
22-04 Stability of high order finite difference and local discontinuous Galerkin schemes with explicit-implicit-null time-marching for high order dissipative and dispersive equations . Meiqi Tan, Juan Cheng , and Chi-Wang Shu.
22-05 High order conservative positivity-preserving discontinuous Galerkin method for stationary hyperbolic equations. Ziyao Xu and Chi-Wang Shu.
22-06 Provably positive central DG schemes via geometric quasilinearization for ideal MHD equations. Kailiang Wu, Haili Jiang and Chi-Wang Shu.
22-07 Discontinuous Galerkin methods for stochastic Maxwell equations with multiplicative noise. Jiawei Sun, Chi-Wang Shu, and Yulong Xin.
22-08 A high order positivity-preserving conservative WENO remapping method Xiaolu Gu, Juan Cheng, Yue Li, and Chi-Wang Shu.
22-09A new type of simplified inverse Lax-Wendroff Boundary Treatment for hyperbolic conservation laws. Shihao Liu, Tingting Li, Ziqiang Cheng, Yan Jiang, Chi-Wang Shu and Mengping Zhang.
22-10 Uniform Stability for Local Discontinuous Galerkin Methods with Implicit-Explicit Runge-Kutta Time Discretizations fo Linear Convection-Diffusion Equation. Haijin Wang, Fengyan Li, Chi-Wang Shu and Qiang Zhang
22-11 Third order maximum-principle-satisfying and positivity-preserving Lax-Wendroff. Ziyao Xu and Chi-Wang Shu.
22-12 A high order positivity-preserving polynomial projection remapping method. Nuo Lei, Juan Cheng and Chi-Wang Shu.
22-13 An entropy stable oscillation-free discontinuous Galerkin method Yong Liu, Jianfang Lu, and Chi-Wang Shu.
22-14 On the conservation of positivity-preserving discontinuous Galerkin methods for stationary hyperbolic equations. Ziyao Xu and Chi-Wang Shu.
22-15 Stability of spectral collocation schemes with explicit-implicit-null time-marching for convection-diffusion and convection-dispersion equations . Meiqi Tan, Juan Cheng, and Chi-Wang Shu.
22-16 RKDG methods with multi-resolution WENO limiter for solving steady-state problems on triangular meshes . Jun Zhu, Chi-Wang Shu and Jianxian Qiu.
22-17 Boundedly rational continuum users model for simultaneous departure and route choice in traffic assignment problems. Liangze Yang, Jie Du, S. C. Wong, Chi-Wang Shu.
22-18 Local characteristic decomposition free high order finite difference WENO schemes for hyperbolic systems endowed with a coordinate system of Riemann invariants. Ziyao Xu and Chi-Wang Shu
21-01 Geometric quasilinearization framework for analysis and design of bound-preserving schemes, Kailiang Wu and Chi-Wang Shu.
21-02 Local discontinuous Galerkin methods for diffusive-viscous wave equations (1), Dan Ling, Chi-Wang Shu, Wenjing Yan.
21-03 A high order moving boundary treatment for convection-diffusion equations, Shihao Liu, Yan Jiang, Chi-Wang Shu, Mengping Zhang and Shuhai Zhang.
21-04 Multi-symplectic discontinuous Galerkin methods for the stochastic Maxwell equations with additive noise, Jiawei Sun, Chi-Wang Shu, Yulong Xing.
21-05 High order entropy stable and positivity-preserving discontinuous Galerkin method for the nonlocal electron heat transport model. Nuo Lei , Juan Cheng and Chi-Wang Shu.
21-06 A fixed point fast sweeping WENO method with inverse Lax-Wendroff boundary treatment for steady state of hyperbolic conservation laws. Liang Li, Chi-Wang Shu, Yang-Tao Zhang.
21-07 L2 Error Estimate to Smooth Solutions for High Order Runge-Kutta Discontinuous Galerkin Method for Scalar Nonlinear Conservation Laws with and without Sonic Points. Jingqi Ai, Yuan Xu, Chi-Wang Shu and Qiang Zhang.
21-08 Optimal error estimates to s mooth solution of the central discontinuous Galerkin methods for nonlinear scalar conservation laws Mengjiao Jiao , Yan Jiang, Chi-Wang Shu and Mengping Zhang.
21-09 An improved simple WENO limiter for discontinuous Galerkin methods solving hyperbolic systems on unstructured meshes. Jie Du, Chi-Wang Shu and Xinghui Zhong.
21-10 An Oscillation-Free Discontinuous Galerkin Method for Hyperbolic Systems. Young Liu, Jianfang Lu, and Chi-Wang Shu.
21-11 Multi-layer perceptron estimator for the total variation bounded constant in limiters for discontinuous Galerkin methods. Xinyue Yu and Chi-Wang Shu.
21-12 Stability Analysis of Inverse Lax-Wendroff Boundary Treatment of High Order Compact Difference Schemes for Parabolic Equations. Tingting Li, Jianfang Lu, and Chi-Wang Shu.
20-01 Development and analysis of two new finite element schemes for a time-domain carpet cloak model, Jichun Li and Chi-Wang Shu.
20-02 Multi-resolution HWENO schemes for hyperbolic conservation laws Jiayin Li1 , Chi-Wang Shu, and Jianxian Qiu
20-03 A high order conservative finite difference scheme for compressible two-medium flows. Feng Zheng , Chi-Wang Shu and Jianxian Qiu
20-04 Stability of high order finite difference schemes with implicit-explicit time-marching for convection-diffusion and convection-dispersion equations Meiqi Tan, Juan Cheng, and Chi-Wang Shu
20-05 Higher-order Runge-Kutta Discontinuous Galerkin methods with milti-resolution WENO limiters for solving steady-state problems. Jun Zhu, Chi-Wang Shu and Jianxian Qiu.
20-06 An Oscillation-Free Discontinuous Galerkin Method for Scalar Hyperbolic Conservation Laws. Jianfang Lu, Yong Liu, and Chi-Wang Shu.
20-07 High-order Runge-Kutta Discontinuous Galerkin methods with a new type of multi-resolution WENO limiters on tetrahedral meshes. Jun Zhu, Chi-Wang Shu and Jianxian Qiu
20-08 Well-posedness and H (div)-conforming finite element approximation of a linearized model for inviscid incompressible flow. G Barrenechea, E Burman, J Guzman
20-09 Convergence of Lagrange finite elements for the Maxwell Eigenvalue Problem in 2D. D Boffi, J Guzman, M Neilan
20-10 Obtaining higher-order Galerkin accuracy when the boundary is polygonally approximated. T Dupont, J Guzman, R Scott
20.11 Exact sequences on Powell–Sabin splits. J Guzmán, A Lischke, M Neilan. Calcolo 57 (2), 1-25
20-12 On the convergence and generalization of physics informed neural networks
Y Shin, J Darbon, GE Karniadakis
20-13 Fractional phase-field crystal modelling: analysis, approximation and pattern formation. IMA Journal of Applied Mathematics 85 (2), 231-262, 2020. M Ainsworth, Z Mao
20-14 On some neural network architectures that can represent viscosity solutions of certain high dimensional Hamilton–Jacobi partial differential equations. J Darbon, T Meng
20-15 On Bayesian posterior mean estimators in imaging sciences and Hamilton-Jacobi Partial Differential Equations. J Darbon, GP Langlois
20-16 On some neural network architectures that can represent viscosity solutions of certain high dimensional Hamilton–Jacobi partial differential equations. February 2020, submitted. J. Darbon, T. Meng.
20-17 “What is the fractional Laplacian?“, J. Comput. Phys., Vol. 404, pp. 109009, 2020. A. Lischke, G. Pang, M. Gulian, F. Song, C. Glusa, X. Zheng, Z. Mao, W. Cai, M. M. Meerschaert, M. Ainsworth, G. E. Karniadakis
20-18 A stabilized semi-implicit Fourier spectral method for nonlinear space-fractional reaction-diffusion equations, Journal of Computational Physics 405, 10914, 2020. H Zhang, X Jiang, F Zeng, GE Karniadakis,
20-19 Extraction of mechanical properties of materials through deep learning from instrumented indentation, Proceedings of the National Academy of Sciences, March 16, 2020. L Lu, M Dao, P Kumar, U Ramamurty, GE Karniadakis, S Suresh
20-20 Physics-informed neural networks for high-speed flows, Computer Methods in Applied Mechanics and Engineering 360, 112789, 2020. Z Mao, AD Jagtap, GE Karniadakis
20-21 Adaptive activation functions accelerate convergence in deep and physics-informed neural networks, Journal of Computational Physics 404, 109136, 2020. AD Jagtap, K Kawaguchi, GE Karniadakis
20-22 Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations, Science 367 (6481), 1026-1030, 2020. M Raissi, A Yazdani, GE Karniadakis
20-23 Multiscale Modeling Meets Machine Learning: What Can We Learn?, Archives of Computational Methods in Engineering, 1-2, 2020. GCY Peng, M Alber, AB Tepole, WR Cannon, S De, GE Karniadakis, E. Kuhl
20-24 A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems, Journal of Computational Physics 401, 109020, 2020. X Meng, GE Karniadakis
20-25 Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations, SIAM Journal on Scientific Computing 42 (1), A292-A317, 2020. L Yang, D Zhang, GE Karniadakis
20-26 Learning in modal space: Solving time-dependent stochastic PDEs using physics-informed neural networks, SIAM Journal on Scientific Computing 42 (2), A639-A665, 2020. D Zhang, L Guo, GE Karniadakis
20-27 An inverse Lax-Wendroff procedure for hyperbolic conservation laws with changing wind direction on the boundary. Jianfang Lu, Chi-Wang Shu, Sirui Tan, and Mengping Zhang
20-28 Weighted ghost fluid discontiuous Galerkin method for multi-medium problems. Yun-Long Liu, Chi-Wang Shu, and A-Man Zhang
20-29 Central discontinuous Galerkin methods on overlapping meshes for wave equations. Yong Liu, Jianfang Lu, Chi-Wang Shu and Mengping Zhang
20-30 A high order positivity-preserving conservative WENO remapping method on 2D quadrilateral meshes Nuo Lei, Juan Cheng and Chi-Wang Shu
20-31 High-order Runge-Kutta discontinuous Galerkin methods with a new type of multi-resolution WENO limiters on triangular meshes. Jun Zhu, Chi-Wang Shu and Jianxian Qiu
20-32 Dissipative and conservative local discontinuous Galerkin methods for the Fornberg-Whitham type equations. Qian Zhang, Yan Xu, Chi-Wang Shu
20-33 Provably Physical-Constraint-Preserving Discontinuous Galerkin Methods for Multidimensional Relativistic MHD Equations. Kailiang Wu and Chi-Wang Shu
20-34 A discontinuous Galerkin method and its error estimate for nonlinear fourth-order wave equations. Qi Tao, Yan Xu, and Chi-Wang Shu
20-35 On the conservation of finite difference WENO schemes in non-rectangular domains using the inverse Lax-Wendroff boundary treatments. Shengrong Ding, Chi-Wang Shu and Mengping Zhang
20-36 Essentially non-oscillatory and weighted essentially non-oscillatory schemes. Chi-Wang Shu
20-37 Error analysis of Runge–Kutta discontinuous Galerkin methods for linear time-dependent partial differential equations. Zheng Sun and Chi-Wang Shu
20-38 Sub-optimal convergence of discontinuous Galerkin methods with centralfluxes for even degree polynomial approximations. Yong Liu, Chi-Wang Shu and Mengping Zhang
20-39 Superconvergence Analysis of the Runge-Kutta Discontinuous Galerkin Methods for a Linear Hyperbolic Equation. Yuan Xu, Xiong Meng, Chi-Wang Shu, and Qing Zhang
19-01 New stability estimates for an unfitted finite element method for two-phase Stokes problem. E Cáceres, J Guzmán, M Olshanskii
19-02 L2-Error estimates for H(div)-conforming schemes applied to a linearised model of inviscid incompressible flow. G Barrenechea, E Burman, J Guzmàn
19-03 Stability and error analysis of a splitting method using Robin-Robin coupling applied to a fluid-structure interaction problem. E Burman, R Durst, J Guzman
19-04 Overcoming the curse of dimensionality for some Hamilton–Jacobi partial differential equations via neural network architectures J Darbon, GP Langlois, T Meng
19-05 Optimal trajectories of a UAV base station using Lagrangian mechanics
Coupechoux, J Darbon, JM Kélif, M Sigelle
19-06 On decomposition models in imaging sciences and multi-time Hamilton-Jacobi partial differential equations. J Darbon, T Meng
19-07 High order conservative Lagrangian schemes for one-dimensional radiative hydrodynamics equations in the equilibrium limit. Juan Cheng, Chi-Wang Shu and Peng Song.
19-08 An ultra-weak DG method with IMEX time-marching for generalized stochastic KdV equations. Yunzhang Li, Chi-Wang Shu, Shanjian Tang.
19-09 On moving mesh WENO schemes with characteristic boundary conditions for Hamilton_Jacobi equations. Yue Li, Juan Cheng, Yinhua Xia and Chi-Wang Shu.
19-10 A new type of third-order finite volume multi-resolution WENO schemes on tetrahedral meshes. Jun Zhu and Chi-Wang Shu.
19-11 Error estimate of the fourth Runge-Kutta Discontinuous Galerkin Methods for Linear Hyperbolic Equations. Yuan Xu, Chi-Wang Shu and Qiang Zhang.
19-12 Entropy Symmetrization and High-Order Accurate Entropy Stable Numberical Schemes for Relativistic MHD Equations. Kailiang Wu and Chi-Wang Shu.
19.13 Optimal Error Estimates of the Semidiscrete Discontinuous Galerkin Methods for Two Dimentional Hyperbolic Equations on Cartesian Meshes using Pk Elements. Young Liu, Chi-Wang Shu, and Mengping Zhang.
19-14 High-order Runge-Kutta discontinuous Galerkin methods with a new type of multi-resolution WENO limiters. Jun Zhu, Jianxian Qiu, and Chi-Wang Shu.
19-15 Assessment of aeroacoustic resolution properties of DC schemes and comparison with DRP schemes. Ziqiang Chang, Jinwei Fang, Chi-Wang Shu and Mengping Zhang.
19-16 Review of entropy stable discontinuous Galerkin methods for Systems of conservation laws on unstructured simplex meshes. Tianheng Chen and Chi-Wang Shu.
19-17 A local discontinuous Galerkin method for nonlinear parabolic SPDEs. Yuzhang Li, Chi-Wang Shu, Shanjian Tang.
19-18 Convergence to steady-state solutions of the new type of high-order multi-resolution WENO schemes: a numerical study. Jun Zu and Chi-Wang Shu.
19-19 A brief review on the convergence to steady state solutions of Euler equations with high-order WENO schemes. Shuhai Zhang, Jun Zhu, and Chi-Wang Shu.
19-20 An ultraweak-local discontinuous Galerkin method for PDEs with high order spati-l derivatives. Qi Tao, Yan Xu, Chi-Wang Shu.
19-21 High order arbitrary Lagrangian-Eulerian finite difference WENO scheme for Hamilton-Jacobi equations. Yue Li, Juan Cheng, Yinhua Xia and Chi-Wang Shu.
19-22. A new type of multi-resolution WENO schemes with increasingly higher order of accuracy on triangular meshes. Jun Zhu and Chi-Wang Shu.
19-23 A Discontinuous Galerkin Method for Stochastic Conservation Laws. Yunzhang Li, Chi-Wang Shu, and Shanjian Tang.
19-24 A dynamic continuum modeling approach to the spatial analysis of air quality and housing location choice in a polycentric city. Liangze Yang, S. C. Wong, Mengping Zhang and Chi-Wang Shu.
19-25 Certified offline-free reduced basis (COFRB) methods for stochastic differential equations driven by arbitrary types of noise. Yong Liu, Tianheng Chen, Yanlai Chen and Chi-Wang Shu.
19-26 Analysis of optimal superconvergence of an ultraweak-local discontinuous Galerkin method for a time dependent fourth-order equation. Yong Liu, Qi Tao and Chi-Wang Shu.
18-01 Towards an efficient finite element method for the integral fractional Laplacian on polygonal domains. M Ainsworth, C Glusa
18-02 Hybrid Finite Element–Spectral Method for the Fractional Laplacian: Approximation Theory and Efficient Solver. M Ainsworth, C Glusa
18-03 The Resiliency of Multilevel Methods on Next Generation Computing Platforms: Probabilistic Model and Its Analysis. CA Glusa, M Ainsworth
18-04 A view from ORNL: Scientific data research opportunities in the big data age. S Klasky, M Wolf, M Ainsworth, C Atkins, J Choi, G Eisenhauer, B Geveci, et al.
18-05 Fully computable a posteriori error bounds for hybridizable discontinuous Galerkin finite element approximations. M Ainsworth, G Fu
18-06 Coupling exascale multiphysics applications: Methods and lessons learned. JY Choi, CS Chang, J Dominski, S Klasky, G Merlo, E Suchyta, et al.
19-07 Multilevel techniques for compression and reduction of scientific data—the univariate case. M Ainsworth, O Tugluk, B Whitney, S Klasky
19-08 Bernstein-Bezier bases for tetrahedral finite elements, Mark Ainsworth and Guosheng Fu.
18-09 Implicit-explicit local discontinuous Galerkin methods with generalized alternating numerical fluxes for convection-diffusion problems. Haijin Wang, Qiang Zhang, Chi-Wang Shu.
18-10 The L2-norm stability analysis of Runge-Kutta discontinuous Galerkin methods for linear hyperbolic equations. Yuan Xu, Qiang Zhang, Chi-Wang Shu, and Haijin Wang.
18-11 Well-balanced finite volume schemes for hydrodynamic equations with general free energy. Jose A. Carrillo, Serafim Kalliadasis, Sergio P. Perez, and Chi-Wang Shu.
18-12 Strong stability of explicit Runge-Kutta Time Discretizations. Zheng Sun and Chi-Wang Shu.
18-13 An entropy stable high-order discontinuous Galerkin method for cross-diffusion in gradient flow systems. Zheng Sun, Jose A. Carrillo and Chi-Wang Shu.
18-14 High order finite difference Hermite WENO schemes for the Hamilton-Jacobi equations on unstructured meshes. Feng Zheng, Chi-Wang Shu and Jianxian Qiu.
18-15 A third-order unconditionally positivity-preserving scheme for production-destruction equations with applications to non-equilibrium flows. Jantao Huang, Weifeng Zhao, and Chi-Wang Shu.
18-16 Completed Repeated Richarson Extrapolation for compressible fluid flows. Nicholas Dicati Pereira da Silva, Carlos Henrique Marchi, Luciano, Kiyoshi, Rafael Brandao de Rezende Borges, Guilherme Bertoldo, Chi-Wang Shu.
18-17 Provably Positive High-Order Schemes for IdealMagnetohydrodynamics: Analysis on General Meshes. Kailiang Wu and Chi-Wang Shu.
18-18 A new type of multi-resolution WENO schemes with increasingly higher order of accuracy. Jun Zhu and Chi-Wang Shu.
18-19 Locally divergence-free spectral-DG methods for ideal magnetohydrodynamic equations on cylindrical coordinates. Yong Liu, Qingyuan Liu, Yuan Liu, Chi-Wang Shu and Mengping Zhang.
18-20 Superconvergence of energy-conserving discontinuous Galerkin methods for linear hyperbolic equations. Young Liu, Chi-Wang Shu and Mengping Zhang.
18-21 Positivity-preserving time discretizations for production-destruction equations with applications to non-equilibrium flows. Juntao Huang and Chi-Wang Shu.
18-22 An energy-conserving ultra-weak discontinuous Galerkin Method for the generalized Korteweg-De Vries Equation. Guosheng Fu and Chi-Wang Shu.
18-23 Optimal energy-conserving discontinuous Galerkin methods for linear symmetric hyperbolic systems. Guosheng Fu and Chi-Wang Shu.
18-24 Modeling and simulation of urban air pollution from the dispersion of vehicle exhaust: A continuum modeling approach. Liangze Yang, Tingting Li, S.C. Wong, Chi-Wang Shu, Mengping Zhang.
18-25 Numerical solutions of stochastic PDEs driven by arbitrary type of noise. Tianheng Chen, Boris Rozovskii and Chi-Wang Shu.
18-26 Stability analysis and error estimates of arbitrary Lagragian-Eulerian discontinuous Galerkin method coupled with Runge-Kutta time-marching for linear conservation laws. Lingling Zhou, Yinhua Xia and Chi Wang Shu.
18-27 Provably positive discontinuous Galerkin methods for multidimensional ideal magnetohydrodynamics. Kailiang Wu and Chi-Wang Shu.
18-28 Local discontinuous Galerkin methods with explicit-implicit-null time discretizations for solving nonlinear diffusion problems. Haijin Wang, Qiang Zhang, Shiping Wang, and Chi-Wang Shu.
18-29 Discontinuous Galerkin methods for Maxwell’s equations in Drude metamaterials on unstructured meshes. Cengke Shi, Lichun Li and Chi-Wang Shu.
18-30 Conservative high order positivity-preserving discontinuous Galerkin methods for linear hyperbolic and radiative transfer equations. Dan Ling, Juan Cheng, Chi-Wang Shu.
18-31 Third order implicit-explicit Runge-Kutta local discontinuous Galerkin methods with suitable boundary treatment for convection-diffusion problems with Dirichlet boundary conditions. Haijin Wang, Qiang Zhang, Chi-Wang Shu.