Kailiang Wu | Mathematics · SUSTech
Kailiang Wu
Professor of Mathematics
Southern University of Science and Technology (SUSTech)
Email: wukl@sustech.edu.cn
Mailing address
Department of Mathematics, School of Science
Southern University of Science and Technology
1088 Xueyuan Avenue, Nanshan District
Shenzhen, Guangdong 518055, China
Biography
Kailiang Wu is a Full Professor in the Department of Mathematics and the Shenzhen International Center for Mathematics at Southern University of Science and Technology (SUSTech). His research focuses on the intersection of numerical analysis, computational physics, and scientific machine learning, with an emphasis on establishing rigorous mathematical foundations for structure-preserving numerical methods and nonlinear stability.
A central question in his research is what determines nonlinear stability beyond von Neumann’s classical linear stability theory, and how stability principles and key structures can guide reliable computation, especially under extreme physical conditions. To address this question, he develops and analyzes high-order numerical methods with provable structure-preserving properties for nonlinear partial differential equations, particularly hyperbolic conservation laws, and applies them to compressible magnetohydrodynamics (MHD) and relativistic hydrodynamics.
Together with collaborators, he developed the geometric quasilinearization (GQL) framework, which “trades higher dimensions for linearity” by converting nonlinear constraints into equivalent linear constraints in higher-dimensional spaces. GQL offers a new approach to the challenge of preserving strongly nonlinear constraints. Its geometric ideas originated in his collaborative research on physical-constraint-preserving (PCP) methods for compressible MHD and helped reveal a deep connection between algebraic admissibility constraints and the differential divergence-free constraint on the magnetic field. His related work also includes optimal convex decomposition theory for efficient high-order bound-preserving methods, connecting these problems with positive functional theory and symmetric groups.
He also developed a weak-to-strong (W2S) principle to uncover the hidden unity underlying nonlinear stability. Building on this principle, he proposed the EPO framework, which unifies fully discrete multi-entropy stability (E), positivity and bound preservation (P), and oscillation elimination (O) for high-order schemes for hyperbolic PDEs. Recently, he resolved the ENO-TV conjecture by revealing a sharp parity dichotomy in the convergence theory of entropy-stable ENO schemes. He also established an entropy-stability transfer theory through shift cohomology.
The same perspective guides his work on learning unknown dynamics from data. Together with collaborators, he studies how structural properties of evolution operators can be incorporated into learning models and algorithms. He also co-developed DUE (Deep Unknown Equations), a framework and open-source software library for modeling unknown equations from data. More recently, he proposed the Alternating Neural Integration (ANI) framework for the intelligent upgrading of scientific simulators. Across these directions, his goal is to connect rigorous mathematical analysis with reliable algorithms and reusable computational tools.
He earned his Ph.D. in computational mathematics from Peking University in 2016, followed by postdoctoral research at the University of Utah and The Ohio State University. He joined SUSTech as an Associate Professor in 2021 and was promoted to Full Professor in 2026.
He is a recipient of the National Science Fund for Distinguished Young Scholars (国家杰出青年科学基金). This project investigates theoretical and computational frameworks for structure preservation and nonlinear stability, with applications to extreme MHD.
Research Interests
Machine Learning and Data-Driven Modeling
Nature Communications, 2026.
Paper
Code
BibTeX
@article{pub2026learningmissingphysicsfromlegacysimulatorswithalternatingneural,
author = {H. Wang and Q. Wang and C. Yuan and K. Wu},
title = {{Learning missing physics from legacy simulators with alternating neural integrators}},
journal = {Nature Communications},
year = {2026},
doi = {10.1038/s41467-026-74002-2},
url = {https://doi.org/10.1038/s41467-026-74002-2}
}
SIAM Review, 2025.
Paper
PDF
arXiv
Code
BibTeX
@article{pub2025dueadeeplearningframeworkandlibraryformodeling,
author = {Junfeng Chen and Kailiang Wu and Dongbin Xiu},
title = {{DUE: A deep learning framework and library for modeling unknown equations}},
journal = {SIAM Review},
year = {2025},
volume = {67},
number = {4},
pages = {873--902},
doi = {10.1137/24M1671827},
eprint = {2504.10373},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/24M1671827}
}
Journal of Computational Physics, 2020.
arXiv
BibTeX
@article{pub2020datadrivendeeplearningofpartialdifferentialequationsin,
author = {Kailiang Wu and Dongbin Xiu},
title = {{Data-driven deep learning of partial differential equations in modal space}},
journal = {Journal of Computational Physics},
year = {2020},
volume = {408},
pages = {109307},
eprint = {1910.06948},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1910.06948}
}
International Conference on Machine Learning (ICML), 2024.
arXiv
BibTeX
@inproceedings{pub2024positionalknowledgeisallyouneedpositioninducedtransformer,
author = {Junfeng Chen and Kailiang Wu},
title = {{Positional knowledge is all you need: Position-induced Transformer (PiT) for operator learning}},
booktitle = {International Conference on Machine Learning (ICML)},
year = {2024},
eprint = {2405.09285},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2405.09285}
}
Journal of Computational Physics, 2023.
Paper
arXiv
BibTeX
@article{pub2023deeposgdeeplearningofoperatorsinsemigroup,
author = {Junfeng Chen and Kailiang Wu},
title = {{Deep-OSG: Deep learning of operators in semigroup}},
journal = {Journal of Computational Physics},
year = {2023},
volume = {493},
pages = {112498},
doi = {10.1016/j.jcp.2023.112498},
eprint = {2302.03358},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2023.112498}
}
SIAM Journal on Scientific Computing, 2020.
arXiv
BibTeX
@article{pub2020structurepreservingmethodforreconstructingunknownhamiltoniansystemsfrom,
author = {Kailiang Wu and Tong Qin and Dongbin Xiu},
title = {{Structure-preserving method for reconstructing unknown Hamiltonian systems from trajectory data}},
journal = {SIAM Journal on Scientific Computing},
year = {2020},
volume = {42},
number = {6},
pages = {A3704--A3729},
eprint = {1905.10396},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1905.10396}
}
Journal of Computational Physics, 2019.
Paper
arXiv
BibTeX
@article{pub2019datadrivengoverningequationsapproximationusingdeepneuralnetworks,
author = {Tong Qin and Kailiang Wu and Dongbin Xiu},
title = {{Data driven governing equations approximation using deep neural networks}},
journal = {Journal of Computational Physics},
year = {2019},
volume = {395},
pages = {620--635},
doi = {10.1016/j.jcp.2019.06.042},
eprint = {1811.05537},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2019.06.042}
}
Journal of Computational Physics, 2022.
arXiv
BibTeX
@article{pub2022deepneuralnetworkmodelingofunknownpartialdifferentialequations,
author = {Zhen Chen and Victor Churchill and Kailiang Wu and Dongbin Xiu},
title = {{Deep neural network modeling of unknown partial differential equations in nodal space}},
journal = {Journal of Computational Physics},
year = {2022},
volume = {449},
pages = {110782},
eprint = {2106.03603},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2106.03603}
}
IEEE Transactions on Artificial Intelligence, 2024.
arXiv
BibTeX
@article{pub2024criticalsamplingforrobustevolutionoperatorlearningofunknowndynamicalsystems,
author = {Ce Zhang and Kailiang Wu and Zhihai He},
title = {{Critical sampling for robust evolution operator learning of unknown dynamical systems}},
journal = {IEEE Transactions on Artificial Intelligence},
year = {2024},
volume = {5},
pages = {2856-2871},
eprint = {2304.07485},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2304.07485}
}
Journal of Scientific Computing, 2020.
arXiv
BibTeX
@article{pub2020methodstorecoverunknownprocessesinpartialdifferentialequations,
author = {Zhen Chen and Kailiang Wu and Dongbin Xiu},
title = {{Methods to recover unknown processes in partial differential equations using data}},
journal = {Journal of Scientific Computing},
year = {2020},
volume = {85},
pages = {23},
eprint = {2003.02387},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2003.02387}
}
Journal of Computational Physics, 2019.
arXiv
BibTeX
@article{pub2019numericalaspectsforapproximatinggoverningequationsusingdata,
author = {Kailiang Wu and Dongbin Xiu},
title = {{Numerical aspects for approximating governing equations using data}},
journal = {Journal of Computational Physics},
year = {2019},
volume = {384},
pages = {200--221},
eprint = {1809.09170},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1809.09170}
}
Commun. Appl. Math. Comput., 2021.
arXiv
BibTeX
@article{pub2021anonintrusivecorrectionalgorithmforclassificationproblemswithcorrupteddata,
author = {Jun Hou and Tong Qin and Kailiang Wu and Dongbin Xiu},
title = {{A non-intrusive correction algorithm for classification problems with corrupted data}},
journal = {Commun. Appl. Math. Comput.},
year = {2021},
volume = {3},
pages = {337--356},
eprint = {2002.04658},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2002.04658}
}
Commun. Appl. Math. Comput., 2019.
Paper
BibTeX
@article{pub2019sequentialapproximationoffunctionsinsobolevspacesusingrandomsamples,
author = {K. Wu and D. Xiu},
title = {{Sequential approximation of functions in Sobolev spaces using random samples}},
journal = {Commun. Appl. Math. Comput.},
year = {2019},
volume = {1},
pages = {449--466},
doi = {10.1007/s42967-019-00028-7},
url = {https://doi.org/10.1007/s42967-019-00028-7}
}
Journal of Computational Physics, 2018.
Paper
BibTeX
@article{pub2018sequentialfunctionapproximationwithnoisydata,
author = {Y. Shin and K. Wu and D. Xiu},
title = {{Sequential function approximation with noisy data}},
journal = {Journal of Computational Physics},
year = {2018},
volume = {371},
pages = {363--381},
doi = {10.1016/j.jcp.2018.05.042},
url = {https://doi.org/10.1016/j.jcp.2018.05.042}
}
Journal of Computational Physics, 2018.
Paper
BibTeX
@article{pub2018sequentialfunctionapproximationonarbitrarilydistributedpointsets,
author = {K. Wu and D. Xiu},
title = {{Sequential function approximation on arbitrarily distributed point sets}},
journal = {Journal of Computational Physics},
year = {2018},
volume = {354},
pages = {370--386},
doi = {10.1016/j.jcp.2017.10.020},
url = {https://doi.org/10.1016/j.jcp.2017.10.020}
}
SIAM Journal on Scientific Computing, 2017.
Paper
BibTeX
@article{pub2017arandomizedtensorquadraturemethodforhighdimensionalpolynomial,
author = {K. Wu and Y. Shin and D. Xiu},
title = {{A randomized tensor quadrature method for high dimensional polynomial approximation}},
journal = {SIAM Journal on Scientific Computing},
year = {2017},
volume = {39},
number = {5},
pages = {A1811--A1833},
doi = {10.1137/16M1081695},
url = {https://doi.org/10.1137/16M1081695}
}Nonlinear Stability and Structure Preservation
SIAM Review, Research Spotlight, 2023.
Paper
PDF
arXiv
BibTeX
@article{pub2023geometricquasilinearizationframeworkforanalysisanddesignofbound,
author = {Kailiang Wu and Chi-Wang Shu},
title = {{Geometric quasilinearization framework for analysis and design of bound-preserving schemes}},
journal = {SIAM Review},
year = {2023},
volume = {65},
number = {4},
pages = {1031--1073},
doi = {10.1137/21M1458247},
eprint = {2111.04722},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/21M1458247}
}
SIAM Journal on Numerical Analysis, 2024.
arXiv
BibTeX
@article{pub2024onoptimalcellaveragedecompositionforhighorderbound,
author = {Shumo Cui and Shengrong Ding and Kailiang Wu},
title = {{On optimal cell average decomposition for high-order bound-preserving schemes of hyperbolic conservation laws}},
journal = {SIAM Journal on Numerical Analysis},
year = {2024},
eprint = {2212.05045},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2212.05045}
}
SIAM Journal on Numerical Analysis, 2018.
Paper
PDF
arXiv
BibTeX
@article{pub2018positivitypreservinganalysisofnumericalschemesforidealmagnetohydrodynamics,
author = {Kailiang Wu},
title = {{Positivity-preserving analysis of numerical schemes for ideal magnetohydrodynamics}},
journal = {SIAM Journal on Numerical Analysis},
year = {2018},
volume = {56},
number = {4},
pages = {2124--2147},
doi = {10.1137/18M1168017},
eprint = {1802.02278},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/18M1168017}
}
Math. Models Methods Appl. Sci. (M3AS), 2017.
Paper
arXiv
BibTeX
@article{pub2017admissiblestatesandphysicalconstraintspreservingschemesforrelativistic,
author = {Kailiang Wu and Huazhong Tang},
title = {{Admissible states and physical-constraints-preserving schemes for relativistic magnetohydrodynamic equations}},
journal = {Math. Models Methods Appl. Sci. (M3AS)},
year = {2017},
volume = {27},
number = {10},
pages = {1871--1928},
doi = {10.1142/S0218202517500348},
eprint = {1603.06660},
archivePrefix = {arXiv},
url = {https://doi.org/10.1142/S0218202517500348}
}
Numerische Mathematik, 2019.
arXiv
BibTeX
@article{pub2019provablypositivehighorderschemesforidealmagnetohydrodynamicsanalysis,
author = {Kailiang Wu and Chi-Wang Shu},
title = {{Provably positive high-order schemes for ideal magnetohydrodynamics: Analysis on general meshes}},
journal = {Numerische Mathematik},
year = {2019},
volume = {142},
number = {4},
pages = {995--1047},
eprint = {1807.11467},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1807.11467}
}
SIAM Journal on Scientific Computing, 2021.
arXiv
BibTeX
@article{pub2021minimumprincipleonspecificentropyandhighorderaccurate,
author = {Kailiang Wu},
title = {{Minimum principle on specific entropy and high-order accurate invariant region preserving numerical methods for relativistic hydrodynamics}},
journal = {SIAM Journal on Scientific Computing},
year = {2021},
volume = {43},
number = {6},
pages = {B1164--B1197},
eprint = {2102.03801},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2102.03801}
}
Mathematics of Computation, 2025.
Paper
PDF (arXiv version)
arXiv
BibTeX
@article{pub2025oedgoscillationeliminatingdiscontinuousgalerkinmethodforhyperbolicconservation,
author = {Manting Peng and Zheng Sun and Kailiang Wu},
title = {{OEDG: Oscillation-eliminating discontinuous Galerkin method for hyperbolic conservation laws}},
journal = {Mathematics of Computation},
year = {2025},
volume = {94},
pages = {1147--1198},
doi = {10.1090/mcom/3998},
eprint = {2310.04807},
archivePrefix = {arXiv},
url = {https://doi.org/10.1090/mcom/3998}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260400301,
author = {Kailiang Wu},
title = {{EPO: A Unified Framework for Entropy Stability, Positivity, and Oscillation Suppression}},
year = {2026},
eprint = {2604.00301},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2604.00301}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260926791,
author = {Huihui Cao and Kailiang Wu and Caiyou Yuan},
title = {{Fully Discrete Multi-Entropy Stability of High-Order Schemes for Compressible MHD: A Weak-to-Strong Framework}},
year = {2026},
eprint = {2609.26791},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2609.26791}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260719283,
author = {Zhuoyun Li and Kailiang Wu},
title = {{Structure of ENO Entropy Dissipation: Parity Dichotomy for the ENO--TV Conjecture and Shift Cohomology}},
year = {2026},
eprint = {2607.19283},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2607.19283}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260809327,
author = {Linfeng Xu and Kailiang Wu},
title = {{High-order fully discrete multi-entropy-stable and bound-preserving schemes for relativistic Euler equations}},
year = {2026},
eprint = {2608.09327},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2608.09327}
}
Mathematics of Computation, 2026.
Paper
arXiv
BibTeX
@article{pub2025onlocalminimumentropyprincipleofhighorderschemes,
author = {Shumo Cui and Kailiang Wu and Linfeng Xu},
title = {{On local minimum entropy principle of high-order schemes for relativistic Euler equations}},
journal = {Mathematics of Computation},
year = {2026},
volume = {95},
number = {362},
pages = {2739-2787},
doi = {10.1090/mcom/4139},
eprint = {2503.12465},
archivePrefix = {arXiv},
url = {https://doi.org/10.1090/mcom/4139}
}
SIAM Journal on Scientific Computing, 2020.
arXiv
BibTeX
@article{pub2020entropysymmetrizationandhighorderaccurateentropystablenumerical,
author = {Kailiang Wu and Chi-Wang Shu},
title = {{Entropy symmetrization and high-order accurate entropy stable numerical schemes for relativistic MHD equations}},
journal = {SIAM Journal on Scientific Computing},
year = {2020},
volume = {42},
number = {4},
pages = {A2230--A2261},
eprint = {1907.07467},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1907.07467}
}
SIAM Journal on Numerical Analysis, 2022.
arXiv
BibTeX
@article{pub2022onenergylawsandstabilityofrungekuttamethods,
author = {Zheng Sun and Yuanzhe Wei and Kailiang Wu},
title = {{On energy laws and stability of Runge--Kutta methods for linear seminegative problems}},
journal = {SIAM Journal on Numerical Analysis},
year = {2022},
volume = {60},
number = {5},
pages = {2448--2481},
eprint = {2201.06501},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2201.06501}
}
On energy laws and stability of first-subdiagonal Padé approximants for linear seminegative problems
Journal of Information and Computing Science, 2026. Accepted
arXiv
BibTeX
@article{pub2026onenergylawsandstabilityoffirstsubdiagonalpadeapproximantsforlinear,
author = {Miaosen Jiao and Zheng Sun and Kailiang Wu},
title = {{On energy laws and stability of first-subdiagonal Pad{\'e} approximants for linear seminegative problems}},
journal = {Journal of Information and Computing Science},
year = {2026},
eprint = {2608.09239},
archivePrefix = {arXiv},
note = {Accepted},
url = {https://arxiv.org/abs/2608.09239}
}
Journal of Computational Physics, 2023.
Paper
arXiv
BibTeX
@article{pub2022istheclassicconvexdecompositionoptimalforboundpreserving,
author = {Shumo Cui and Shengrong Ding and Kailiang Wu},
title = {{Is the classic convex decomposition optimal for bound-preserving schemes in multiple dimensions?}},
journal = {Journal of Computational Physics},
year = {2023},
volume = {476},
pages = {111882},
doi = {10.1016/j.jcp.2022.111882},
eprint = {2207.08849},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2022.111882}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260910476,
author = {Shengrong Ding and Shumo Cui and Remi Abgrall and Kailiang Wu},
title = {{Invariant domain preservation for hybrid point-value and cell-average discretizations of hyperbolic equations on general meshes}},
year = {2026},
eprint = {2609.10476},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2609.10476}
}
SIAM Journal on Scientific Computing, 2025.
arXiv
BibTeX
@article{pub2025anovelandsimpleinvariantdomainpreservingframeworkfor,
author = {R{\'e}mi Abgrall and Miaosen Jiao and Yongle Liu and Kailiang Wu},
title = {{A novel and simple invariant-domain-preserving framework for PAMPA scheme: 1D case}},
journal = {SIAM Journal on Scientific Computing},
year = {2025},
eprint = {2412.03423},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2412.03423}
}
Communications in Computational Physics, 2026.
Paper
arXiv
BibTeX
@article{pub2025boundpreservingpointaveragemomentpolynomialinterpretedpampaschemeonedimensionalcase,
author = {R{\'e}mi Abgrall and Miaosen Jiao and Yongle Liu and Kailiang Wu},
title = {{Bound-preserving Point-Average-Moment PolynomiAl-interpreted (PAMPA) scheme: One-dimensional case}},
journal = {Communications in Computational Physics},
year = {2026},
volume = {39},
number = {1},
pages = {29-58},
doi = {10.4208/cicp.oa-2024-0266},
eprint = {2410.14292},
archivePrefix = {arXiv},
url = {https://doi.org/10.4208/cicp.oa-2024-0266}
}
SIAM Journal on Scientific Computing, 2024.
Paper
arXiv
BibTeX
@article{pub2024boundpreservingframeworkforcentralupwindschemesforgeneral,
author = {Shumo Cui and Alexander Kurganov and Kailiang Wu},
title = {{Bound-preserving framework for central-upwind schemes for general hyperbolic conservation laws}},
journal = {SIAM Journal on Scientific Computing},
year = {2024},
volume = {46},
number = {5},
pages = {A2899--A2924},
doi = {10.1137/23M1628024},
eprint = {2403.13420},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/23M1628024}
}
Journal of Computational Physics, 2025.
Paper
BibTeX
@article{pub2025positivitypreservingnewlowdssipationcentralupwindschemesfor,
author = {S. Cui and Y. Gu and A. Kurganov and K. Wu and R. Xin},
title = {{Positivity-preserving new low-dissipation central-upwind schemes for compressible Euler equations}},
journal = {Journal of Computational Physics},
year = {2025},
doi = {10.1016/j.jcp.2025.114189},
url = {https://doi.org/10.1016/j.jcp.2025.114189}
}
Journal of Computational Physics, 2025.
Paper
arXiv
BibTeX
@article{pub2024boundpreservingoedgmethodforawrasclezhangtraffic,
author = {Wei Chen and Shumo Cui and Kailiang Wu and Tao Xiong},
title = {{Bound-preserving OEDG schemes for Aw--Rascle--Zhang traffic models on networks}},
journal = {Journal of Computational Physics},
year = {2025},
volume = {520},
pages = {113507},
doi = {10.1016/j.jcp.2024.113507},
eprint = {2409.16269},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2024.113507}
}
Journal of Computational Physics, 2026.
Paper
BibTeX
@article{pub2026cosdgaconvexoscillationsuppressingframeworkforhighorderdiscontinuousgalerkin,
author = {Huihui Cao and Yunqing Huang and Zhuoyun Li and Kailiang Wu},
title = {{COS(DG): A Convex Oscillation-Suppressing Framework for High-Order Discontinuous Galerkin Methods}},
journal = {Journal of Computational Physics},
year = {2026},
volume = {554},
pages = {114755},
doi = {10.1016/j.jcp.2026.114755},
url = {https://doi.org/10.1016/j.jcp.2026.114755}
}
Journal of Computational Physics, 2027.
Paper
BibTeX
@article{pub2026cossvconvexoscillationsuppressingspectralvolumeschemeswithboundpreservationfor,
author = {Ruifang Yan and Huihui Cao and Na Liu and Kailiang Wu},
title = {{COS(SV): Convex Oscillation-Suppressing Spectral Volume Schemes with Bound Preservation for Hyperbolic Conservation Laws}},
journal = {Journal of Computational Physics},
year = {2027},
volume = {568},
pages = {115411},
doi = {10.1016/j.jcp.2026.115411},
url = {https://doi.org/10.1016/j.jcp.2026.115411}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260926195,
author = {Manting Peng and Zhuoyun Li and Kailiang Wu},
title = {{Runge--Kutta-Aligned Oscillation Elimination: Restoring Superconvergence for Fully Discrete Shock-Capturing DG Schemes}},
year = {2026},
eprint = {2609.26195},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2609.26195}
}
SIAM Journal on Scientific Computing, 2026.
Paper
arXiv
BibTeX
@article{pub2025oscillationeliminatingcentraldgschemesforhyperbolicconservationlaws,
author = {Manting Peng and Kailiang Wu and Caiyou Yuan},
title = {{Oscillation-eliminating central DG schemes on Cartesian meshes for hyperbolic conservation laws}},
journal = {SIAM Journal on Scientific Computing},
year = {2026},
volume = {48},
number = {2},
pages = {A695-A725},
doi = {10.1137/25m1730697},
eprint = {2503.12473},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/25m1730697}
}
SIAM Journal on Scientific Computing, 2025.
Paper
arXiv
BibTeX
@article{pub2024spectralvolumefromadgperspectiveoscillationeliminationstability,
author = {Zhuoyun Li and Kailiang Wu},
title = {{Spectral volume from a discontinuous Galerkin perspective: oscillation elimination, stability, and optimal error estimates}},
journal = {SIAM Journal on Scientific Computing},
year = {2025},
volume = {47},
number = {2},
pages = {A1304-A1333},
doi = {10.1137/24m167799x},
eprint = {2409.10871},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/24m167799x}
}
Journal of Computational Physics, 2024.
Paper
arXiv
BibTeX
@article{pub2024highorderoscillationeliminatinghermitewenomethodforhyperbolic,
author = {Chuan Fan and Kailiang Wu},
title = {{High-order oscillation-eliminating Hermite WENO method for hyperbolic conservation laws}},
journal = {Journal of Computational Physics},
year = {2024},
volume = {519},
pages = {113435},
doi = {10.1016/j.jcp.2024.113435},
eprint = {2409.09632},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2024.113435}
}
Journal of Computational Physics, 2025.
arXiv
BibTeX
@article{pub2025robustdgschemesonunstructuredtriangularmeshesoscillationelimination,
author = {Shengrong Ding and Shumo Cui and Kailiang Wu},
title = {{Robust DG schemes on unstructured triangular meshes: Oscillation elimination and bound preservation via optimal convex decomposition}},
journal = {Journal of Computational Physics},
year = {2025},
eprint = {2409.09620},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2409.09620}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260926194,
author = {Chuan Fan and Kailiang Wu},
title = {{Compact Finite-Average-Moment Schemes with Single-Step Oscillation Elimination for Hyperbolic Conservation Laws}},
year = {2026},
eprint = {2609.26194},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2609.26194}
}
Numerische Mathematik, 2021.
arXiv
BibTeX
@article{pub2021provablyphysicalconstraintpreservingdiscontinuousgalerkinmethodsformultidimensional,
author = {Kailiang Wu and Chi-Wang Shu},
title = {{Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations}},
journal = {Numerische Mathematik},
year = {2021},
volume = {148},
pages = {699--741},
eprint = {2002.03371},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2002.03371}
}
SIAM Journal on Numerical Analysis, 2023.
arXiv
BibTeX
@article{pub2023provablypositivecentraldiscontinuousgalerkinschemesviageometricquasilinearization,
author = {Kailiang Wu and Haili Jiang and Chi-Wang Shu},
title = {{Provably positive central discontinuous Galerkin schemes via geometric quasilinearization for ideal MHD equations}},
journal = {SIAM Journal on Numerical Analysis},
year = {2023},
volume = {61},
pages = {250--285},
eprint = {2203.14853},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2203.14853}
}
SIAM Journal on Scientific Computing, 2024.
Paper
arXiv
BibTeX
@article{pub2024anewdiscretelydivergencefreepositivitypreservinghighorder,
author = {Shengrong Ding and Kailiang Wu},
title = {{A new discretely divergence-free positivity-preserving high-order finite volume method for ideal MHD equations}},
journal = {SIAM Journal on Scientific Computing},
year = {2024},
volume = {46},
number = {1},
pages = {A50--A79},
doi = {10.1137/23M1562081},
eprint = {2305.14820},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/23M1562081}
}
SIAM Journal on Scientific Computing, 2024.
Paper
arXiv
BibTeX
@article{pub2024anewlocallydivergencefreepathconservativecentralupwind,
author = {Alina Chertock and Alexander Kurganov and Michael Redle and Kailiang Wu},
title = {{A new locally divergence-free path-conservative central-upwind scheme for ideal and shallow water magnetohydrodynamics}},
journal = {SIAM Journal on Scientific Computing},
year = {2024},
volume = {46},
number = {3},
pages = {A1998--A2024},
doi = {10.1137/22M1539009},
eprint = {2212.02682},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/22M1539009}
}
Journal of Computational Physics, 2024.
Paper
arXiv
BibTeX
@article{pub2024gqlbasedboundpreservingandlocallydivergencefreecentral,
author = {Shengrong Ding and Kailiang Wu},
title = {{GQL-based bound-preserving and locally divergence-free central discontinuous Galerkin schemes for relativistic magnetohydrodynamics}},
journal = {Journal of Computational Physics},
year = {2024},
volume = {514},
pages = {113208},
doi = {10.1016/j.jcp.2024.113208},
eprint = {2402.15437},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2024.113208}
}
Journal of Computational Physics, 2025.
arXiv
BibTeX
@article{pub2025structurepreservingoscillationeliminatingdiscontinuousgalerkinschemesforideal,
author = {Mengqing Liu and Kailiang Wu},
title = {{Structure-preserving oscillation-eliminating discontinuous Galerkin schemes for ideal MHD equations: Locally divergence-free and positivity-preserving}},
journal = {Journal of Computational Physics},
year = {2025},
eprint = {2404.16794},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2404.16794}
}
Journal of Computational Physics, 2026.
Paper
BibTeX
@article{pub2026highorderpositivitypreservingandgloballydivergencefreediscontinuousgalerkinmethodsfor,
author = {Mengqing Liu and Kailiang Wu and Caiyou Yuan},
title = {{High-order positivity-preserving and globally divergence-free discontinuous Galerkin methods for ideal magnetohydrodynamics with conditional energy conservation}},
journal = {Journal of Computational Physics},
year = {2026},
volume = {562},
pages = {115031},
doi = {10.1016/j.jcp.2026.115031},
url = {https://doi.org/10.1016/j.jcp.2026.115031}
}
Math. Models Methods Appl. Sci. (M3AS), 2026. Accepted
arXiv
BibTeX
@article{pub2026provablypositivitypreservinggloballydivergencefreecentraldgmethodsforidealmhd,
author = {Ruifang Yan and Huihui Cao and Kailiang Wu},
title = {{Provably positivity-preserving, globally divergence-free central DG methods for ideal MHD system}},
journal = {Math. Models Methods Appl. Sci. (M3AS)},
year = {2026},
eprint = {2508.08913},
archivePrefix = {arXiv},
note = {Accepted},
url = {https://arxiv.org/abs/2508.08913}
}
Journal of Computational Physics, 2026. In press
Paper
arXiv
BibTeX
@article{pub2026anactivefluxtypeschemeforidealmhdwithprovablepositivityand,
author = {Mengqing Liu and Dongwen Pang and Remi Abgrall and Kailiang Wu},
title = {{An active-flux-type scheme for ideal MHD with provable positivity and a point-value-level discrete divergence-free constraint}},
journal = {Journal of Computational Physics},
year = {2026},
doi = {10.1016/j.jcp.2026.115319},
eprint = {2510.19721},
archivePrefix = {arXiv},
note = {In press},
url = {https://doi.org/10.1016/j.jcp.2026.115319}
}
Provably positivity-preserving constrained transport scheme for 2D and 3D ideal magnetohydrodynamics
Journal of Computational Physics, 2025.
arXiv
BibTeX
@article{pub2025provablypositivitypreservingconstrainedtransportschemefor2dand3didealmagnetohydrodynamics,
author = {Dongwen Pang and Kailiang Wu},
title = {{Provably positivity-preserving constrained transport scheme for 2D and 3D ideal magnetohydrodynamics}},
journal = {Journal of Computational Physics},
year = {2025},
volume = {541},
pages = {114312},
eprint = {2410.05173},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2410.05173}
}
Z. Angew. Math. Phys., 2018.
arXiv
BibTeX
@article{pub2018onphysicalconstraintspreservingschemesforspecialrelativisticmagnetohydrodynamicswithageneral,
author = {Kailiang Wu and Huazhong Tang},
title = {{On physical-constraints-preserving schemes for special relativistic magnetohydrodynamics with a general equation of state}},
journal = {Z. Angew. Math. Phys.},
year = {2018},
volume = {69},
pages = {84},
eprint = {1709.05838},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1709.05838}
}
SIAM Journal on Scientific Computing, 2018.
arXiv
BibTeX
@article{pub2018aprovablypositivediscontinuousgalerkinmethodformultidimensionalideal,
author = {Kailiang Wu and Chi-Wang Shu},
title = {{A provably positive discontinuous Galerkin method for multidimensional ideal magnetohydrodynamics}},
journal = {SIAM Journal on Scientific Computing},
year = {2018},
volume = {40},
number = {5},
pages = {B1302--B1329},
eprint = {1807.00246},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1807.00246}
}
Journal of Scientific Computing, 2024.
Paper
BibTeX
@article{pub2024highorderstructurepreservingfinitedifferencewenoschemeformhdequationswith,
author = {W. Chen and K. Wu and T. Xiong},
title = {{High order structure-preserving finite difference WENO schemes for MHD equations with gravitation in all sonic Mach numbers}},
journal = {Journal of Scientific Computing},
year = {2024},
volume = {99},
pages = {36},
doi = {10.1007/s10915-024-02492-7},
url = {https://doi.org/10.1007/s10915-024-02492-7}
}
Journal of Computational Physics, 2023.
arXiv
BibTeX
@article{pub2023highorderasymptoticpreservingfinitedifferencewenoschemeswith,
author = {Wei Chen and Kailiang Wu and Tao Xiong},
title = {{High order asymptotic preserving finite difference WENO schemes with constrained transport for MHD equations in all sonic Mach numbers}},
journal = {Journal of Computational Physics},
year = {2023},
volume = {488},
pages = {112240},
eprint = {2211.16655},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2211.16655}
}
Monthly Notices of the Royal Astronomical Society (MNRAS), 2025.
Paper
BibTeX
@article{pub2025divergencefreefinitevolumewenoschemeforrelativisticmagnetohydrodynamics,
author = {S. Ding and K. Wu and C. Yuan},
title = {{Divergence-free finite volume WENO scheme for relativistic magnetohydrodynamics preserving positivity and subluminal velocity}},
journal = {Monthly Notices of the Royal Astronomical Society (MNRAS)},
year = {2025},
doi = {10.1093/mnras/staf280},
url = {https://doi.org/10.1093/mnras/staf280}
}
Physical Review D, 2017.
Paper
arXiv
BibTeX
@article{pub2017designofprovablyphysicalconstraintpreservingmethodsforgeneral,
author = {Kailiang Wu},
title = {{Design of provably physical-constraint-preserving methods for general relativistic hydrodynamics}},
journal = {Physical Review D},
year = {2017},
doi = {10.1103/PhysRevD.95.103001},
eprint = {1610.06274},
archivePrefix = {arXiv},
url = {https://doi.org/10.1103/PhysRevD.95.103001}
}
Astrophys. J. Suppl. Ser. (ApJS), 2017.
arXiv
BibTeX
@article{pub2017physicalconstraintpreservingcentraldiscontinuousgalerkinmethodsforspecial,
author = {Kailiang Wu and Huazhong Tang},
title = {{Physical-constraint-preserving central discontinuous Galerkin methods for special relativistic hydrodynamics with a general equation of state}},
journal = {Astrophys. J. Suppl. Ser. (ApJS)},
year = {2017},
volume = {228},
number = {1},
pages = {3},
eprint = {1607.08332},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1607.08332}
}
Journal of Computational Physics, 2015.
arXiv
BibTeX
@article{pub2015highorderaccuratephysicalconstraintspreservingfinitedifferenceweno,
author = {Kailiang Wu and Huazhong Tang},
title = {{High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics}},
journal = {Journal of Computational Physics},
year = {2015},
volume = {298},
pages = {539--564},
eprint = {1504.07707},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1504.07707}
}
Journal of Computational Physics, 2025.
arXiv
BibTeX
@article{pub2025robustdiscontinuousgalerkinmethodsmaintainingphysicalconstraintsforgeneral,
author = {Huihui Cao and Manting Peng and Kailiang Wu},
title = {{Robust discontinuous Galerkin methods maintaining physical constraints for general relativistic hydrodynamics}},
journal = {Journal of Computational Physics},
year = {2025},
eprint = {2410.05000},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2410.05000}
}
Journal of Computational Physics, 2026. Accepted
arXiv
BibTeX
@article{pub2026gqlbasedphysicalconstraintpreservinghighorderfinitedifferenceschemesforspecial,
author = {Linfeng Xu and Shengrong Ding and Kailiang Wu},
title = {{GQL-based physical-constraint-preserving high-order finite difference schemes for special relativistic hydrodynamics in arbitrary dimensions}},
journal = {Journal of Computational Physics},
year = {2026},
eprint = {2606.31992},
archivePrefix = {arXiv},
note = {Accepted},
url = {https://arxiv.org/abs/2606.31992}
}
Journal of Computational Physics, 2022.
arXiv
BibTeX
@article{pub2022aphysicalconstraintpreservingfinitevolumemethodforspecial,
author = {Yaping Chen and Kailiang Wu},
title = {{A physical-constraint-preserving finite volume WENO method for special relativistic hydrodynamics on unstructured meshes}},
journal = {Journal of Computational Physics},
year = {2022},
volume = {466},
pages = {111398},
eprint = {2207.09385},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2207.09385}
}
Journal of Computational Physics, 2026.
Paper
BibTeX
@article{pub2026highorderaccurateboundpreservingadaptivemovingmeshfinitevolumemethodsfor,
author = {C. Yuan and Z. Zhang and H. Tang and K. Wu},
title = {{High-order accurate bound-preserving adaptive moving mesh finite volume methods for 2D and 3D special relativistic hydrodynamics}},
journal = {Journal of Computational Physics},
year = {2026},
volume = {554},
pages = {114728},
doi = {10.1016/j.jcp.2026.114728},
url = {https://doi.org/10.1016/j.jcp.2026.114728}
}
Journal of Scientific Computing, 2024.
arXiv
BibTeX
@article{pub2024highorderaccurateentropystableschemesforrelativistichydrodynamicswithageneral,
author = {Linfeng Xu and Shengrong Ding and Kailiang Wu},
title = {{High-order accurate entropy stable schemes for relativistic hydrodynamics with general Synge-type equation of state}},
journal = {Journal of Scientific Computing},
year = {2024},
volume = {98},
pages = {43},
eprint = {2409.10872},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2409.10872}
}
Journal of Computational Physics, 2024.
Paper
arXiv
BibTeX
@article{pub2024provablyconvergentnewtonraphsonmethodsforrecoveringprimitivevariables,
author = {Chaoyi Cai and Jianxian Qiu and Kailiang Wu},
title = {{Provably convergent Newton-Raphson methods for recovering primitive variables with applications to physical-constraint-preserving Hermite WENO schemes for relativistic hydrodynamics}},
journal = {Journal of Computational Physics},
year = {2024},
volume = {498},
pages = {112669},
doi = {10.1016/j.jcp.2023.112669},
eprint = {2305.14805},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2023.112669}
}
SIAM Journal on Scientific Computing, 2021.
arXiv
BibTeX
@article{pub2021uniformlyhighorderstructurepreservingdiscontinuousgalerkinmethodsfor,
author = {Kailiang Wu and Yulong Xing},
title = {{Uniformly high-order structure-preserving discontinuous Galerkin methods for Euler equations with gravitation: Positivity and well-balancedness}},
journal = {SIAM Journal on Scientific Computing},
year = {2021},
volume = {43},
number = {1},
pages = {A472--A510},
eprint = {2005.07166},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2005.07166}
}
Journal of Computational Physics, 2023.
Paper
BibTeX
@article{pub2023onpositivitypreservingwellbalancedfinitevolumemethodsfor,
author = {Y. Ren and K. Wu and J. Qiu and Y. Xing},
title = {{On high order positivity-preserving well-balanced finite volume methods for the Euler equations with gravitation}},
journal = {Journal of Computational Physics},
year = {2023},
volume = {492},
pages = {112429},
doi = {10.1016/j.jcp.2023.112429},
url = {https://doi.org/10.1016/j.jcp.2023.112429}
}
Journal of Computational Physics, 2022.
arXiv
BibTeX
@article{pub2022positivitypreservingwellbalancedcentraldiscontinuousgalerkinschemesfor,
author = {Haili Jiang and Huazhong Tang and Kailiang Wu},
title = {{Positivity-preserving well-balanced central discontinuous Galerkin schemes for the Euler equations under gravitational fields}},
journal = {Journal of Computational Physics},
year = {2022},
volume = {463},
pages = {111297},
eprint = {2207.09398},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2207.09398}
}
Journal of Computational Physics, 2025.
arXiv
BibTeX
@article{pub2025highorderaccuratestructurepreservingfinitevolumeschemeson,
author = {Zhihao Zhang and Huazhong Tang and Kailiang Wu},
title = {{High-order accurate structure-preserving finite volume schemes on adaptive moving meshes for shallow water equations: Well balancedness and positivity}},
journal = {Journal of Computational Physics},
year = {2025},
eprint = {2409.09600},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2409.09600}
}
Journal of Computational Physics, 2024.
arXiv
BibTeX
@article{pub2024highorderaccuratepositivitypreservingandwellbalanceddiscontinuous,
author = {Jiangfu Wang and Huazhong Tang and Kailiang Wu},
title = {{High-order accurate positivity-preserving and well-balanced discontinuous Galerkin schemes for ten-moment Gaussian closure equations with source terms}},
journal = {Journal of Computational Physics},
year = {2024},
eprint = {2402.15446},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2402.15446}
}
Journal of Scientific Computing, 2025.
Paper
BibTeX
@article{pub2025physicalconstraintpreservinghighorderfinitevolumewenomethodviageometricquasilinearization,
author = {L. Y. Win and Y. Chen and Y. Nie and L. Cai and K. Wu},
title = {{Physical-constraint-preserving high-order finite volume WENO method via geometric quasilinearization for Chaplygin gas dynamics}},
journal = {Journal of Scientific Computing},
year = {2025},
volume = {105},
pages = {33},
doi = {10.1007/s10915-025-03059-w},
url = {https://doi.org/10.1007/s10915-025-03059-w}
}
Math. Models Methods Appl. Sci. (M3AS), 2024.
Paper
BibTeX
@article{pub2024uniformlyhighorderboundpreservingoedgschemesfortwo,
author = {R. Yan and R. Abgrall and K. Wu},
title = {{Uniformly high-order bound-preserving OEDG schemes for two-phase flows}},
journal = {Math. Models Methods Appl. Sci. (M3AS)},
year = {2024},
doi = {10.1142/S0218202524500544},
url = {https://doi.org/10.1142/S0218202524500544}
}
Annals of Applied Mathematics, 2024.
Paper
BibTeX
@article{pub2024oscillationeliminatingdiscontinuousgalerkinmethodsformulticomponentchemicallyreactingflows,
author = {J. Du and C. Fan and K. Wu},
title = {{Oscillation-eliminating discontinuous Galerkin methods for multicomponent chemically reacting flows}},
journal = {Annals of Applied Mathematics},
year = {2024},
volume = {40},
pages = {412-444},
doi = {10.4208/aam.oa-2024-0029},
url = {https://doi.org/10.4208/aam.oa-2024-0029}
}
Constraint-Preserving High-Order Compact OEDG Method for Spherically Symmetric Einstein-Euler System
Communications in Mathematical Research, 2025.
Paper
arXiv
BibTeX
@article{pub2025constraintpreservinghighordercompactoedgmethodforsphericallysymmetriceinsteineuler,
author = {Yuchen Huang and Manting Peng and Kailiang Wu},
title = {{Constraint-Preserving High-Order Compact OEDG Method for Spherically Symmetric Einstein-Euler System}},
journal = {Communications in Mathematical Research},
year = {2025},
volume = {41},
number = {4},
pages = {370--414},
doi = {10.4208/cmr.2025-0052},
eprint = {2512.03496},
archivePrefix = {arXiv},
url = {https://doi.org/10.4208/cmr.2025-0052}
}
arXiv, 2025. Preprint
arXiv
BibTeX
@misc{pubarxiv251018380,
author = {Chuan Fan and Qian Huang and Kailiang Wu},
title = {{Provably realizability-preserving finite volume method for quadrature-based moment models of kinetic equations}},
year = {2025},
eprint = {2510.18380},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2510.18380}
}
SIAM Journal on Scientific Computing, 2020.
arXiv
BibTeX
@article{pub2020structurepreservingmethodforreconstructingunknownhamiltoniansystemsfrom,
author = {Kailiang Wu and Tong Qin and Dongbin Xiu},
title = {{Structure-preserving method for reconstructing unknown Hamiltonian systems from trajectory data}},
journal = {SIAM Journal on Scientific Computing},
year = {2020},
volume = {42},
number = {6},
pages = {A3704--A3729},
eprint = {1905.10396},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1905.10396}
}
Journal of Computational Physics, 2017.
Paper
arXiv
BibTeX
@article{pub2017astochasticgalerkinmethodforfirstorderquasilinearhyperbolic,
author = {Kailiang Wu and Huazhong Tang and Dongbin Xiu},
title = {{A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty}},
journal = {Journal of Computational Physics},
year = {2017},
volume = {345},
pages = {224--244},
doi = {10.1016/j.jcp.2017.05.027},
eprint = {1601.04121},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2017.05.027}
}Computational Fluid Dynamics and Astrophysics
Math. Models Methods Appl. Sci. (M3AS), 2017.
Paper
arXiv
BibTeX
@article{pub2017admissiblestatesandphysicalconstraintspreservingschemesforrelativistic,
author = {Kailiang Wu and Huazhong Tang},
title = {{Admissible states and physical-constraints-preserving schemes for relativistic magnetohydrodynamic equations}},
journal = {Math. Models Methods Appl. Sci. (M3AS)},
year = {2017},
volume = {27},
number = {10},
pages = {1871--1928},
doi = {10.1142/S0218202517500348},
eprint = {1603.06660},
archivePrefix = {arXiv},
url = {https://doi.org/10.1142/S0218202517500348}
}
Numerische Mathematik, 2019.
arXiv
BibTeX
@article{pub2019provablypositivehighorderschemesforidealmagnetohydrodynamicsanalysis,
author = {Kailiang Wu and Chi-Wang Shu},
title = {{Provably positive high-order schemes for ideal magnetohydrodynamics: Analysis on general meshes}},
journal = {Numerische Mathematik},
year = {2019},
volume = {142},
number = {4},
pages = {995--1047},
eprint = {1807.11467},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1807.11467}
}
SIAM Journal on Numerical Analysis, 2018.
Paper
PDF
arXiv
BibTeX
@article{pub2018positivitypreservinganalysisofnumericalschemesforidealmagnetohydrodynamics,
author = {Kailiang Wu},
title = {{Positivity-preserving analysis of numerical schemes for ideal magnetohydrodynamics}},
journal = {SIAM Journal on Numerical Analysis},
year = {2018},
volume = {56},
number = {4},
pages = {2124--2147},
doi = {10.1137/18M1168017},
eprint = {1802.02278},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/18M1168017}
}
Numerische Mathematik, 2021.
arXiv
BibTeX
@article{pub2021provablyphysicalconstraintpreservingdiscontinuousgalerkinmethodsformultidimensional,
author = {Kailiang Wu and Chi-Wang Shu},
title = {{Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations}},
journal = {Numerische Mathematik},
year = {2021},
volume = {148},
pages = {699--741},
eprint = {2002.03371},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2002.03371}
}
SIAM Journal on Scientific Computing, 2021.
arXiv
BibTeX
@article{pub2021minimumprincipleonspecificentropyandhighorderaccurate,
author = {Kailiang Wu},
title = {{Minimum principle on specific entropy and high-order accurate invariant region preserving numerical methods for relativistic hydrodynamics}},
journal = {SIAM Journal on Scientific Computing},
year = {2021},
volume = {43},
number = {6},
pages = {B1164--B1197},
eprint = {2102.03801},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2102.03801}
}
Physical Review D, 2017.
Paper
arXiv
BibTeX
@article{pub2017designofprovablyphysicalconstraintpreservingmethodsforgeneral,
author = {Kailiang Wu},
title = {{Design of provably physical-constraint-preserving methods for general relativistic hydrodynamics}},
journal = {Physical Review D},
year = {2017},
doi = {10.1103/PhysRevD.95.103001},
eprint = {1610.06274},
archivePrefix = {arXiv},
url = {https://doi.org/10.1103/PhysRevD.95.103001}
}
SIAM Journal on Scientific Computing, 2020.
arXiv
BibTeX
@article{pub2020entropysymmetrizationandhighorderaccurateentropystablenumerical,
author = {Kailiang Wu and Chi-Wang Shu},
title = {{Entropy symmetrization and high-order accurate entropy stable numerical schemes for relativistic MHD equations}},
journal = {SIAM Journal on Scientific Computing},
year = {2020},
volume = {42},
number = {4},
pages = {A2230--A2261},
eprint = {1907.07467},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1907.07467}
}
Journal of Computational Physics, 2015.
arXiv
BibTeX
@article{pub2015highorderaccuratephysicalconstraintspreservingfinitedifferenceweno,
author = {Kailiang Wu and Huazhong Tang},
title = {{High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics}},
journal = {Journal of Computational Physics},
year = {2015},
volume = {298},
pages = {539--564},
eprint = {1504.07707},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1504.07707}
}
Astrophys. J. Suppl. Ser. (ApJS), 2017.
arXiv
BibTeX
@article{pub2017physicalconstraintpreservingcentraldiscontinuousgalerkinmethodsforspecial,
author = {Kailiang Wu and Huazhong Tang},
title = {{Physical-constraint-preserving central discontinuous Galerkin methods for special relativistic hydrodynamics with a general equation of state}},
journal = {Astrophys. J. Suppl. Ser. (ApJS)},
year = {2017},
volume = {228},
number = {1},
pages = {3},
eprint = {1607.08332},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1607.08332}
}
SIAM Journal on Numerical Analysis, 2025.
Paper
BibTeX
@article{pub2025provablyconvergentandrobustnewtonraphsonmethodanew,
author = {C. Cai and J. Qiu and K. Wu},
title = {{Provably Convergent Newton--Raphson Method: Theoretically Robust Recovery of Primitive Variables in Relativistic MHD}},
journal = {SIAM Journal on Numerical Analysis},
year = {2025},
doi = {10.1137/24M1651873},
url = {https://doi.org/10.1137/24M1651873}
}
Journal of Computational Physics, 2024.
Paper
arXiv
BibTeX
@article{pub2024provablyconvergentnewtonraphsonmethodsforrecoveringprimitivevariables,
author = {Chaoyi Cai and Jianxian Qiu and Kailiang Wu},
title = {{Provably convergent Newton-Raphson methods for recovering primitive variables with applications to physical-constraint-preserving Hermite WENO schemes for relativistic hydrodynamics}},
journal = {Journal of Computational Physics},
year = {2024},
volume = {498},
pages = {112669},
doi = {10.1016/j.jcp.2023.112669},
eprint = {2305.14805},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2023.112669}
}
Journal of Computational Physics, 2026. Accepted
Paper
BibTeX
@article{pub2026robustandprovablyconvergentprimitivevariablerecoveryforrelativistichydrodynamicswithsynge,
author = {J. Yue and F. Du and K. Wu},
title = {{Robust and provably convergent primitive variable recovery for relativistic hydrodynamics with Synge-type equations of state}},
journal = {Journal of Computational Physics},
year = {2026},
doi = {10.1016/j.jcp.2026.115155},
note = {Accepted},
url = {https://doi.org/10.1016/j.jcp.2026.115155}
}
SIAM Journal on Scientific Computing, 2018.
arXiv
BibTeX
@article{pub2018aprovablypositivediscontinuousgalerkinmethodformultidimensionalideal,
author = {Kailiang Wu and Chi-Wang Shu},
title = {{A provably positive discontinuous Galerkin method for multidimensional ideal magnetohydrodynamics}},
journal = {SIAM Journal on Scientific Computing},
year = {2018},
volume = {40},
number = {5},
pages = {B1302--B1329},
eprint = {1807.00246},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1807.00246}
}
SIAM Journal on Numerical Analysis, 2023.
arXiv
BibTeX
@article{pub2023provablypositivecentraldiscontinuousgalerkinschemesviageometricquasilinearization,
author = {Kailiang Wu and Haili Jiang and Chi-Wang Shu},
title = {{Provably positive central discontinuous Galerkin schemes via geometric quasilinearization for ideal MHD equations}},
journal = {SIAM Journal on Numerical Analysis},
year = {2023},
volume = {61},
pages = {250--285},
eprint = {2203.14853},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2203.14853}
}
SIAM Journal on Scientific Computing, 2024.
Paper
arXiv
BibTeX
@article{pub2024anewdiscretelydivergencefreepositivitypreservinghighorder,
author = {Shengrong Ding and Kailiang Wu},
title = {{A new discretely divergence-free positivity-preserving high-order finite volume method for ideal MHD equations}},
journal = {SIAM Journal on Scientific Computing},
year = {2024},
volume = {46},
number = {1},
pages = {A50--A79},
doi = {10.1137/23M1562081},
eprint = {2305.14820},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/23M1562081}
}
Journal of Computational Physics, 2024.
Paper
arXiv
BibTeX
@article{pub2024gqlbasedboundpreservingandlocallydivergencefreecentral,
author = {Shengrong Ding and Kailiang Wu},
title = {{GQL-based bound-preserving and locally divergence-free central discontinuous Galerkin schemes for relativistic magnetohydrodynamics}},
journal = {Journal of Computational Physics},
year = {2024},
volume = {514},
pages = {113208},
doi = {10.1016/j.jcp.2024.113208},
eprint = {2402.15437},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2024.113208}
}
Monthly Notices of the Royal Astronomical Society (MNRAS), 2025.
Paper
BibTeX
@article{pub2025divergencefreefinitevolumewenoschemeforrelativisticmagnetohydrodynamics,
author = {S. Ding and K. Wu and C. Yuan},
title = {{Divergence-free finite volume WENO scheme for relativistic magnetohydrodynamics preserving positivity and subluminal velocity}},
journal = {Monthly Notices of the Royal Astronomical Society (MNRAS)},
year = {2025},
doi = {10.1093/mnras/staf280},
url = {https://doi.org/10.1093/mnras/staf280}
}
Journal of Computational Physics, 2025.
arXiv
BibTeX
@article{pub2025structurepreservingoscillationeliminatingdiscontinuousgalerkinschemesforideal,
author = {Mengqing Liu and Kailiang Wu},
title = {{Structure-preserving oscillation-eliminating discontinuous Galerkin schemes for ideal MHD equations: Locally divergence-free and positivity-preserving}},
journal = {Journal of Computational Physics},
year = {2025},
eprint = {2404.16794},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2404.16794}
}
Journal of Computational Physics, 2026.
Paper
BibTeX
@article{pub2026highorderpositivitypreservingandgloballydivergencefreediscontinuousgalerkinmethodsfor,
author = {Mengqing Liu and Kailiang Wu and Caiyou Yuan},
title = {{High-order positivity-preserving and globally divergence-free discontinuous Galerkin methods for ideal magnetohydrodynamics with conditional energy conservation}},
journal = {Journal of Computational Physics},
year = {2026},
volume = {562},
pages = {115031},
doi = {10.1016/j.jcp.2026.115031},
url = {https://doi.org/10.1016/j.jcp.2026.115031}
}
Math. Models Methods Appl. Sci. (M3AS), 2026. Accepted
arXiv
BibTeX
@article{pub2026provablypositivitypreservinggloballydivergencefreecentraldgmethodsforidealmhd,
author = {Ruifang Yan and Huihui Cao and Kailiang Wu},
title = {{Provably positivity-preserving, globally divergence-free central DG methods for ideal MHD system}},
journal = {Math. Models Methods Appl. Sci. (M3AS)},
year = {2026},
eprint = {2508.08913},
archivePrefix = {arXiv},
note = {Accepted},
url = {https://arxiv.org/abs/2508.08913}
}
Journal of Computational Physics, 2026. In press
Paper
arXiv
BibTeX
@article{pub2026anactivefluxtypeschemeforidealmhdwithprovablepositivityand,
author = {Mengqing Liu and Dongwen Pang and Remi Abgrall and Kailiang Wu},
title = {{An active-flux-type scheme for ideal MHD with provable positivity and a point-value-level discrete divergence-free constraint}},
journal = {Journal of Computational Physics},
year = {2026},
doi = {10.1016/j.jcp.2026.115319},
eprint = {2510.19721},
archivePrefix = {arXiv},
note = {In press},
url = {https://doi.org/10.1016/j.jcp.2026.115319}
}
Provably positivity-preserving constrained transport scheme for 2D and 3D ideal magnetohydrodynamics
Journal of Computational Physics, 2025.
arXiv
BibTeX
@article{pub2025provablypositivitypreservingconstrainedtransportschemefor2dand3didealmagnetohydrodynamics,
author = {Dongwen Pang and Kailiang Wu},
title = {{Provably positivity-preserving constrained transport scheme for 2D and 3D ideal magnetohydrodynamics}},
journal = {Journal of Computational Physics},
year = {2025},
volume = {541},
pages = {114312},
eprint = {2410.05173},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2410.05173}
}
Journal of Scientific Computing, 2024.
Paper
BibTeX
@article{pub2024highorderstructurepreservingfinitedifferencewenoschemeformhdequationswith,
author = {W. Chen and K. Wu and T. Xiong},
title = {{High order structure-preserving finite difference WENO schemes for MHD equations with gravitation in all sonic Mach numbers}},
journal = {Journal of Scientific Computing},
year = {2024},
volume = {99},
pages = {36},
doi = {10.1007/s10915-024-02492-7},
url = {https://doi.org/10.1007/s10915-024-02492-7}
}
Journal of Computational Physics, 2023.
arXiv
BibTeX
@article{pub2023highorderasymptoticpreservingfinitedifferencewenoschemeswith,
author = {Wei Chen and Kailiang Wu and Tao Xiong},
title = {{High order asymptotic preserving finite difference WENO schemes with constrained transport for MHD equations in all sonic Mach numbers}},
journal = {Journal of Computational Physics},
year = {2023},
volume = {488},
pages = {112240},
eprint = {2211.16655},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2211.16655}
}
Z. Angew. Math. Phys., 2018.
arXiv
BibTeX
@article{pub2018onphysicalconstraintspreservingschemesforspecialrelativisticmagnetohydrodynamicswithageneral,
author = {Kailiang Wu and Huazhong Tang},
title = {{On physical-constraints-preserving schemes for special relativistic magnetohydrodynamics with a general equation of state}},
journal = {Z. Angew. Math. Phys.},
year = {2018},
volume = {69},
pages = {84},
eprint = {1709.05838},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1709.05838}
}
Communications in Computational Physics, 2021.
Paper
BibTeX
@article{pub2021awenobasedstochasticgalerkinschemeforidealmhdequationswithrandom,
author = {K. Wu and D. Xiu and X. Zhong},
title = {{A WENO-based stochastic Galerkin scheme for ideal MHD equations with random inputs}},
journal = {Communications in Computational Physics},
year = {2021},
volume = {30},
number = {2},
pages = {423--447},
doi = {10.4208/cicp.OA-2020-0167},
url = {https://doi.org/10.4208/cicp.OA-2020-0167}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260926791,
author = {Huihui Cao and Kailiang Wu and Caiyou Yuan},
title = {{Fully Discrete Multi-Entropy Stability of High-Order Schemes for Compressible MHD: A Weak-to-Strong Framework}},
year = {2026},
eprint = {2609.26791},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2609.26791}
}
Journal of Computational Physics, 2025.
arXiv
BibTeX
@article{pub2025robustdiscontinuousgalerkinmethodsmaintainingphysicalconstraintsforgeneral,
author = {Huihui Cao and Manting Peng and Kailiang Wu},
title = {{Robust discontinuous Galerkin methods maintaining physical constraints for general relativistic hydrodynamics}},
journal = {Journal of Computational Physics},
year = {2025},
eprint = {2410.05000},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2410.05000}
}
Constraint-Preserving High-Order Compact OEDG Method for Spherically Symmetric Einstein-Euler System
Communications in Mathematical Research, 2025.
Paper
arXiv
BibTeX
@article{pub2025constraintpreservinghighordercompactoedgmethodforsphericallysymmetriceinsteineuler,
author = {Yuchen Huang and Manting Peng and Kailiang Wu},
title = {{Constraint-Preserving High-Order Compact OEDG Method for Spherically Symmetric Einstein-Euler System}},
journal = {Communications in Mathematical Research},
year = {2025},
volume = {41},
number = {4},
pages = {370--414},
doi = {10.4208/cmr.2025-0052},
eprint = {2512.03496},
archivePrefix = {arXiv},
url = {https://doi.org/10.4208/cmr.2025-0052}
}
Journal of Computational Physics, 2026. Accepted
arXiv
BibTeX
@article{pub2026gqlbasedphysicalconstraintpreservinghighorderfinitedifferenceschemesforspecial,
author = {Linfeng Xu and Shengrong Ding and Kailiang Wu},
title = {{GQL-based physical-constraint-preserving high-order finite difference schemes for special relativistic hydrodynamics in arbitrary dimensions}},
journal = {Journal of Computational Physics},
year = {2026},
eprint = {2606.31992},
archivePrefix = {arXiv},
note = {Accepted},
url = {https://arxiv.org/abs/2606.31992}
}
Journal of Computational Physics, 2026.
Paper
BibTeX
@article{pub2026highorderaccurateboundpreservingadaptivemovingmeshfinitevolumemethodsfor,
author = {C. Yuan and Z. Zhang and H. Tang and K. Wu},
title = {{High-order accurate bound-preserving adaptive moving mesh finite volume methods for 2D and 3D special relativistic hydrodynamics}},
journal = {Journal of Computational Physics},
year = {2026},
volume = {554},
pages = {114728},
doi = {10.1016/j.jcp.2026.114728},
url = {https://doi.org/10.1016/j.jcp.2026.114728}
}
Journal of Computational Physics, 2022.
arXiv
BibTeX
@article{pub2022aphysicalconstraintpreservingfinitevolumemethodforspecial,
author = {Yaping Chen and Kailiang Wu},
title = {{A physical-constraint-preserving finite volume WENO method for special relativistic hydrodynamics on unstructured meshes}},
journal = {Journal of Computational Physics},
year = {2022},
volume = {466},
pages = {111398},
eprint = {2207.09385},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2207.09385}
}
Mathematics of Computation, 2026.
Paper
arXiv
BibTeX
@article{pub2025onlocalminimumentropyprincipleofhighorderschemes,
author = {Shumo Cui and Kailiang Wu and Linfeng Xu},
title = {{On local minimum entropy principle of high-order schemes for relativistic Euler equations}},
journal = {Mathematics of Computation},
year = {2026},
volume = {95},
number = {362},
pages = {2739-2787},
doi = {10.1090/mcom/4139},
eprint = {2503.12465},
archivePrefix = {arXiv},
url = {https://doi.org/10.1090/mcom/4139}
}
Journal of Scientific Computing, 2024.
arXiv
BibTeX
@article{pub2024highorderaccurateentropystableschemesforrelativistichydrodynamicswithageneral,
author = {Linfeng Xu and Shengrong Ding and Kailiang Wu},
title = {{High-order accurate entropy stable schemes for relativistic hydrodynamics with general Synge-type equation of state}},
journal = {Journal of Scientific Computing},
year = {2024},
volume = {98},
pages = {43},
eprint = {2409.10872},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2409.10872}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260809327,
author = {Linfeng Xu and Kailiang Wu},
title = {{High-order fully discrete multi-entropy-stable and bound-preserving schemes for relativistic Euler equations}},
year = {2026},
eprint = {2608.09327},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2608.09327}
}
SIAM Journal on Scientific Computing, 2021.
arXiv
BibTeX
@article{pub2021uniformlyhighorderstructurepreservingdiscontinuousgalerkinmethodsfor,
author = {Kailiang Wu and Yulong Xing},
title = {{Uniformly high-order structure-preserving discontinuous Galerkin methods for Euler equations with gravitation: Positivity and well-balancedness}},
journal = {SIAM Journal on Scientific Computing},
year = {2021},
volume = {43},
number = {1},
pages = {A472--A510},
eprint = {2005.07166},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2005.07166}
}
Journal of Computational Physics, 2023.
Paper
BibTeX
@article{pub2023onpositivitypreservingwellbalancedfinitevolumemethodsfor,
author = {Y. Ren and K. Wu and J. Qiu and Y. Xing},
title = {{On high order positivity-preserving well-balanced finite volume methods for the Euler equations with gravitation}},
journal = {Journal of Computational Physics},
year = {2023},
volume = {492},
pages = {112429},
doi = {10.1016/j.jcp.2023.112429},
url = {https://doi.org/10.1016/j.jcp.2023.112429}
}
Journal of Computational Physics, 2022.
arXiv
BibTeX
@article{pub2022positivitypreservingwellbalancedcentraldiscontinuousgalerkinschemesfor,
author = {Haili Jiang and Huazhong Tang and Kailiang Wu},
title = {{Positivity-preserving well-balanced central discontinuous Galerkin schemes for the Euler equations under gravitational fields}},
journal = {Journal of Computational Physics},
year = {2022},
volume = {463},
pages = {111297},
eprint = {2207.09398},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2207.09398}
}
Journal of Computational Physics, 2025.
arXiv
BibTeX
@article{pub2025highorderaccuratestructurepreservingfinitevolumeschemeson,
author = {Zhihao Zhang and Huazhong Tang and Kailiang Wu},
title = {{High-order accurate structure-preserving finite volume schemes on adaptive moving meshes for shallow water equations: Well balancedness and positivity}},
journal = {Journal of Computational Physics},
year = {2025},
eprint = {2409.09600},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2409.09600}
}
SIAM Journal on Scientific Computing, 2024.
Paper
arXiv
BibTeX
@article{pub2024anewlocallydivergencefreepathconservativecentralupwind,
author = {Alina Chertock and Alexander Kurganov and Michael Redle and Kailiang Wu},
title = {{A new locally divergence-free path-conservative central-upwind scheme for ideal and shallow water magnetohydrodynamics}},
journal = {SIAM Journal on Scientific Computing},
year = {2024},
volume = {46},
number = {3},
pages = {A1998--A2024},
doi = {10.1137/22M1539009},
eprint = {2212.02682},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/22M1539009}
}
Journal of Computational Physics, 2025.
Paper
BibTeX
@article{pub2025positivitypreservingnewlowdssipationcentralupwindschemesfor,
author = {S. Cui and Y. Gu and A. Kurganov and K. Wu and R. Xin},
title = {{Positivity-preserving new low-dissipation central-upwind schemes for compressible Euler equations}},
journal = {Journal of Computational Physics},
year = {2025},
doi = {10.1016/j.jcp.2025.114189},
url = {https://doi.org/10.1016/j.jcp.2025.114189}
}
SIAM Journal on Scientific Computing, 2024.
Paper
arXiv
BibTeX
@article{pub2024boundpreservingframeworkforcentralupwindschemesforgeneral,
author = {Shumo Cui and Alexander Kurganov and Kailiang Wu},
title = {{Bound-preserving framework for central-upwind schemes for general hyperbolic conservation laws}},
journal = {SIAM Journal on Scientific Computing},
year = {2024},
volume = {46},
number = {5},
pages = {A2899--A2924},
doi = {10.1137/23M1628024},
eprint = {2403.13420},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/23M1628024}
}
Journal of Computational Physics, 2024.
arXiv
BibTeX
@article{pub2024highorderaccuratepositivitypreservingandwellbalanceddiscontinuous,
author = {Jiangfu Wang and Huazhong Tang and Kailiang Wu},
title = {{High-order accurate positivity-preserving and well-balanced discontinuous Galerkin schemes for ten-moment Gaussian closure equations with source terms}},
journal = {Journal of Computational Physics},
year = {2024},
eprint = {2402.15446},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2402.15446}
}
Math. Models Methods Appl. Sci. (M3AS), 2024.
Paper
BibTeX
@article{pub2024uniformlyhighorderboundpreservingoedgschemesfortwo,
author = {R. Yan and R. Abgrall and K. Wu},
title = {{Uniformly high-order bound-preserving OEDG schemes for two-phase flows}},
journal = {Math. Models Methods Appl. Sci. (M3AS)},
year = {2024},
doi = {10.1142/S0218202524500544},
url = {https://doi.org/10.1142/S0218202524500544}
}
Annals of Applied Mathematics, 2024.
Paper
BibTeX
@article{pub2024oscillationeliminatingdiscontinuousgalerkinmethodsformulticomponentchemicallyreactingflows,
author = {J. Du and C. Fan and K. Wu},
title = {{Oscillation-eliminating discontinuous Galerkin methods for multicomponent chemically reacting flows}},
journal = {Annals of Applied Mathematics},
year = {2024},
volume = {40},
pages = {412-444},
doi = {10.4208/aam.oa-2024-0029},
url = {https://doi.org/10.4208/aam.oa-2024-0029}
}
Journal of Scientific Computing, 2025.
Paper
BibTeX
@article{pub2025physicalconstraintpreservinghighorderfinitevolumewenomethodviageometricquasilinearization,
author = {L. Y. Win and Y. Chen and Y. Nie and L. Cai and K. Wu},
title = {{Physical-constraint-preserving high-order finite volume WENO method via geometric quasilinearization for Chaplygin gas dynamics}},
journal = {Journal of Scientific Computing},
year = {2025},
volume = {105},
pages = {33},
doi = {10.1007/s10915-025-03059-w},
url = {https://doi.org/10.1007/s10915-025-03059-w}
}
arXiv, 2025. Preprint
arXiv
BibTeX
@misc{pubarxiv251018380,
author = {Chuan Fan and Qian Huang and Kailiang Wu},
title = {{Provably realizability-preserving finite volume method for quadrature-based moment models of kinetic equations}},
year = {2025},
eprint = {2510.18380},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2510.18380}
}
Numer. Math. Theor. Meth. Appl., 2017.
Paper
arXiv
BibTeX
@article{pub2017rungekuttadiscontinuouslocalevolutiongalerkinmethodsfortheshallowwaterequations,
author = {Yangyu Kuang and Kailiang Wu and Huazhong Tang},
title = {{Runge-Kutta discontinuous local evolution Galerkin methods for the shallow water equations on the cubed-sphere grid}},
journal = {Numer. Math. Theor. Meth. Appl.},
year = {2017},
volume = {10},
number = {2},
pages = {373--419},
doi = {10.4208/nmtma.2017.s09},
eprint = {1608.06700},
archivePrefix = {arXiv},
url = {https://doi.org/10.4208/nmtma.2017.s09}
}
Applied Mathematics and Mechanics, 2016.
Paper
arXiv
BibTeX
@article{pub2016anewtonmultigridmethodforsteadystateshallowwaterequationswithtopography,
author = {Kailiang Wu and Huazhong Tang},
title = {{A Newton multigrid method for steady-state shallow water equations with topography and dry areas}},
journal = {Applied Mathematics and Mechanics},
year = {2016},
volume = {37},
number = {11},
pages = {1441--1466},
doi = {10.1007/s10483-016-2108-6},
eprint = {1608.06721},
archivePrefix = {arXiv},
url = {https://doi.org/10.1007/s10483-016-2108-6}
}
SIAM Journal on Scientific Computing, 2016.
Paper
arXiv
BibTeX
@article{pub2016adirecteuleriangrpschemeforsphericallysymmetricgeneral,
author = {Kailiang Wu and Huazhong Tang},
title = {{A direct Eulerian GRP scheme for spherically symmetric general relativistic hydrodynamics}},
journal = {SIAM Journal on Scientific Computing},
year = {2016},
volume = {38},
number = {3},
pages = {B458--B489},
doi = {10.1137/16M1055657},
eprint = {1601.00931},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/16M1055657}
}
East Asian J. Appl. Math., 2014.
Paper
BibTeX
@article{pub2014athirdorderaccuratedirecteuleriangrpschemeforonedimensionalrelativistic,
author = {K. Wu and Z. Yang and H. Tang},
title = {{A third-order accurate direct Eulerian GRP scheme for one-dimensional relativistic hydrodynamics}},
journal = {East Asian J. Appl. Math.},
year = {2014},
volume = {4},
number = {2},
pages = {95--131},
doi = {10.4208/eajam.101013.100314a},
url = {https://doi.org/10.4208/eajam.101013.100314a}
}
Journal of Computational Physics, 2014.
Paper
BibTeX
@article{pub2014finitevolumelocalevolutiongalerkinmethodfortwodimensional,
author = {K. Wu and H. Tang},
title = {{Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics}},
journal = {Journal of Computational Physics},
year = {2014},
volume = {256},
pages = {277--307},
doi = {10.1016/j.jcp.2013.08.057},
url = {https://doi.org/10.1016/j.jcp.2013.08.057}
}
Journal of Computational Physics, 2014.
Paper
BibTeX
@article{pub2014athirdorderaccuratedirecteuleriangrpschemefor,
author = {K. Wu and Z. Yang and H. Tang},
title = {{A third-order accurate direct Eulerian GRP scheme for the Euler equations in gas dynamics}},
journal = {Journal of Computational Physics},
year = {2014},
volume = {264},
pages = {177--208},
doi = {10.1016/j.jcp.2014.01.041},
url = {https://doi.org/10.1016/j.jcp.2014.01.041}
}High-Order Accurate Numerical Methods
SIAM Journal on Numerical Analysis, 2024.
arXiv
BibTeX
@article{pub2024onoptimalcellaveragedecompositionforhighorderbound,
author = {Shumo Cui and Shengrong Ding and Kailiang Wu},
title = {{On optimal cell average decomposition for high-order bound-preserving schemes of hyperbolic conservation laws}},
journal = {SIAM Journal on Numerical Analysis},
year = {2024},
eprint = {2212.05045},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2212.05045}
}
Mathematics of Computation, 2025.
Paper
PDF (arXiv version)
arXiv
BibTeX
@article{pub2025oedgoscillationeliminatingdiscontinuousgalerkinmethodforhyperbolicconservation,
author = {Manting Peng and Zheng Sun and Kailiang Wu},
title = {{OEDG: Oscillation-eliminating discontinuous Galerkin method for hyperbolic conservation laws}},
journal = {Mathematics of Computation},
year = {2025},
volume = {94},
pages = {1147--1198},
doi = {10.1090/mcom/3998},
eprint = {2310.04807},
archivePrefix = {arXiv},
url = {https://doi.org/10.1090/mcom/3998}
}
Numerische Mathematik, 2019.
arXiv
BibTeX
@article{pub2019provablypositivehighorderschemesforidealmagnetohydrodynamicsanalysis,
author = {Kailiang Wu and Chi-Wang Shu},
title = {{Provably positive high-order schemes for ideal magnetohydrodynamics: Analysis on general meshes}},
journal = {Numerische Mathematik},
year = {2019},
volume = {142},
number = {4},
pages = {995--1047},
eprint = {1807.11467},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1807.11467}
}
SIAM Journal on Scientific Computing, 2021.
arXiv
BibTeX
@article{pub2021minimumprincipleonspecificentropyandhighorderaccurate,
author = {Kailiang Wu},
title = {{Minimum principle on specific entropy and high-order accurate invariant region preserving numerical methods for relativistic hydrodynamics}},
journal = {SIAM Journal on Scientific Computing},
year = {2021},
volume = {43},
number = {6},
pages = {B1164--B1197},
eprint = {2102.03801},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2102.03801}
}
SIAM Journal on Numerical Analysis, 2018.
Paper
PDF
arXiv
BibTeX
@article{pub2018positivitypreservinganalysisofnumericalschemesforidealmagnetohydrodynamics,
author = {Kailiang Wu},
title = {{Positivity-preserving analysis of numerical schemes for ideal magnetohydrodynamics}},
journal = {SIAM Journal on Numerical Analysis},
year = {2018},
volume = {56},
number = {4},
pages = {2124--2147},
doi = {10.1137/18M1168017},
eprint = {1802.02278},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/18M1168017}
}
SIAM Journal on Scientific Computing, 2018.
arXiv
BibTeX
@article{pub2018aprovablypositivediscontinuousgalerkinmethodformultidimensionalideal,
author = {Kailiang Wu and Chi-Wang Shu},
title = {{A provably positive discontinuous Galerkin method for multidimensional ideal magnetohydrodynamics}},
journal = {SIAM Journal on Scientific Computing},
year = {2018},
volume = {40},
number = {5},
pages = {B1302--B1329},
eprint = {1807.00246},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1807.00246}
}
Math. Models Methods Appl. Sci. (M3AS), 2017.
Paper
arXiv
BibTeX
@article{pub2017admissiblestatesandphysicalconstraintspreservingschemesforrelativistic,
author = {Kailiang Wu and Huazhong Tang},
title = {{Admissible states and physical-constraints-preserving schemes for relativistic magnetohydrodynamic equations}},
journal = {Math. Models Methods Appl. Sci. (M3AS)},
year = {2017},
volume = {27},
number = {10},
pages = {1871--1928},
doi = {10.1142/S0218202517500348},
eprint = {1603.06660},
archivePrefix = {arXiv},
url = {https://doi.org/10.1142/S0218202517500348}
}
SIAM Journal on Numerical Analysis, 2022.
arXiv
BibTeX
@article{pub2022onenergylawsandstabilityofrungekuttamethods,
author = {Zheng Sun and Yuanzhe Wei and Kailiang Wu},
title = {{On energy laws and stability of Runge--Kutta methods for linear seminegative problems}},
journal = {SIAM Journal on Numerical Analysis},
year = {2022},
volume = {60},
number = {5},
pages = {2448--2481},
eprint = {2201.06501},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2201.06501}
}
Journal of Computational Physics, 2023.
Paper
arXiv
BibTeX
@article{pub2022istheclassicconvexdecompositionoptimalforboundpreserving,
author = {Shumo Cui and Shengrong Ding and Kailiang Wu},
title = {{Is the classic convex decomposition optimal for bound-preserving schemes in multiple dimensions?}},
journal = {Journal of Computational Physics},
year = {2023},
volume = {476},
pages = {111882},
doi = {10.1016/j.jcp.2022.111882},
eprint = {2207.08849},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2022.111882}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260631931,
author = {Manting Peng and Kailiang Wu},
title = {{Hidden Accuracy and Superconvergence Analysis of Central Discontinuous Galerkin Methods on Overlapping Meshes}},
year = {2026},
eprint = {2606.31931},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2606.31931}
}
On energy laws and stability of first-subdiagonal Padé approximants for linear seminegative problems
Journal of Information and Computing Science, 2026. Accepted
arXiv
BibTeX
@article{pub2026onenergylawsandstabilityoffirstsubdiagonalpadeapproximantsforlinear,
author = {Miaosen Jiao and Zheng Sun and Kailiang Wu},
title = {{On energy laws and stability of first-subdiagonal Pad{\'e} approximants for linear seminegative problems}},
journal = {Journal of Information and Computing Science},
year = {2026},
eprint = {2608.09239},
archivePrefix = {arXiv},
note = {Accepted},
url = {https://arxiv.org/abs/2608.09239}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260400301,
author = {Kailiang Wu},
title = {{EPO: A Unified Framework for Entropy Stability, Positivity, and Oscillation Suppression}},
year = {2026},
eprint = {2604.00301},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2604.00301}
}
Journal of Computational Physics, 2026.
Paper
BibTeX
@article{pub2026cosdgaconvexoscillationsuppressingframeworkforhighorderdiscontinuousgalerkin,
author = {Huihui Cao and Yunqing Huang and Zhuoyun Li and Kailiang Wu},
title = {{COS(DG): A Convex Oscillation-Suppressing Framework for High-Order Discontinuous Galerkin Methods}},
journal = {Journal of Computational Physics},
year = {2026},
volume = {554},
pages = {114755},
doi = {10.1016/j.jcp.2026.114755},
url = {https://doi.org/10.1016/j.jcp.2026.114755}
}
Journal of Computational Physics, 2027.
Paper
BibTeX
@article{pub2026cossvconvexoscillationsuppressingspectralvolumeschemeswithboundpreservationfor,
author = {Ruifang Yan and Huihui Cao and Na Liu and Kailiang Wu},
title = {{COS(SV): Convex Oscillation-Suppressing Spectral Volume Schemes with Bound Preservation for Hyperbolic Conservation Laws}},
journal = {Journal of Computational Physics},
year = {2027},
volume = {568},
pages = {115411},
doi = {10.1016/j.jcp.2026.115411},
url = {https://doi.org/10.1016/j.jcp.2026.115411}
}
SIAM Journal on Scientific Computing, 2025.
Paper
arXiv
BibTeX
@article{pub2024spectralvolumefromadgperspectiveoscillationeliminationstability,
author = {Zhuoyun Li and Kailiang Wu},
title = {{Spectral volume from a discontinuous Galerkin perspective: oscillation elimination, stability, and optimal error estimates}},
journal = {SIAM Journal on Scientific Computing},
year = {2025},
volume = {47},
number = {2},
pages = {A1304-A1333},
doi = {10.1137/24m167799x},
eprint = {2409.10871},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/24m167799x}
}
SIAM Journal on Scientific Computing, 2026.
Paper
arXiv
BibTeX
@article{pub2025oscillationeliminatingcentraldgschemesforhyperbolicconservationlaws,
author = {Manting Peng and Kailiang Wu and Caiyou Yuan},
title = {{Oscillation-eliminating central DG schemes on Cartesian meshes for hyperbolic conservation laws}},
journal = {SIAM Journal on Scientific Computing},
year = {2026},
volume = {48},
number = {2},
pages = {A695-A725},
doi = {10.1137/25m1730697},
eprint = {2503.12473},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/25m1730697}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260926195,
author = {Manting Peng and Zhuoyun Li and Kailiang Wu},
title = {{Runge--Kutta-Aligned Oscillation Elimination: Restoring Superconvergence for Fully Discrete Shock-Capturing DG Schemes}},
year = {2026},
eprint = {2609.26195},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2609.26195}
}
Journal of Computational Physics, 2024.
Paper
arXiv
BibTeX
@article{pub2024highorderoscillationeliminatinghermitewenomethodforhyperbolic,
author = {Chuan Fan and Kailiang Wu},
title = {{High-order oscillation-eliminating Hermite WENO method for hyperbolic conservation laws}},
journal = {Journal of Computational Physics},
year = {2024},
volume = {519},
pages = {113435},
doi = {10.1016/j.jcp.2024.113435},
eprint = {2409.09632},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2024.113435}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260926194,
author = {Chuan Fan and Kailiang Wu},
title = {{Compact Finite-Average-Moment Schemes with Single-Step Oscillation Elimination for Hyperbolic Conservation Laws}},
year = {2026},
eprint = {2609.26194},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2609.26194}
}
Journal of Computational Physics, 2025.
arXiv
BibTeX
@article{pub2025robustdgschemesonunstructuredtriangularmeshesoscillationelimination,
author = {Shengrong Ding and Shumo Cui and Kailiang Wu},
title = {{Robust DG schemes on unstructured triangular meshes: Oscillation elimination and bound preservation via optimal convex decomposition}},
journal = {Journal of Computational Physics},
year = {2025},
eprint = {2409.09620},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2409.09620}
}
Math. Models Methods Appl. Sci. (M3AS), 2024.
Paper
BibTeX
@article{pub2024uniformlyhighorderboundpreservingoedgschemesfortwo,
author = {R. Yan and R. Abgrall and K. Wu},
title = {{Uniformly high-order bound-preserving OEDG schemes for two-phase flows}},
journal = {Math. Models Methods Appl. Sci. (M3AS)},
year = {2024},
doi = {10.1142/S0218202524500544},
url = {https://doi.org/10.1142/S0218202524500544}
}
Journal of Computational Physics, 2025.
arXiv
BibTeX
@article{pub2025structurepreservingoscillationeliminatingdiscontinuousgalerkinschemesforideal,
author = {Mengqing Liu and Kailiang Wu},
title = {{Structure-preserving oscillation-eliminating discontinuous Galerkin schemes for ideal MHD equations: Locally divergence-free and positivity-preserving}},
journal = {Journal of Computational Physics},
year = {2025},
eprint = {2404.16794},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2404.16794}
}
Constraint-Preserving High-Order Compact OEDG Method for Spherically Symmetric Einstein-Euler System
Communications in Mathematical Research, 2025.
Paper
arXiv
BibTeX
@article{pub2025constraintpreservinghighordercompactoedgmethodforsphericallysymmetriceinsteineuler,
author = {Yuchen Huang and Manting Peng and Kailiang Wu},
title = {{Constraint-Preserving High-Order Compact OEDG Method for Spherically Symmetric Einstein-Euler System}},
journal = {Communications in Mathematical Research},
year = {2025},
volume = {41},
number = {4},
pages = {370--414},
doi = {10.4208/cmr.2025-0052},
eprint = {2512.03496},
archivePrefix = {arXiv},
url = {https://doi.org/10.4208/cmr.2025-0052}
}
Annals of Applied Mathematics, 2024.
Paper
BibTeX
@article{pub2024oscillationeliminatingdiscontinuousgalerkinmethodsformulticomponentchemicallyreactingflows,
author = {J. Du and C. Fan and K. Wu},
title = {{Oscillation-eliminating discontinuous Galerkin methods for multicomponent chemically reacting flows}},
journal = {Annals of Applied Mathematics},
year = {2024},
volume = {40},
pages = {412-444},
doi = {10.4208/aam.oa-2024-0029},
url = {https://doi.org/10.4208/aam.oa-2024-0029}
}
Journal of Computational Physics, 2025.
Paper
arXiv
BibTeX
@article{pub2024boundpreservingoedgmethodforawrasclezhangtraffic,
author = {Wei Chen and Shumo Cui and Kailiang Wu and Tao Xiong},
title = {{Bound-preserving OEDG schemes for Aw--Rascle--Zhang traffic models on networks}},
journal = {Journal of Computational Physics},
year = {2025},
volume = {520},
pages = {113507},
doi = {10.1016/j.jcp.2024.113507},
eprint = {2409.16269},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2024.113507}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260910476,
author = {Shengrong Ding and Shumo Cui and Remi Abgrall and Kailiang Wu},
title = {{Invariant domain preservation for hybrid point-value and cell-average discretizations of hyperbolic equations on general meshes}},
year = {2026},
eprint = {2609.10476},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2609.10476}
}
SIAM Journal on Scientific Computing, 2025.
arXiv
BibTeX
@article{pub2025anovelandsimpleinvariantdomainpreservingframeworkfor,
author = {R{\'e}mi Abgrall and Miaosen Jiao and Yongle Liu and Kailiang Wu},
title = {{A novel and simple invariant-domain-preserving framework for PAMPA scheme: 1D case}},
journal = {SIAM Journal on Scientific Computing},
year = {2025},
eprint = {2412.03423},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2412.03423}
}
Communications in Computational Physics, 2026.
Paper
arXiv
BibTeX
@article{pub2025boundpreservingpointaveragemomentpolynomialinterpretedpampaschemeonedimensionalcase,
author = {R{\'e}mi Abgrall and Miaosen Jiao and Yongle Liu and Kailiang Wu},
title = {{Bound-preserving Point-Average-Moment PolynomiAl-interpreted (PAMPA) scheme: One-dimensional case}},
journal = {Communications in Computational Physics},
year = {2026},
volume = {39},
number = {1},
pages = {29-58},
doi = {10.4208/cicp.oa-2024-0266},
eprint = {2410.14292},
archivePrefix = {arXiv},
url = {https://doi.org/10.4208/cicp.oa-2024-0266}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260719283,
author = {Zhuoyun Li and Kailiang Wu},
title = {{Structure of ENO Entropy Dissipation: Parity Dichotomy for the ENO--TV Conjecture and Shift Cohomology}},
year = {2026},
eprint = {2607.19283},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2607.19283}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260926791,
author = {Huihui Cao and Kailiang Wu and Caiyou Yuan},
title = {{Fully Discrete Multi-Entropy Stability of High-Order Schemes for Compressible MHD: A Weak-to-Strong Framework}},
year = {2026},
eprint = {2609.26791},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2609.26791}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260809327,
author = {Linfeng Xu and Kailiang Wu},
title = {{High-order fully discrete multi-entropy-stable and bound-preserving schemes for relativistic Euler equations}},
year = {2026},
eprint = {2608.09327},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2608.09327}
}
Mathematics of Computation, 2026.
Paper
arXiv
BibTeX
@article{pub2025onlocalminimumentropyprincipleofhighorderschemes,
author = {Shumo Cui and Kailiang Wu and Linfeng Xu},
title = {{On local minimum entropy principle of high-order schemes for relativistic Euler equations}},
journal = {Mathematics of Computation},
year = {2026},
volume = {95},
number = {362},
pages = {2739-2787},
doi = {10.1090/mcom/4139},
eprint = {2503.12465},
archivePrefix = {arXiv},
url = {https://doi.org/10.1090/mcom/4139}
}
Numerische Mathematik, 2021.
arXiv
BibTeX
@article{pub2021provablyphysicalconstraintpreservingdiscontinuousgalerkinmethodsformultidimensional,
author = {Kailiang Wu and Chi-Wang Shu},
title = {{Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations}},
journal = {Numerische Mathematik},
year = {2021},
volume = {148},
pages = {699--741},
eprint = {2002.03371},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2002.03371}
}
SIAM Journal on Numerical Analysis, 2023.
arXiv
BibTeX
@article{pub2023provablypositivecentraldiscontinuousgalerkinschemesviageometricquasilinearization,
author = {Kailiang Wu and Haili Jiang and Chi-Wang Shu},
title = {{Provably positive central discontinuous Galerkin schemes via geometric quasilinearization for ideal MHD equations}},
journal = {SIAM Journal on Numerical Analysis},
year = {2023},
volume = {61},
pages = {250--285},
eprint = {2203.14853},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2203.14853}
}
SIAM Journal on Scientific Computing, 2024.
Paper
arXiv
BibTeX
@article{pub2024anewdiscretelydivergencefreepositivitypreservinghighorder,
author = {Shengrong Ding and Kailiang Wu},
title = {{A new discretely divergence-free positivity-preserving high-order finite volume method for ideal MHD equations}},
journal = {SIAM Journal on Scientific Computing},
year = {2024},
volume = {46},
number = {1},
pages = {A50--A79},
doi = {10.1137/23M1562081},
eprint = {2305.14820},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/23M1562081}
}
Journal of Computational Physics, 2024.
Paper
arXiv
BibTeX
@article{pub2024gqlbasedboundpreservingandlocallydivergencefreecentral,
author = {Shengrong Ding and Kailiang Wu},
title = {{GQL-based bound-preserving and locally divergence-free central discontinuous Galerkin schemes for relativistic magnetohydrodynamics}},
journal = {Journal of Computational Physics},
year = {2024},
volume = {514},
pages = {113208},
doi = {10.1016/j.jcp.2024.113208},
eprint = {2402.15437},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2024.113208}
}
Math. Models Methods Appl. Sci. (M3AS), 2026. Accepted
arXiv
BibTeX
@article{pub2026provablypositivitypreservinggloballydivergencefreecentraldgmethodsforidealmhd,
author = {Ruifang Yan and Huihui Cao and Kailiang Wu},
title = {{Provably positivity-preserving, globally divergence-free central DG methods for ideal MHD system}},
journal = {Math. Models Methods Appl. Sci. (M3AS)},
year = {2026},
eprint = {2508.08913},
archivePrefix = {arXiv},
note = {Accepted},
url = {https://arxiv.org/abs/2508.08913}
}
Journal of Computational Physics, 2026. In press
Paper
arXiv
BibTeX
@article{pub2026anactivefluxtypeschemeforidealmhdwithprovablepositivityand,
author = {Mengqing Liu and Dongwen Pang and Remi Abgrall and Kailiang Wu},
title = {{An active-flux-type scheme for ideal MHD with provable positivity and a point-value-level discrete divergence-free constraint}},
journal = {Journal of Computational Physics},
year = {2026},
doi = {10.1016/j.jcp.2026.115319},
eprint = {2510.19721},
archivePrefix = {arXiv},
note = {In press},
url = {https://doi.org/10.1016/j.jcp.2026.115319}
}
Monthly Notices of the Royal Astronomical Society (MNRAS), 2025.
Paper
BibTeX
@article{pub2025divergencefreefinitevolumewenoschemeforrelativisticmagnetohydrodynamics,
author = {S. Ding and K. Wu and C. Yuan},
title = {{Divergence-free finite volume WENO scheme for relativistic magnetohydrodynamics preserving positivity and subluminal velocity}},
journal = {Monthly Notices of the Royal Astronomical Society (MNRAS)},
year = {2025},
doi = {10.1093/mnras/staf280},
url = {https://doi.org/10.1093/mnras/staf280}
}
Journal of Computational Physics, 2026.
Paper
BibTeX
@article{pub2026highorderpositivitypreservingandgloballydivergencefreediscontinuousgalerkinmethodsfor,
author = {Mengqing Liu and Kailiang Wu and Caiyou Yuan},
title = {{High-order positivity-preserving and globally divergence-free discontinuous Galerkin methods for ideal magnetohydrodynamics with conditional energy conservation}},
journal = {Journal of Computational Physics},
year = {2026},
volume = {562},
pages = {115031},
doi = {10.1016/j.jcp.2026.115031},
url = {https://doi.org/10.1016/j.jcp.2026.115031}
}
Journal of Scientific Computing, 2024.
Paper
BibTeX
@article{pub2024highorderstructurepreservingfinitedifferencewenoschemeformhdequationswith,
author = {W. Chen and K. Wu and T. Xiong},
title = {{High order structure-preserving finite difference WENO schemes for MHD equations with gravitation in all sonic Mach numbers}},
journal = {Journal of Scientific Computing},
year = {2024},
volume = {99},
pages = {36},
doi = {10.1007/s10915-024-02492-7},
url = {https://doi.org/10.1007/s10915-024-02492-7}
}
Journal of Computational Physics, 2023.
arXiv
BibTeX
@article{pub2023highorderasymptoticpreservingfinitedifferencewenoschemeswith,
author = {Wei Chen and Kailiang Wu and Tao Xiong},
title = {{High order asymptotic preserving finite difference WENO schemes with constrained transport for MHD equations in all sonic Mach numbers}},
journal = {Journal of Computational Physics},
year = {2023},
volume = {488},
pages = {112240},
eprint = {2211.16655},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2211.16655}
}
Astrophys. J. Suppl. Ser. (ApJS), 2017.
arXiv
BibTeX
@article{pub2017physicalconstraintpreservingcentraldiscontinuousgalerkinmethodsforspecial,
author = {Kailiang Wu and Huazhong Tang},
title = {{Physical-constraint-preserving central discontinuous Galerkin methods for special relativistic hydrodynamics with a general equation of state}},
journal = {Astrophys. J. Suppl. Ser. (ApJS)},
year = {2017},
volume = {228},
number = {1},
pages = {3},
eprint = {1607.08332},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1607.08332}
}
Journal of Computational Physics, 2015.
arXiv
BibTeX
@article{pub2015highorderaccuratephysicalconstraintspreservingfinitedifferenceweno,
author = {Kailiang Wu and Huazhong Tang},
title = {{High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics}},
journal = {Journal of Computational Physics},
year = {2015},
volume = {298},
pages = {539--564},
eprint = {1504.07707},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1504.07707}
}
Journal of Computational Physics, 2025.
arXiv
BibTeX
@article{pub2025robustdiscontinuousgalerkinmethodsmaintainingphysicalconstraintsforgeneral,
author = {Huihui Cao and Manting Peng and Kailiang Wu},
title = {{Robust discontinuous Galerkin methods maintaining physical constraints for general relativistic hydrodynamics}},
journal = {Journal of Computational Physics},
year = {2025},
eprint = {2410.05000},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2410.05000}
}
Journal of Computational Physics, 2026. Accepted
arXiv
BibTeX
@article{pub2026gqlbasedphysicalconstraintpreservinghighorderfinitedifferenceschemesforspecial,
author = {Linfeng Xu and Shengrong Ding and Kailiang Wu},
title = {{GQL-based physical-constraint-preserving high-order finite difference schemes for special relativistic hydrodynamics in arbitrary dimensions}},
journal = {Journal of Computational Physics},
year = {2026},
eprint = {2606.31992},
archivePrefix = {arXiv},
note = {Accepted},
url = {https://arxiv.org/abs/2606.31992}
}
Journal of Computational Physics, 2026.
Paper
BibTeX
@article{pub2026highorderaccurateboundpreservingadaptivemovingmeshfinitevolumemethodsfor,
author = {C. Yuan and Z. Zhang and H. Tang and K. Wu},
title = {{High-order accurate bound-preserving adaptive moving mesh finite volume methods for 2D and 3D special relativistic hydrodynamics}},
journal = {Journal of Computational Physics},
year = {2026},
volume = {554},
pages = {114728},
doi = {10.1016/j.jcp.2026.114728},
url = {https://doi.org/10.1016/j.jcp.2026.114728}
}
Physical Review D, 2017.
Paper
arXiv
BibTeX
@article{pub2017designofprovablyphysicalconstraintpreservingmethodsforgeneral,
author = {Kailiang Wu},
title = {{Design of provably physical-constraint-preserving methods for general relativistic hydrodynamics}},
journal = {Physical Review D},
year = {2017},
doi = {10.1103/PhysRevD.95.103001},
eprint = {1610.06274},
archivePrefix = {arXiv},
url = {https://doi.org/10.1103/PhysRevD.95.103001}
}
SIAM Journal on Scientific Computing, 2020.
arXiv
BibTeX
@article{pub2020entropysymmetrizationandhighorderaccurateentropystablenumerical,
author = {Kailiang Wu and Chi-Wang Shu},
title = {{Entropy symmetrization and high-order accurate entropy stable numerical schemes for relativistic MHD equations}},
journal = {SIAM Journal on Scientific Computing},
year = {2020},
volume = {42},
number = {4},
pages = {A2230--A2261},
eprint = {1907.07467},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1907.07467}
}
Journal of Scientific Computing, 2024.
arXiv
BibTeX
@article{pub2024highorderaccurateentropystableschemesforrelativistichydrodynamicswithageneral,
author = {Linfeng Xu and Shengrong Ding and Kailiang Wu},
title = {{High-order accurate entropy stable schemes for relativistic hydrodynamics with general Synge-type equation of state}},
journal = {Journal of Scientific Computing},
year = {2024},
volume = {98},
pages = {43},
eprint = {2409.10872},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2409.10872}
}
Journal of Computational Physics, 2024.
Paper
arXiv
BibTeX
@article{pub2024provablyconvergentnewtonraphsonmethodsforrecoveringprimitivevariables,
author = {Chaoyi Cai and Jianxian Qiu and Kailiang Wu},
title = {{Provably convergent Newton-Raphson methods for recovering primitive variables with applications to physical-constraint-preserving Hermite WENO schemes for relativistic hydrodynamics}},
journal = {Journal of Computational Physics},
year = {2024},
volume = {498},
pages = {112669},
doi = {10.1016/j.jcp.2023.112669},
eprint = {2305.14805},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2023.112669}
}
SIAM Journal on Scientific Computing, 2021.
arXiv
BibTeX
@article{pub2021uniformlyhighorderstructurepreservingdiscontinuousgalerkinmethodsfor,
author = {Kailiang Wu and Yulong Xing},
title = {{Uniformly high-order structure-preserving discontinuous Galerkin methods for Euler equations with gravitation: Positivity and well-balancedness}},
journal = {SIAM Journal on Scientific Computing},
year = {2021},
volume = {43},
number = {1},
pages = {A472--A510},
eprint = {2005.07166},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2005.07166}
}
Journal of Computational Physics, 2023.
Paper
BibTeX
@article{pub2023onpositivitypreservingwellbalancedfinitevolumemethodsfor,
author = {Y. Ren and K. Wu and J. Qiu and Y. Xing},
title = {{On high order positivity-preserving well-balanced finite volume methods for the Euler equations with gravitation}},
journal = {Journal of Computational Physics},
year = {2023},
volume = {492},
pages = {112429},
doi = {10.1016/j.jcp.2023.112429},
url = {https://doi.org/10.1016/j.jcp.2023.112429}
}
Journal of Computational Physics, 2022.
arXiv
BibTeX
@article{pub2022positivitypreservingwellbalancedcentraldiscontinuousgalerkinschemesfor,
author = {Haili Jiang and Huazhong Tang and Kailiang Wu},
title = {{Positivity-preserving well-balanced central discontinuous Galerkin schemes for the Euler equations under gravitational fields}},
journal = {Journal of Computational Physics},
year = {2022},
volume = {463},
pages = {111297},
eprint = {2207.09398},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2207.09398}
}
Journal of Computational Physics, 2025.
arXiv
BibTeX
@article{pub2025highorderaccuratestructurepreservingfinitevolumeschemeson,
author = {Zhihao Zhang and Huazhong Tang and Kailiang Wu},
title = {{High-order accurate structure-preserving finite volume schemes on adaptive moving meshes for shallow water equations: Well balancedness and positivity}},
journal = {Journal of Computational Physics},
year = {2025},
eprint = {2409.09600},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2409.09600}
}
Journal of Computational Physics, 2024.
arXiv
BibTeX
@article{pub2024highorderaccuratepositivitypreservingandwellbalanceddiscontinuous,
author = {Jiangfu Wang and Huazhong Tang and Kailiang Wu},
title = {{High-order accurate positivity-preserving and well-balanced discontinuous Galerkin schemes for ten-moment Gaussian closure equations with source terms}},
journal = {Journal of Computational Physics},
year = {2024},
eprint = {2402.15446},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2402.15446}
}
Journal of Scientific Computing, 2025.
Paper
BibTeX
@article{pub2025physicalconstraintpreservinghighorderfinitevolumewenomethodviageometricquasilinearization,
author = {L. Y. Win and Y. Chen and Y. Nie and L. Cai and K. Wu},
title = {{Physical-constraint-preserving high-order finite volume WENO method via geometric quasilinearization for Chaplygin gas dynamics}},
journal = {Journal of Scientific Computing},
year = {2025},
volume = {105},
pages = {33},
doi = {10.1007/s10915-025-03059-w},
url = {https://doi.org/10.1007/s10915-025-03059-w}
}
Numer. Math. Theor. Meth. Appl., 2017.
Paper
arXiv
BibTeX
@article{pub2017rungekuttadiscontinuouslocalevolutiongalerkinmethodsfortheshallowwaterequations,
author = {Yangyu Kuang and Kailiang Wu and Huazhong Tang},
title = {{Runge-Kutta discontinuous local evolution Galerkin methods for the shallow water equations on the cubed-sphere grid}},
journal = {Numer. Math. Theor. Meth. Appl.},
year = {2017},
volume = {10},
number = {2},
pages = {373--419},
doi = {10.4208/nmtma.2017.s09},
eprint = {1608.06700},
archivePrefix = {arXiv},
url = {https://doi.org/10.4208/nmtma.2017.s09}
}
Communications in Computational Physics, 2021.
Paper
BibTeX
@article{pub2021awenobasedstochasticgalerkinschemeforidealmhdequationswithrandom,
author = {K. Wu and D. Xiu and X. Zhong},
title = {{A WENO-based stochastic Galerkin scheme for ideal MHD equations with random inputs}},
journal = {Communications in Computational Physics},
year = {2021},
volume = {30},
number = {2},
pages = {423--447},
doi = {10.4208/cicp.OA-2020-0167},
url = {https://doi.org/10.4208/cicp.OA-2020-0167}
}
Journal of Computational Physics, 2017.
Paper
arXiv
BibTeX
@article{pub2017astochasticgalerkinmethodforfirstorderquasilinearhyperbolic,
author = {Kailiang Wu and Huazhong Tang and Dongbin Xiu},
title = {{A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty}},
journal = {Journal of Computational Physics},
year = {2017},
volume = {345},
pages = {224--244},
doi = {10.1016/j.jcp.2017.05.027},
eprint = {1601.04121},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2017.05.027}
}
SIAM Journal on Scientific Computing, 2017.
Paper
BibTeX
@article{pub2017arandomizedtensorquadraturemethodforhighdimensionalpolynomial,
author = {K. Wu and Y. Shin and D. Xiu},
title = {{A randomized tensor quadrature method for high dimensional polynomial approximation}},
journal = {SIAM Journal on Scientific Computing},
year = {2017},
volume = {39},
number = {5},
pages = {A1811--A1833},
doi = {10.1137/16M1081695},
url = {https://doi.org/10.1137/16M1081695}
}
Journal of Computational Physics, 2014.
Paper
BibTeX
@article{pub2014athirdorderaccuratedirecteuleriangrpschemefor,
author = {K. Wu and Z. Yang and H. Tang},
title = {{A third-order accurate direct Eulerian GRP scheme for the Euler equations in gas dynamics}},
journal = {Journal of Computational Physics},
year = {2014},
volume = {264},
pages = {177--208},
doi = {10.1016/j.jcp.2014.01.041},
url = {https://doi.org/10.1016/j.jcp.2014.01.041}
}
East Asian J. Appl. Math., 2014.
Paper
BibTeX
@article{pub2014athirdorderaccuratedirecteuleriangrpschemeforonedimensionalrelativistic,
author = {K. Wu and Z. Yang and H. Tang},
title = {{A third-order accurate direct Eulerian GRP scheme for one-dimensional relativistic hydrodynamics}},
journal = {East Asian J. Appl. Math.},
year = {2014},
volume = {4},
number = {2},
pages = {95--131},
doi = {10.4208/eajam.101013.100314a},
url = {https://doi.org/10.4208/eajam.101013.100314a}
}Geometric Quasilinearization (GQL)
SIAM Review, Research Spotlight, 2023.
Paper
PDF
arXiv
BibTeX
@article{pub2023geometricquasilinearizationframeworkforanalysisanddesignofbound,
author = {Kailiang Wu and Chi-Wang Shu},
title = {{Geometric quasilinearization framework for analysis and design of bound-preserving schemes}},
journal = {SIAM Review},
year = {2023},
volume = {65},
number = {4},
pages = {1031--1073},
doi = {10.1137/21M1458247},
eprint = {2111.04722},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/21M1458247}
}
Math. Models Methods Appl. Sci. (M3AS), 2017.
Paper
arXiv
BibTeX
@article{pub2017admissiblestatesandphysicalconstraintspreservingschemesforrelativistic,
author = {Kailiang Wu and Huazhong Tang},
title = {{Admissible states and physical-constraints-preserving schemes for relativistic magnetohydrodynamic equations}},
journal = {Math. Models Methods Appl. Sci. (M3AS)},
year = {2017},
volume = {27},
number = {10},
pages = {1871--1928},
doi = {10.1142/S0218202517500348},
eprint = {1603.06660},
archivePrefix = {arXiv},
url = {https://doi.org/10.1142/S0218202517500348}
}
SIAM Journal on Numerical Analysis, 2018.
Paper
PDF
arXiv
BibTeX
@article{pub2018positivitypreservinganalysisofnumericalschemesforidealmagnetohydrodynamics,
author = {Kailiang Wu},
title = {{Positivity-preserving analysis of numerical schemes for ideal magnetohydrodynamics}},
journal = {SIAM Journal on Numerical Analysis},
year = {2018},
volume = {56},
number = {4},
pages = {2124--2147},
doi = {10.1137/18M1168017},
eprint = {1802.02278},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/18M1168017}
}
SIAM Journal on Numerical Analysis, 2023.
arXiv
BibTeX
@article{pub2023provablypositivecentraldiscontinuousgalerkinschemesviageometricquasilinearization,
author = {Kailiang Wu and Haili Jiang and Chi-Wang Shu},
title = {{Provably positive central discontinuous Galerkin schemes via geometric quasilinearization for ideal MHD equations}},
journal = {SIAM Journal on Numerical Analysis},
year = {2023},
volume = {61},
pages = {250--285},
eprint = {2203.14853},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2203.14853}
}
Journal of Computational Physics, 2024.
Paper
arXiv
BibTeX
@article{pub2024gqlbasedboundpreservingandlocallydivergencefreecentral,
author = {Shengrong Ding and Kailiang Wu},
title = {{GQL-based bound-preserving and locally divergence-free central discontinuous Galerkin schemes for relativistic magnetohydrodynamics}},
journal = {Journal of Computational Physics},
year = {2024},
volume = {514},
pages = {113208},
doi = {10.1016/j.jcp.2024.113208},
eprint = {2402.15437},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2024.113208}
}
Numerische Mathematik, 2021.
arXiv
BibTeX
@article{pub2021provablyphysicalconstraintpreservingdiscontinuousgalerkinmethodsformultidimensional,
author = {Kailiang Wu and Chi-Wang Shu},
title = {{Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations}},
journal = {Numerische Mathematik},
year = {2021},
volume = {148},
pages = {699--741},
eprint = {2002.03371},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2002.03371}
}
SIAM Journal on Scientific Computing, 2021.
arXiv
BibTeX
@article{pub2021minimumprincipleonspecificentropyandhighorderaccurate,
author = {Kailiang Wu},
title = {{Minimum principle on specific entropy and high-order accurate invariant region preserving numerical methods for relativistic hydrodynamics}},
journal = {SIAM Journal on Scientific Computing},
year = {2021},
volume = {43},
number = {6},
pages = {B1164--B1197},
eprint = {2102.03801},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2102.03801}
}
Mathematics of Computation, 2026.
Paper
arXiv
BibTeX
@article{pub2025onlocalminimumentropyprincipleofhighorderschemes,
author = {Shumo Cui and Kailiang Wu and Linfeng Xu},
title = {{On local minimum entropy principle of high-order schemes for relativistic Euler equations}},
journal = {Mathematics of Computation},
year = {2026},
volume = {95},
number = {362},
pages = {2739-2787},
doi = {10.1090/mcom/4139},
eprint = {2503.12465},
archivePrefix = {arXiv},
url = {https://doi.org/10.1090/mcom/4139}
}
Journal of Computational Physics, 2026. Accepted
arXiv
BibTeX
@article{pub2026gqlbasedphysicalconstraintpreservinghighorderfinitedifferenceschemesforspecial,
author = {Linfeng Xu and Shengrong Ding and Kailiang Wu},
title = {{GQL-based physical-constraint-preserving high-order finite difference schemes for special relativistic hydrodynamics in arbitrary dimensions}},
journal = {Journal of Computational Physics},
year = {2026},
eprint = {2606.31992},
archivePrefix = {arXiv},
note = {Accepted},
url = {https://arxiv.org/abs/2606.31992}
}
Journal of Scientific Computing, 2025.
Paper
BibTeX
@article{pub2025physicalconstraintpreservinghighorderfinitevolumewenomethodviageometricquasilinearization,
author = {L. Y. Win and Y. Chen and Y. Nie and L. Cai and K. Wu},
title = {{Physical-constraint-preserving high-order finite volume WENO method via geometric quasilinearization for Chaplygin gas dynamics}},
journal = {Journal of Scientific Computing},
year = {2025},
volume = {105},
pages = {33},
doi = {10.1007/s10915-025-03059-w},
url = {https://doi.org/10.1007/s10915-025-03059-w}
}
Journal of Computational Physics, 2024.
arXiv
BibTeX
@article{pub2024highorderaccuratepositivitypreservingandwellbalanceddiscontinuous,
author = {Jiangfu Wang and Huazhong Tang and Kailiang Wu},
title = {{High-order accurate positivity-preserving and well-balanced discontinuous Galerkin schemes for ten-moment Gaussian closure equations with source terms}},
journal = {Journal of Computational Physics},
year = {2024},
eprint = {2402.15446},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2402.15446}
}
SIAM Journal on Scientific Computing, 2024.
Paper
arXiv
BibTeX
@article{pub2024anewdiscretelydivergencefreepositivitypreservinghighorder,
author = {Shengrong Ding and Kailiang Wu},
title = {{A new discretely divergence-free positivity-preserving high-order finite volume method for ideal MHD equations}},
journal = {SIAM Journal on Scientific Computing},
year = {2024},
volume = {46},
number = {1},
pages = {A50--A79},
doi = {10.1137/23M1562081},
eprint = {2305.14820},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/23M1562081}
}
Journal of Computational Physics, 2022.
arXiv
BibTeX
@article{pub2022aphysicalconstraintpreservingfinitevolumemethodforspecial,
author = {Yaping Chen and Kailiang Wu},
title = {{A physical-constraint-preserving finite volume WENO method for special relativistic hydrodynamics on unstructured meshes}},
journal = {Journal of Computational Physics},
year = {2022},
volume = {466},
pages = {111398},
eprint = {2207.09385},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2207.09385}
}
Monthly Notices of the Royal Astronomical Society (MNRAS), 2025.
Paper
BibTeX
@article{pub2025divergencefreefinitevolumewenoschemeforrelativisticmagnetohydrodynamics,
author = {S. Ding and K. Wu and C. Yuan},
title = {{Divergence-free finite volume WENO scheme for relativistic magnetohydrodynamics preserving positivity and subluminal velocity}},
journal = {Monthly Notices of the Royal Astronomical Society (MNRAS)},
year = {2025},
doi = {10.1093/mnras/staf280},
url = {https://doi.org/10.1093/mnras/staf280}
}
Communications in Computational Physics, 2026.
Paper
arXiv
BibTeX
@article{pub2025boundpreservingpointaveragemomentpolynomialinterpretedpampaschemeonedimensionalcase,
author = {R{\'e}mi Abgrall and Miaosen Jiao and Yongle Liu and Kailiang Wu},
title = {{Bound-preserving Point-Average-Moment PolynomiAl-interpreted (PAMPA) scheme: One-dimensional case}},
journal = {Communications in Computational Physics},
year = {2026},
volume = {39},
number = {1},
pages = {29-58},
doi = {10.4208/cicp.oa-2024-0266},
eprint = {2410.14292},
archivePrefix = {arXiv},
url = {https://doi.org/10.4208/cicp.oa-2024-0266}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260910476,
author = {Shengrong Ding and Shumo Cui and Remi Abgrall and Kailiang Wu},
title = {{Invariant domain preservation for hybrid point-value and cell-average discretizations of hyperbolic equations on general meshes}},
year = {2026},
eprint = {2609.10476},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2609.10476}
}
Provably positivity-preserving constrained transport scheme for 2D and 3D ideal magnetohydrodynamics
Journal of Computational Physics, 2025.
arXiv
BibTeX
@article{pub2025provablypositivitypreservingconstrainedtransportschemefor2dand3didealmagnetohydrodynamics,
author = {Dongwen Pang and Kailiang Wu},
title = {{Provably positivity-preserving constrained transport scheme for 2D and 3D ideal magnetohydrodynamics}},
journal = {Journal of Computational Physics},
year = {2025},
volume = {541},
pages = {114312},
eprint = {2410.05173},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2410.05173}
}
Journal of Computational Physics, 2025.
arXiv
BibTeX
@article{pub2025structurepreservingoscillationeliminatingdiscontinuousgalerkinschemesforideal,
author = {Mengqing Liu and Kailiang Wu},
title = {{Structure-preserving oscillation-eliminating discontinuous Galerkin schemes for ideal MHD equations: Locally divergence-free and positivity-preserving}},
journal = {Journal of Computational Physics},
year = {2025},
eprint = {2404.16794},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2404.16794}
}
Journal of Computational Physics, 2025.
arXiv
BibTeX
@article{pub2025robustdiscontinuousgalerkinmethodsmaintainingphysicalconstraintsforgeneral,
author = {Huihui Cao and Manting Peng and Kailiang Wu},
title = {{Robust discontinuous Galerkin methods maintaining physical constraints for general relativistic hydrodynamics}},
journal = {Journal of Computational Physics},
year = {2025},
eprint = {2410.05000},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2410.05000}
}
Journal of Computational Physics, 2025.
Paper
arXiv
BibTeX
@article{pub2024boundpreservingoedgmethodforawrasclezhangtraffic,
author = {Wei Chen and Shumo Cui and Kailiang Wu and Tao Xiong},
title = {{Bound-preserving OEDG schemes for Aw--Rascle--Zhang traffic models on networks}},
journal = {Journal of Computational Physics},
year = {2025},
volume = {520},
pages = {113507},
doi = {10.1016/j.jcp.2024.113507},
eprint = {2409.16269},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2024.113507}
}
Math. Models Methods Appl. Sci. (M3AS), 2026. Accepted
arXiv
BibTeX
@article{pub2026provablypositivitypreservinggloballydivergencefreecentraldgmethodsforidealmhd,
author = {Ruifang Yan and Huihui Cao and Kailiang Wu},
title = {{Provably positivity-preserving, globally divergence-free central DG methods for ideal MHD system}},
journal = {Math. Models Methods Appl. Sci. (M3AS)},
year = {2026},
eprint = {2508.08913},
archivePrefix = {arXiv},
note = {Accepted},
url = {https://arxiv.org/abs/2508.08913}
}
Journal of Computational Physics, 2026. In press
Paper
arXiv
BibTeX
@article{pub2026anactivefluxtypeschemeforidealmhdwithprovablepositivityand,
author = {Mengqing Liu and Dongwen Pang and Remi Abgrall and Kailiang Wu},
title = {{An active-flux-type scheme for ideal MHD with provable positivity and a point-value-level discrete divergence-free constraint}},
journal = {Journal of Computational Physics},
year = {2026},
doi = {10.1016/j.jcp.2026.115319},
eprint = {2510.19721},
archivePrefix = {arXiv},
note = {In press},
url = {https://doi.org/10.1016/j.jcp.2026.115319}
}Oscillation-Eliminating (OE) Approach and its Variants
Mathematics of Computation, 2025.
Paper
PDF (arXiv version)
arXiv
BibTeX
@article{pub2025oedgoscillationeliminatingdiscontinuousgalerkinmethodforhyperbolicconservation,
author = {Manting Peng and Zheng Sun and Kailiang Wu},
title = {{OEDG: Oscillation-eliminating discontinuous Galerkin method for hyperbolic conservation laws}},
journal = {Mathematics of Computation},
year = {2025},
volume = {94},
pages = {1147--1198},
doi = {10.1090/mcom/3998},
eprint = {2310.04807},
archivePrefix = {arXiv},
url = {https://doi.org/10.1090/mcom/3998}
}
Journal of Computational Physics, 2026.
Paper
BibTeX
@article{pub2026cosdgaconvexoscillationsuppressingframeworkforhighorderdiscontinuousgalerkin,
author = {Huihui Cao and Yunqing Huang and Zhuoyun Li and Kailiang Wu},
title = {{COS(DG): A Convex Oscillation-Suppressing Framework for High-Order Discontinuous Galerkin Methods}},
journal = {Journal of Computational Physics},
year = {2026},
volume = {554},
pages = {114755},
doi = {10.1016/j.jcp.2026.114755},
url = {https://doi.org/10.1016/j.jcp.2026.114755}
}
Journal of Computational Physics, 2027.
Paper
BibTeX
@article{pub2026cossvconvexoscillationsuppressingspectralvolumeschemeswithboundpreservationfor,
author = {Ruifang Yan and Huihui Cao and Na Liu and Kailiang Wu},
title = {{COS(SV): Convex Oscillation-Suppressing Spectral Volume Schemes with Bound Preservation for Hyperbolic Conservation Laws}},
journal = {Journal of Computational Physics},
year = {2027},
volume = {568},
pages = {115411},
doi = {10.1016/j.jcp.2026.115411},
url = {https://doi.org/10.1016/j.jcp.2026.115411}
}
SIAM Journal on Scientific Computing, 2025.
Paper
arXiv
BibTeX
@article{pub2024spectralvolumefromadgperspectiveoscillationeliminationstability,
author = {Zhuoyun Li and Kailiang Wu},
title = {{Spectral volume from a discontinuous Galerkin perspective: oscillation elimination, stability, and optimal error estimates}},
journal = {SIAM Journal on Scientific Computing},
year = {2025},
volume = {47},
number = {2},
pages = {A1304-A1333},
doi = {10.1137/24m167799x},
eprint = {2409.10871},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/24m167799x}
}
SIAM Journal on Scientific Computing, 2026.
Paper
arXiv
BibTeX
@article{pub2025oscillationeliminatingcentraldgschemesforhyperbolicconservationlaws,
author = {Manting Peng and Kailiang Wu and Caiyou Yuan},
title = {{Oscillation-eliminating central DG schemes on Cartesian meshes for hyperbolic conservation laws}},
journal = {SIAM Journal on Scientific Computing},
year = {2026},
volume = {48},
number = {2},
pages = {A695-A725},
doi = {10.1137/25m1730697},
eprint = {2503.12473},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/25m1730697}
}
Journal of Computational Physics, 2024.
Paper
arXiv
BibTeX
@article{pub2024highorderoscillationeliminatinghermitewenomethodforhyperbolic,
author = {Chuan Fan and Kailiang Wu},
title = {{High-order oscillation-eliminating Hermite WENO method for hyperbolic conservation laws}},
journal = {Journal of Computational Physics},
year = {2024},
volume = {519},
pages = {113435},
doi = {10.1016/j.jcp.2024.113435},
eprint = {2409.09632},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2024.113435}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260400301,
author = {Kailiang Wu},
title = {{EPO: A Unified Framework for Entropy Stability, Positivity, and Oscillation Suppression}},
year = {2026},
eprint = {2604.00301},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2604.00301}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260926195,
author = {Manting Peng and Zhuoyun Li and Kailiang Wu},
title = {{Runge--Kutta-Aligned Oscillation Elimination: Restoring Superconvergence for Fully Discrete Shock-Capturing DG Schemes}},
year = {2026},
eprint = {2609.26195},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2609.26195}
}
arXiv, 2026. Preprint
arXiv
BibTeX
@misc{pubarxiv260926194,
author = {Chuan Fan and Kailiang Wu},
title = {{Compact Finite-Average-Moment Schemes with Single-Step Oscillation Elimination for Hyperbolic Conservation Laws}},
year = {2026},
eprint = {2609.26194},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2609.26194}
}
Journal of Computational Physics, 2025.
arXiv
BibTeX
@article{pub2025robustdgschemesonunstructuredtriangularmeshesoscillationelimination,
author = {Shengrong Ding and Shumo Cui and Kailiang Wu},
title = {{Robust DG schemes on unstructured triangular meshes: Oscillation elimination and bound preservation via optimal convex decomposition}},
journal = {Journal of Computational Physics},
year = {2025},
eprint = {2409.09620},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2409.09620}
}
Math. Models Methods Appl. Sci. (M3AS), 2024.
Paper
BibTeX
@article{pub2024uniformlyhighorderboundpreservingoedgschemesfortwo,
author = {R. Yan and R. Abgrall and K. Wu},
title = {{Uniformly high-order bound-preserving OEDG schemes for two-phase flows}},
journal = {Math. Models Methods Appl. Sci. (M3AS)},
year = {2024},
doi = {10.1142/S0218202524500544},
url = {https://doi.org/10.1142/S0218202524500544}
}
Journal of Computational Physics, 2025.
arXiv
BibTeX
@article{pub2025structurepreservingoscillationeliminatingdiscontinuousgalerkinschemesforideal,
author = {Mengqing Liu and Kailiang Wu},
title = {{Structure-preserving oscillation-eliminating discontinuous Galerkin schemes for ideal MHD equations: Locally divergence-free and positivity-preserving}},
journal = {Journal of Computational Physics},
year = {2025},
eprint = {2404.16794},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2404.16794}
}
Journal of Computational Physics, 2025.
arXiv
BibTeX
@article{pub2025robustdiscontinuousgalerkinmethodsmaintainingphysicalconstraintsforgeneral,
author = {Huihui Cao and Manting Peng and Kailiang Wu},
title = {{Robust discontinuous Galerkin methods maintaining physical constraints for general relativistic hydrodynamics}},
journal = {Journal of Computational Physics},
year = {2025},
eprint = {2410.05000},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2410.05000}
}
Constraint-Preserving High-Order Compact OEDG Method for Spherically Symmetric Einstein-Euler System
Communications in Mathematical Research, 2025.
Paper
arXiv
BibTeX
@article{pub2025constraintpreservinghighordercompactoedgmethodforsphericallysymmetriceinsteineuler,
author = {Yuchen Huang and Manting Peng and Kailiang Wu},
title = {{Constraint-Preserving High-Order Compact OEDG Method for Spherically Symmetric Einstein-Euler System}},
journal = {Communications in Mathematical Research},
year = {2025},
volume = {41},
number = {4},
pages = {370--414},
doi = {10.4208/cmr.2025-0052},
eprint = {2512.03496},
archivePrefix = {arXiv},
url = {https://doi.org/10.4208/cmr.2025-0052}
}
Annals of Applied Mathematics, 2024.
Paper
BibTeX
@article{pub2024oscillationeliminatingdiscontinuousgalerkinmethodsformulticomponentchemicallyreactingflows,
author = {J. Du and C. Fan and K. Wu},
title = {{Oscillation-eliminating discontinuous Galerkin methods for multicomponent chemically reacting flows}},
journal = {Annals of Applied Mathematics},
year = {2024},
volume = {40},
pages = {412-444},
doi = {10.4208/aam.oa-2024-0029},
url = {https://doi.org/10.4208/aam.oa-2024-0029}
}
Journal of Computational Physics, 2025.
Paper
arXiv
BibTeX
@article{pub2024boundpreservingoedgmethodforawrasclezhangtraffic,
author = {Wei Chen and Shumo Cui and Kailiang Wu and Tao Xiong},
title = {{Bound-preserving OEDG schemes for Aw--Rascle--Zhang traffic models on networks}},
journal = {Journal of Computational Physics},
year = {2025},
volume = {520},
pages = {113507},
doi = {10.1016/j.jcp.2024.113507},
eprint = {2409.16269},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2024.113507}
}
Math. Models Methods Appl. Sci. (M3AS), 2026. Accepted
arXiv
BibTeX
@article{pub2026provablypositivitypreservinggloballydivergencefreecentraldgmethodsforidealmhd,
author = {Ruifang Yan and Huihui Cao and Kailiang Wu},
title = {{Provably positivity-preserving, globally divergence-free central DG methods for ideal MHD system}},
journal = {Math. Models Methods Appl. Sci. (M3AS)},
year = {2026},
eprint = {2508.08913},
archivePrefix = {arXiv},
note = {Accepted},
url = {https://arxiv.org/abs/2508.08913}
}
Journal of Computational Physics, 2026. In press
Paper
arXiv
BibTeX
@article{pub2026anactivefluxtypeschemeforidealmhdwithprovablepositivityand,
author = {Mengqing Liu and Dongwen Pang and Remi Abgrall and Kailiang Wu},
title = {{An active-flux-type scheme for ideal MHD with provable positivity and a point-value-level discrete divergence-free constraint}},
journal = {Journal of Computational Physics},
year = {2026},
doi = {10.1016/j.jcp.2026.115319},
eprint = {2510.19721},
archivePrefix = {arXiv},
note = {In press},
url = {https://doi.org/10.1016/j.jcp.2026.115319}
}Uncertainty Quantification and Approximation Theory
SIAM Journal on Scientific Computing, 2017.
Paper
BibTeX
@article{pub2017arandomizedtensorquadraturemethodforhighdimensionalpolynomial,
author = {K. Wu and Y. Shin and D. Xiu},
title = {{A randomized tensor quadrature method for high dimensional polynomial approximation}},
journal = {SIAM Journal on Scientific Computing},
year = {2017},
volume = {39},
number = {5},
pages = {A1811--A1833},
doi = {10.1137/16M1081695},
url = {https://doi.org/10.1137/16M1081695}
}
Commun. Appl. Math. Comput., 2019.
Paper
BibTeX
@article{pub2019sequentialapproximationoffunctionsinsobolevspacesusingrandomsamples,
author = {K. Wu and D. Xiu},
title = {{Sequential approximation of functions in Sobolev spaces using random samples}},
journal = {Commun. Appl. Math. Comput.},
year = {2019},
volume = {1},
pages = {449--466},
doi = {10.1007/s42967-019-00028-7},
url = {https://doi.org/10.1007/s42967-019-00028-7}
}
Journal of Computational Physics, 2018.
Paper
BibTeX
@article{pub2018sequentialfunctionapproximationonarbitrarilydistributedpointsets,
author = {K. Wu and D. Xiu},
title = {{Sequential function approximation on arbitrarily distributed point sets}},
journal = {Journal of Computational Physics},
year = {2018},
volume = {354},
pages = {370--386},
doi = {10.1016/j.jcp.2017.10.020},
url = {https://doi.org/10.1016/j.jcp.2017.10.020}
}
Journal of Computational Physics, 2018.
Paper
BibTeX
@article{pub2018sequentialfunctionapproximationwithnoisydata,
author = {Y. Shin and K. Wu and D. Xiu},
title = {{Sequential function approximation with noisy data}},
journal = {Journal of Computational Physics},
year = {2018},
volume = {371},
pages = {363--381},
doi = {10.1016/j.jcp.2018.05.042},
url = {https://doi.org/10.1016/j.jcp.2018.05.042}
}
Journal of Computational Physics, 2017.
Paper
arXiv
BibTeX
@article{pub2017astochasticgalerkinmethodforfirstorderquasilinearhyperbolic,
author = {Kailiang Wu and Huazhong Tang and Dongbin Xiu},
title = {{A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty}},
journal = {Journal of Computational Physics},
year = {2017},
volume = {345},
pages = {224--244},
doi = {10.1016/j.jcp.2017.05.027},
eprint = {1601.04121},
archivePrefix = {arXiv},
url = {https://doi.org/10.1016/j.jcp.2017.05.027}
}
Communications in Computational Physics, 2021.
Paper
BibTeX
@article{pub2021awenobasedstochasticgalerkinschemeforidealmhdequationswithrandom,
author = {K. Wu and D. Xiu and X. Zhong},
title = {{A WENO-based stochastic Galerkin scheme for ideal MHD equations with random inputs}},
journal = {Communications in Computational Physics},
year = {2021},
volume = {30},
number = {2},
pages = {423--447},
doi = {10.4208/cicp.OA-2020-0167},
url = {https://doi.org/10.4208/cicp.OA-2020-0167}
}
Journal of Computational Physics, 2019.
arXiv
BibTeX
@article{pub2019numericalaspectsforapproximatinggoverningequationsusingdata,
author = {Kailiang Wu and Dongbin Xiu},
title = {{Numerical aspects for approximating governing equations using data}},
journal = {Journal of Computational Physics},
year = {2019},
volume = {384},
pages = {200--221},
eprint = {1809.09170},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1809.09170}
}
IEEE Transactions on Artificial Intelligence, 2024.
arXiv
BibTeX
@article{pub2024criticalsamplingforrobustevolutionoperatorlearningofunknowndynamicalsystems,
author = {Ce Zhang and Kailiang Wu and Zhihai He},
title = {{Critical sampling for robust evolution operator learning of unknown dynamical systems}},
journal = {IEEE Transactions on Artificial Intelligence},
year = {2024},
volume = {5},
pages = {2856-2871},
eprint = {2304.07485},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2304.07485}
}
arXiv, 2025. Preprint
arXiv
BibTeX
@misc{pubarxiv251018380,
author = {Chuan Fan and Qian Huang and Kailiang Wu},
title = {{Provably realizability-preserving finite volume method for quadrature-based moment models of kinetic equations}},
year = {2025},
eprint = {2510.18380},
archivePrefix = {arXiv},
note = {Preprint},
url = {https://arxiv.org/abs/2510.18380}
}Research Grants
- NSFC, National Science Fund for Distinguished Young Scholars (2027/01–2031/12 · )
- Shenzhen Natural Science Foundation, General Program (2025/10–2028/10 · )
- Distinguished Young Scientists Team Program, College of Science of SUSTech (2025/07–2026/07 · )
- National Basic Research, Science Challenge Project (2025/01–2027/12 · )
- National Natural Science Foundation of China (NSFC), Major Research Program (2024/01–2026/12 · )
- Shenzhen City Setup Funds (2023/07–2026/12 · )
- Shenzhen Distinguished Young Scholar (2023/04–2028/04 · )
- National Natural Science Foundation of China (NSFC), General Program (2022/01–2026/12 · )
- National Youth Talents Program (2021–2024 · )
Awarded to outstanding young scientists returning to China.
Honors and Awards
- 2026 · Youth Science Award of Applied Mathematics, CSIAM.
- 2026 · Stanford/Elsevier World’s Top 2% Scientists.
- 2026 · SUSTech Fang Keng Faculty Award.
- 2025 · Guangdong Provincial Science and Technology Award — Youth Science and Technology Innovation Award.
- 2025 · Stanford/Elsevier World’s Top 2% Scientists.
- 2025 · SUSTech President’s Research Award (3 per year).
- 2025 · SUSTech Young Professor Award (2 per year).
- 2024 · Stanford/Elsevier World’s Top 2% Scientists.
- 2019 · Zhong Jiaqing Mathematics Award, Chinese Mathematical Society.
One of the three major mathematics awards of the Chinese Mathematical Society; 4 recipients every two years. - 2016 · Outstanding Ph.D. Graduates Award of Peking University.
- 2015 · Outstanding Youth Paper Award (First Prize), China Society for Computational Mathematics.
Awarded every two years to 1–2 young scholars with the most outstanding papers.
Invited Lectures
- Invited Speaker, International Conference on Hyperbolic Problems: Theory, Numerics, and Applications (HYP 2026)
- Plenary Speaker, 21st National Conference on Numerical Methods for Fluid Dynamics
- Plenary Speaker, 12th Conference on Finite Element Methods
- Plenary Speaker, 2024 Beijing–Tianjin–Hebei+ Conference on Computational Mathematics
- Invited Speaker, International Conference on Applied Mathematics
Selected publications
Nature Communications, 2026.
Paper
Code
BibTeX
@article{pub2026learningmissingphysicsfromlegacysimulatorswithalternatingneural,
author = {H. Wang and Q. Wang and C. Yuan and K. Wu},
title = {{Learning missing physics from legacy simulators with alternating neural integrators}},
journal = {Nature Communications},
year = {2026},
doi = {10.1038/s41467-026-74002-2},
url = {https://doi.org/10.1038/s41467-026-74002-2}
}
SIAM Review, 2026. In press
PDF
arXiv
BibTeX
@article{pub2026highordernumericalmethodspreservinginvariantdomainforhyperbolicandrelatedsystems,
author = {Kailiang Wu and Xiangxiong Zhang and Chi-Wang Shu},
title = {{High order numerical methods preserving invariant domain for hyperbolic and related systems}},
journal = {SIAM Review},
year = {2026},
eprint = {2512.09116},
archivePrefix = {arXiv},
note = {In press},
url = {https://arxiv.org/abs/2512.09116}
}
SIAM Review, 2025.
Paper
PDF
arXiv
Code
BibTeX
@article{pub2025dueadeeplearningframeworkandlibraryformodeling,
author = {Junfeng Chen and Kailiang Wu and Dongbin Xiu},
title = {{DUE: A deep learning framework and library for modeling unknown equations}},
journal = {SIAM Review},
year = {2025},
volume = {67},
number = {4},
pages = {873--902},
doi = {10.1137/24M1671827},
eprint = {2504.10373},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/24M1671827}
}
Mathematics of Computation, 2025.
Paper
PDF (arXiv version)
arXiv
BibTeX
@article{pub2025oedgoscillationeliminatingdiscontinuousgalerkinmethodforhyperbolicconservation,
author = {Manting Peng and Zheng Sun and Kailiang Wu},
title = {{OEDG: Oscillation-eliminating discontinuous Galerkin method for hyperbolic conservation laws}},
journal = {Mathematics of Computation},
year = {2025},
volume = {94},
pages = {1147--1198},
doi = {10.1090/mcom/3998},
eprint = {2310.04807},
archivePrefix = {arXiv},
url = {https://doi.org/10.1090/mcom/3998}
}
SIAM Journal on Numerical Analysis, 2024.
arXiv
BibTeX
@article{pub2024onoptimalcellaveragedecompositionforhighorderbound,
author = {Shumo Cui and Shengrong Ding and Kailiang Wu},
title = {{On optimal cell average decomposition for high-order bound-preserving schemes of hyperbolic conservation laws}},
journal = {SIAM Journal on Numerical Analysis},
year = {2024},
eprint = {2212.05045},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2212.05045}
}
SIAM Review, Research Spotlight, 2023.
Paper
PDF
arXiv
BibTeX
@article{pub2023geometricquasilinearizationframeworkforanalysisanddesignofbound,
author = {Kailiang Wu and Chi-Wang Shu},
title = {{Geometric quasilinearization framework for analysis and design of bound-preserving schemes}},
journal = {SIAM Review},
year = {2023},
volume = {65},
number = {4},
pages = {1031--1073},
doi = {10.1137/21M1458247},
eprint = {2111.04722},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/21M1458247}
}
SIAM Journal on Scientific Computing, 2021.
arXiv
BibTeX
@article{pub2021minimumprincipleonspecificentropyandhighorderaccurate,
author = {Kailiang Wu},
title = {{Minimum principle on specific entropy and high-order accurate invariant region preserving numerical methods for relativistic hydrodynamics}},
journal = {SIAM Journal on Scientific Computing},
year = {2021},
volume = {43},
number = {6},
pages = {B1164--B1197},
eprint = {2102.03801},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2102.03801}
}
Journal of Computational Physics, 2020.
arXiv
BibTeX
@article{pub2020datadrivendeeplearningofpartialdifferentialequationsin,
author = {Kailiang Wu and Dongbin Xiu},
title = {{Data-driven deep learning of partial differential equations in modal space}},
journal = {Journal of Computational Physics},
year = {2020},
volume = {408},
pages = {109307},
eprint = {1910.06948},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1910.06948}
}
Numerische Mathematik, 2019.
arXiv
BibTeX
@article{pub2019provablypositivehighorderschemesforidealmagnetohydrodynamicsanalysis,
author = {Kailiang Wu and Chi-Wang Shu},
title = {{Provably positive high-order schemes for ideal magnetohydrodynamics: Analysis on general meshes}},
journal = {Numerische Mathematik},
year = {2019},
volume = {142},
number = {4},
pages = {995--1047},
eprint = {1807.11467},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1807.11467}
}
SIAM Journal on Numerical Analysis, 2018.
Paper
PDF
arXiv
BibTeX
@article{pub2018positivitypreservinganalysisofnumericalschemesforidealmagnetohydrodynamics,
author = {Kailiang Wu},
title = {{Positivity-preserving analysis of numerical schemes for ideal magnetohydrodynamics}},
journal = {SIAM Journal on Numerical Analysis},
year = {2018},
volume = {56},
number = {4},
pages = {2124--2147},
doi = {10.1137/18M1168017},
eprint = {1802.02278},
archivePrefix = {arXiv},
url = {https://doi.org/10.1137/18M1168017}
}
Math. Models Methods Appl. Sci. (M3AS), 2017.
Paper
arXiv
BibTeX
@article{pub2017admissiblestatesandphysicalconstraintspreservingschemesforrelativistic,
author = {Kailiang Wu and Huazhong Tang},
title = {{Admissible states and physical-constraints-preserving schemes for relativistic magnetohydrodynamic equations}},
journal = {Math. Models Methods Appl. Sci. (M3AS)},
year = {2017},
volume = {27},
number = {10},
pages = {1871--1928},
doi = {10.1142/S0218202517500348},
eprint = {1603.06660},
archivePrefix = {arXiv},
url = {https://doi.org/10.1142/S0218202517500348}
}Ph.D. student and postdoctoral fellow positions are available in my group. Interested candidates may send their CVs to wukl@sustech.edu.cn