Edit Profile (opens in new tab) Wu, Kailiang Co-Author Distance Author ID: wu.kailiang Published as: Wu, Kailiang Documents Indexed: 61 Publications since 1997, including 11 Additional arXiv Preprints Co-Authors: 31 Co-Authors with 47 Joint Publications 923 Co-Co-Authors all top 5 Co-Authors 4 single-authored 14 Xiu, Dongbin 13 Tang, Huazhong 6 Shu, Chi-Wang 5 Ding, Shengrong 3 Qin, Tong 2 Chen, Zhen 2 Cui, Shumo 2 Fuerst, S. V. 2 Jiang, Haili 2 Qiu, Jianxian 2 Shin, Yeonjong 2 Sun, Zheng 2 Xing, Yulong 2 Yang, Zhicheng 1 Abriak, Nor-Edine 1 Becquart, F. 1 Cai, Chaoyi 1 Chen, Junfeng 1 Chen, Yaping 1 Chertock, Alina E. 1 Churchill, Victor 1 Czulak, A. 1 Felten, C. J. 1 Fuller, Mark E. 1 He, Zhihai 1 Hou, Jun 1 Kithes, A. G. 1 Kuang, Yangyu 1 Kurganov, Alexander 1 Liu, Joseph T. C. 1 Peng, Manting 1 Pizette, Patrick 1 Redle, Michael 1 Rémond, Sébastien 1 Ren, Yupeng 1 Wang, Jiangfu 1 Wei, Yuanzhe 1 Xiong, Tao 1 Xu, Linfeng 1 Zhang, Ce 1 Zhong, Xinghui all top 5 Serials 17 Journal of Computational Physics 8 SIAM Journal on Scientific Computing 3 SIAM Journal on Numerical Analysis 2 Astronomy and Astrophysics 2 Numerische Mathematik 2 Journal of Scientific Computing 2 Communications on Applied Mathematics and Computation 1 Archives of Mechanics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Theoretical Computer Science 1 Computational Mechanics 1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 1 SIAM Review 1 Archive of Applied Mechanics 1 Waves in Random and Complex Media 1 Communications in Computational Physics 1 Numerical Mathematics: Theory, Methods and Applications 1 East Asian Journal on Applied Mathematics 1 AMM. Applied Mathematics and Mechanics. (English Edition) all top 5 Fields 42 Numerical analysis (65-XX) 28 Fluid mechanics (76-XX) 24 Partial differential equations (35-XX) 6 Computer science (68-XX) 4 Dynamical systems and ergodic theory (37-XX) 3 Approximations and expansions (41-XX) 3 Relativity and gravitational theory (83-XX) 3 Astronomy and astrophysics (85-XX) 2 Statistics (62-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Ordinary differential equations (34-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) 1 Statistical mechanics, structure of matter (82-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 37 Publications have been cited 447 times in 217 Documents Cited by ▼ Year ▼ Data driven governing equations approximation using deep neural networks. Zbl 1455.65125 Qin, Tong; Wu, Kailiang; Xiu, Dongbin 54 2019 High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics. Zbl 1349.76550 Wu, Kailiang; Tang, Huazhong 42 2015 Data-driven deep learning of partial differential equations in modal space. Zbl 07505629 Wu, Kailiang; Xiu, Dongbin 39 2020 Positivity-preserving analysis of numerical schemes for ideal magnetohydrodynamics. Zbl 1391.76369 Wu, Kailiang 32 2018 Numerical aspects for approximating governing equations using data. Zbl 1451.65008 Wu, Kailiang; Xiu, Dongbin 27 2019 A provably positive discontinuous Galerkin method for multidimensional ideal magnetohydrodynamics. Zbl 1404.65184 Wu, Kailiang; Shu, Chi-Wang 27 2018 Provably positive high-order schemes for ideal magnetohydrodynamics: analysis on general meshes. Zbl 1419.76446 Wu, Kailiang; Shu, Chi-Wang 24 2019 Admissible states and physical-constraints-preserving schemes for relativistic magnetohydrodynamic equations. Zbl 1371.76096 Wu, Kailiang; Tang, Huazhong 23 2017 A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty. Zbl 1380.65315 Wu, Kailiang; Tang, Huazhong; Xiu, Dongbin 18 2017 Entropy symmetrization and high-order accurate entropy stable numerical schemes for relativistic MHD equations. Zbl 1450.65089 Wu, Kailiang; Shu, Chi-Wang 16 2020 Desingularized meshless method for solving Laplace equation with over-specified boundary conditions using regularization techniques. Zbl 1165.65073 Chen, K. H.; Kao, J. H.; Chen, J. T.; Wu, K. L. 15 2009 A third-order accurate direct Eulerian GRP scheme for the Euler equations in gas dynamics. Zbl 1349.76551 Wu, Kailiang; Yang, Zhicheng; Tang, Huazhong 14 2014 Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics. Zbl 1349.76408 Wu, Kailiang; Tang, Huazhong 13 2014 Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations. Zbl 1480.65271 Wu, Kailiang; Shu, Chi-Wang 13 2021 A third-order accurate direct Eulerian GRP scheme for one-dimensional relativistic hydrodynamics. Zbl 1309.76145 Wu, Kailiang; Yang, Zhicheng; Tang, Huazhong 12 2014 A direct Eulerian GRP scheme for spherically symmetric general relativistic hydrodynamics. Zbl 1419.76468 Wu, Kailiang; Tang, Huazhong 12 2016 Minimum principle on specific entropy and high-order accurate invariant-region-preserving numerical methods for relativistic hydrodynamics. Zbl 1500.65073 Wu, Kailiang 10 2021 Uniformly high-order structure-preserving discontinuous Galerkin methods for Euler equations with gravitation: positivity and well-balancedness. Zbl 1466.65150 Wu, Kailiang; Xing, Yulong 10 2021 Deep neural network modeling of unknown partial differential equations in nodal space. Zbl 07524779 Chen, Zhen; Churchill, Victor; Wu, Kailiang; Xiu, Dongbin 9 2022 Structure-preserving method for reconstructing unknown Hamiltonian systems from trajectory data. Zbl 1462.65219 Wu, Kailiang; Qin, Tong; Xiu, Dongbin 8 2020 On physical-constraints-preserving schemes for special relativistic magnetohydrodynamics with a general equation of state. Zbl 1394.65149 Wu, Kailiang; Tang, Huazhong 7 2018 A randomized tensor quadrature method for high dimensional polynomial approximation. Zbl 1373.65012 Wu, Kailiang; Shin, Yeonjong; Xiu, Dongbin 5 2017 Runge-Kutta discontinuous local evolution Galerkin methods for the shallow water equations on the cubed-sphere grid. Zbl 1399.65255 Kuang, Yangyu; Wu, Kailiang; Tang, Huazhong 4 2017 A physical-constraint-preserving finite volume WENO method for special relativistic hydrodynamics on unstructured meshes. Zbl 07561075 Chen, Yaping; Wu, Kailiang 4 2022 Sequential function approximation with noisy data. Zbl 1415.65035 Shin, Yeonjong; Wu, Kailiang; Xiu, Dongbin 4 2018 A WENO-based stochastic Galerkin scheme for ideal MHD equations with random inputs. Zbl 1473.65217 Wu, Kailiang; Xiu, Dongbin; Zhong, Xinghui 3 2021 Geometric quasilinearization framework for analysis and design of bound-preserving schemes. Zbl 1527.65082 Wu, Kailiang; Shu, Chi-Wang 3 2023 Sequential function approximation on arbitrarily distributed point sets. Zbl 1380.65034 Wu, Kailiang; Xiu, Dongbin 2 2018 Discrete mechanics and the finite element method. Zbl 1068.70500 Chen, J.-B.; Guo, H.-Y.; Wu, K. 2 2003 Radiation transfer of emission lines in curved space-time. Zbl 1062.85007 Fuerst, S. V.; Wu, K. 2 2004 A Newton multigrid method for steady-state shallow water equations with topography and dry areas. Zbl 1367.76037 Wu, Kailiang; Tang, Huazhong 2 2016 Methods to recover unknown processes in partial differential equations using data. Zbl 1455.65159 Chen, Zhen; Wu, Kailiang; Xiu, Dongbin 2 2020 Positivity-preserving well-balanced central discontinuous Galerkin schemes for the Euler equations under gravitational fields. Zbl 07536787 Jiang, Haili; Tang, Huazhong; Wu, Kailiang 2 2022 On energy laws and stability of Runge-Kutta methods for linear seminegative problems. Zbl 1502.65143 Sun, Zheng; Wei, Yuanzhe; Wu, Kailiang 2 2022 Provably positive central discontinuous Galerkin schemes via geometric quasilinearization for ideal MHD equations. Zbl 1516.65102 Wu, Kailiang; Jiang, Haili; Shu, Chi-Wang 2 2023 High order asymptotic preserving finite difference WENO schemes with constrained transport for MHD equations in all sonic Mach numbers. Zbl 07696996 Chen, Wei; Wu, Kailiang; Xiong, Tao 2 2023 Line emission from optically thick relativistic accretion tori. Zbl 1141.85002 Fuerst, S. V.; Wu, K. 1 2007 Geometric quasilinearization framework for analysis and design of bound-preserving schemes. Zbl 1527.65082 Wu, Kailiang; Shu, Chi-Wang 3 2023 Provably positive central discontinuous Galerkin schemes via geometric quasilinearization for ideal MHD equations. Zbl 1516.65102 Wu, Kailiang; Jiang, Haili; Shu, Chi-Wang 2 2023 High order asymptotic preserving finite difference WENO schemes with constrained transport for MHD equations in all sonic Mach numbers. Zbl 07696996 Chen, Wei; Wu, Kailiang; Xiong, Tao 2 2023 Deep neural network modeling of unknown partial differential equations in nodal space. Zbl 07524779 Chen, Zhen; Churchill, Victor; Wu, Kailiang; Xiu, Dongbin 9 2022 A physical-constraint-preserving finite volume WENO method for special relativistic hydrodynamics on unstructured meshes. Zbl 07561075 Chen, Yaping; Wu, Kailiang 4 2022 Positivity-preserving well-balanced central discontinuous Galerkin schemes for the Euler equations under gravitational fields. Zbl 07536787 Jiang, Haili; Tang, Huazhong; Wu, Kailiang 2 2022 On energy laws and stability of Runge-Kutta methods for linear seminegative problems. Zbl 1502.65143 Sun, Zheng; Wei, Yuanzhe; Wu, Kailiang 2 2022 Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations. Zbl 1480.65271 Wu, Kailiang; Shu, Chi-Wang 13 2021 Minimum principle on specific entropy and high-order accurate invariant-region-preserving numerical methods for relativistic hydrodynamics. Zbl 1500.65073 Wu, Kailiang 10 2021 Uniformly high-order structure-preserving discontinuous Galerkin methods for Euler equations with gravitation: positivity and well-balancedness. Zbl 1466.65150 Wu, Kailiang; Xing, Yulong 10 2021 A WENO-based stochastic Galerkin scheme for ideal MHD equations with random inputs. Zbl 1473.65217 Wu, Kailiang; Xiu, Dongbin; Zhong, Xinghui 3 2021 Data-driven deep learning of partial differential equations in modal space. Zbl 07505629 Wu, Kailiang; Xiu, Dongbin 39 2020 Entropy symmetrization and high-order accurate entropy stable numerical schemes for relativistic MHD equations. Zbl 1450.65089 Wu, Kailiang; Shu, Chi-Wang 16 2020 Structure-preserving method for reconstructing unknown Hamiltonian systems from trajectory data. Zbl 1462.65219 Wu, Kailiang; Qin, Tong; Xiu, Dongbin 8 2020 Methods to recover unknown processes in partial differential equations using data. Zbl 1455.65159 Chen, Zhen; Wu, Kailiang; Xiu, Dongbin 2 2020 Data driven governing equations approximation using deep neural networks. Zbl 1455.65125 Qin, Tong; Wu, Kailiang; Xiu, Dongbin 54 2019 Numerical aspects for approximating governing equations using data. Zbl 1451.65008 Wu, Kailiang; Xiu, Dongbin 27 2019 Provably positive high-order schemes for ideal magnetohydrodynamics: analysis on general meshes. Zbl 1419.76446 Wu, Kailiang; Shu, Chi-Wang 24 2019 Positivity-preserving analysis of numerical schemes for ideal magnetohydrodynamics. Zbl 1391.76369 Wu, Kailiang 32 2018 A provably positive discontinuous Galerkin method for multidimensional ideal magnetohydrodynamics. Zbl 1404.65184 Wu, Kailiang; Shu, Chi-Wang 27 2018 On physical-constraints-preserving schemes for special relativistic magnetohydrodynamics with a general equation of state. Zbl 1394.65149 Wu, Kailiang; Tang, Huazhong 7 2018 Sequential function approximation with noisy data. Zbl 1415.65035 Shin, Yeonjong; Wu, Kailiang; Xiu, Dongbin 4 2018 Sequential function approximation on arbitrarily distributed point sets. Zbl 1380.65034 Wu, Kailiang; Xiu, Dongbin 2 2018 Admissible states and physical-constraints-preserving schemes for relativistic magnetohydrodynamic equations. Zbl 1371.76096 Wu, Kailiang; Tang, Huazhong 23 2017 A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty. Zbl 1380.65315 Wu, Kailiang; Tang, Huazhong; Xiu, Dongbin 18 2017 A randomized tensor quadrature method for high dimensional polynomial approximation. Zbl 1373.65012 Wu, Kailiang; Shin, Yeonjong; Xiu, Dongbin 5 2017 Runge-Kutta discontinuous local evolution Galerkin methods for the shallow water equations on the cubed-sphere grid. Zbl 1399.65255 Kuang, Yangyu; Wu, Kailiang; Tang, Huazhong 4 2017 A direct Eulerian GRP scheme for spherically symmetric general relativistic hydrodynamics. Zbl 1419.76468 Wu, Kailiang; Tang, Huazhong 12 2016 A Newton multigrid method for steady-state shallow water equations with topography and dry areas. Zbl 1367.76037 Wu, Kailiang; Tang, Huazhong 2 2016 High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics. Zbl 1349.76550 Wu, Kailiang; Tang, Huazhong 42 2015 A third-order accurate direct Eulerian GRP scheme for the Euler equations in gas dynamics. Zbl 1349.76551 Wu, Kailiang; Yang, Zhicheng; Tang, Huazhong 14 2014 Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics. Zbl 1349.76408 Wu, Kailiang; Tang, Huazhong 13 2014 A third-order accurate direct Eulerian GRP scheme for one-dimensional relativistic hydrodynamics. Zbl 1309.76145 Wu, Kailiang; Yang, Zhicheng; Tang, Huazhong 12 2014 Desingularized meshless method for solving Laplace equation with over-specified boundary conditions using regularization techniques. Zbl 1165.65073 Chen, K. H.; Kao, J. H.; Chen, J. T.; Wu, K. L. 15 2009 Line emission from optically thick relativistic accretion tori. Zbl 1141.85002 Fuerst, S. V.; Wu, K. 1 2007 Radiation transfer of emission lines in curved space-time. Zbl 1062.85007 Fuerst, S. V.; Wu, K. 2 2004 Discrete mechanics and the finite element method. Zbl 1068.70500 Chen, J.-B.; Guo, H.-Y.; Wu, K. 2 2003 all cited Publications top 5 cited Publications all top 5 Cited by 391 Authors 31 Wu, Kailiang 21 Tang, Huazhong 14 Xiu, Dongbin 13 Shu, Chi-Wang 9 Duan, Junming 5 Li, Jiequan 4 Chen, Zhen 4 Narayan, Akil C. 4 Tartakovsky, Daniel M. 4 Xing, Yulong 3 Bhoriya, Deepak 3 Chen, Yaping 3 Churchill, Victor 3 Ding, Shengrong 3 Don, Wai Sun 3 Frank, Martin 3 He, Xiaoming 3 Ho, Lam Si Tung 3 Hu, Guanghui 3 Kang, Sung Ha 3 Klingenberg, Christian 3 Kuang, Yangyu 3 Kumar, Harish 3 Kusch, Jonas 3 Liao, Wenjing 3 Sun, Zheng 3 Tran, Giang N. 3 Wang, Baoshan 3 Xu, Hao 3 Zhang, Dongxiao 3 Zhao, Weifeng 3 Zhong, Xinghui 2 Amat Plata, Sergio 2 Balsara, Dinshaw S. 2 Birke, Claudius 2 Biswas, Biswarup 2 Bortz, David M. 2 Boscheri, Walter 2 Chakraborty, Souvik 2 Chandrashekar, Praveen 2 Chang, Haibin 2 Chou, Ching-Shan 2 Cyr, Eric C. 2 Dai, Dihan 2 Doostan, Alireza 2 Dürrwächter, Jakob 2 Dzanic, Tarik 2 Epshteyn, Yekaterina 2 Feng, Xueshang 2 Gao, Zhen 2 Gassner, Gregor J. 2 Gerster, Stephan 2 Gu, Yaguang 2 Gu, Yiqi 2 He, Yuchen 2 Herty, Michael Matthias 2 Huang, Juntao 2 Jiang, Haili 2 Karniadakis, George Em 2 Kutz, J. Nathan 2 Kuzmin, Dmitri 2 Li, Peng 2 Liao, Qifeng 2 Liu, Hao 2 Liu, Mengqing 2 Liu, Yingjie 2 Lu, Hannah 2 Messenger, Daniel A. 2 Meyer, Fabian 2 Ming, Ju 2 Nazarov, Murtazo 2 Perdikaris, Paris G. 2 Qin, Tong 2 Qiu, Changxin 2 Qiu, Jianxian 2 Rueda-Ramírez, Andrés Mauricio 2 Schlachter, Louisa 2 Shadid, John N. 2 Tomas, Ignacio 2 Tripura, Tapas 2 Wang, Jianxun 2 Wang, Zhongjian 2 Witherden, Freddie D. 2 Xia, Yinhua 2 Xiao, Tianbai 2 Xu, Yan 2 Yang, Haizhao 2 Zhang, Qinglong 2 Zhang, Weijie 2 Zhang, Zhiwen 2 Zhao, Jian 1 Abreu, Eduardo 1 Baggenstos, Jonas 1 Bakarji, Joseph 1 Beck, Andrea D. 1 Beise, Hans-Peter 1 Bendickson, Aaron 1 Bhouri, Mohamed Aziz 1 Bierbooms, Wim 1 Bonilla, Marceline S. ...and 291 more Authors all top 5 Cited in 51 Serials 81 Journal of Computational Physics 16 Journal of Scientific Computing 14 SIAM Journal on Scientific Computing 13 Communications in Computational Physics 9 Computer Methods in Applied Mechanics and Engineering 6 Computers and Fluids 5 Applied Mathematics and Computation 4 Computers & Mathematics with Applications 4 SIAM Journal on Numerical Analysis 4 Applied Numerical Mathematics 4 SIAM/ASA Journal on Uncertainty Quantification 3 Journal of Computational and Applied Mathematics 3 Physica D 3 Communications on Applied Mathematics and Computation 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Mathematics of Computation 2 Bulletin of Mathematical Biology 2 Numerische Mathematik 2 Computational Mechanics 2 SIAM Review 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Discrete and Continuous Dynamical Systems. Series S 2 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Classical and Quantum Gravity 1 Computer Physics Communications 1 Journal of Mathematical Biology 1 Chaos, Solitons and Fractals 1 Calcolo 1 Journal of Approximation Theory 1 Journal of Computational Mathematics 1 Neural Networks 1 European Journal of Applied Mathematics 1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 ETNA. Electronic Transactions on Numerical Analysis 1 Mathematical Problems in Engineering 1 Nonlinear Dynamics 1 Discrete and Continuous Dynamical Systems. Series B 1 Journal of Machine Learning Research (JMLR) 1 Journal of Numerical Mathematics 1 Multiscale Modeling & Simulation 1 Analysis and Applications (Singapore) 1 Oberwolfach Reports 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Advances in Applied Mathematics and Mechanics 1 Science China. Mathematics 1 Journal of Agricultural, Biological, and Environmental Statistics 1 East Asian Journal on Applied Mathematics 1 AMM. Applied Mathematics and Mechanics. (English Edition) 1 Journal of Nonlinear and Variational Analysis 1 Sampling Theory, Signal Processing, and Data Analysis all top 5 Cited in 27 Fields 169 Numerical analysis (65-XX) 101 Fluid mechanics (76-XX) 100 Partial differential equations (35-XX) 57 Computer science (68-XX) 23 Dynamical systems and ergodic theory (37-XX) 18 Statistics (62-XX) 10 Systems theory; control (93-XX) 9 Approximations and expansions (41-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 6 Mechanics of deformable solids (74-XX) 5 Probability theory and stochastic processes (60-XX) 5 Biology and other natural sciences (92-XX) 4 Mechanics of particles and systems (70-XX) 4 Operations research, mathematical programming (90-XX) 3 Ordinary differential equations (34-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Statistical mechanics, structure of matter (82-XX) 3 Relativity and gravitational theory (83-XX) 3 Astronomy and astrophysics (85-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Optics, electromagnetic theory (78-XX) 2 Geophysics (86-XX) 1 General and overarching topics; collections (00-XX) 1 Real functions (26-XX) 1 Operator theory (47-XX) 1 General topology (54-XX) 1 Quantum theory (81-XX) Citations by Year