Zuodong Wang (王作栋)

PhD student in Numerical Analysis for Partial Differential Equations (PDEs)
zuodong.wang[ατ]inria.fr
Ecole Nationale des Ponts et Chaussées (ENPC-CERMICS)
French Institute for Research in Numerical Science and Technology (INRIA - SERENA)

Welcome to my academic webpage!

About me

I am a PhD student in numerical analysis under the direction of Alexandre Ern, Zhaonan Dong at CERMICS, École des Ponts ParisTech and SERENA team, Inria Centre de Paris. I am also co-supervised by Jean-Luc Guermond at Texas A&M University.

As an applied mathematician, I am mainly interested in design, test and analyze efficient numerical schemes for PDEs. My work mainly focus on structure-preserving schemes for nonlinear PDEs, including hyperbolic conservation laws, PDEs with stiff sourse, and nonlinear parabolic problems.

As a guy with diplôme d'ingénieur (engineer degree in French), I am also interested in 1) the implementation with C++, Python, Matlab and Julia(currently using). 2) Physics-related mathematical modeling.

I am currently speaking Chinese, English, French and studying Japanese.

Research interests

  • Mathematical aspects:

    •        -    Hyperbolic Conservation Laws
           -    Semi-linear Parabolic problems
           -    PDEs with stiff sourse term
           -    Invariant Domain Preserving schemes
           -    Asymptotic Preserving schemes
           -    A posteriori error analysis for linear problems

  • Application aspects:

    •        -    Fluid Mechanics
           -    Neutron Transport
           -    Phase Field model
           -    Wave equation
           -    Adaptive algorithm

    Publications and preprints

    [5] - [Preprint] A priori and a posteriori error estimates of a DG-CG method for the wave equation in second order formulation
    - 2024, Z.Dong, L. Mascotto and Z. Wang - [link]

    [4] - Mass conservative limiting and applications to the approximation of the steady-state radiation transport equations
    - Journal of Computational Physics, 2025 - J.-L. Guermond and Z. Wang - [link]

    [3] - Asymptotic and invariant-domain preserving schemes for scalar conservation equations with stiff source terms and multiple equilibrium points
    - Journal of Scientific Computing, 2024 - A. Ern, J.-L. Guermond and Z. Wang - [link]

    [2] - Hybrid high-order methods for elliptic PDEs on curved and complicated domains
    - 13th ICOSAHOM 2020/2021 Conference Proceeding, 2022 - Z. Dong and Z. Wang - [link]

    [1] - The Proof of 2n Circle Arrangement Conjecture
    - Pure Mathematics, 2017 - Z. Wang - [link]

    Talks

    Asymptotic-preserving and invariant-domain preserving schemes for scalar hyperbolic conservation laws with stiff source term
    International Conference on Applied Mathematics (ICAM) - Hongkong (China) - 2024 - [slides]
    The 6th SIAM Texas-Louisiana Sectional Meeting (SIAM TX-LA) - Lafayette (USA) - 2023 - [slides]
    Monotonicity, sonic points and convergence of a stabilized FEM scheme for hyperbolic conservation laws
    Finite Element Rodeo - Houston (USA) - 2024 - [slides]

    Experiences

  • Internships:

    •        -    Testing some advanced numerical methods for hyperbolic, parabolic and elliptic PDEs.- [report]
                 SERENA team, INRIA, paris (France), October 2022 - April 2023.
           -    Analysis of an invariant-domain-preserving scheme for conservation laws and hyperbolic systems.- [report]
                 SERENA team, INRIA, paris (France), May 2022 - September 2022.
           -    Hybrid high-order method for elliptic PDEs on curved and complicated domains.- [report]
                 SERENA team, INRIA, paris (France), June 2021 - September 2021.


  • Visiting scholar:

    •        -    Design, analyse and test Invariant-domain-preserving schemes for hyperbolic problems.
                 Mathematical Departement, Texas A&M University, College Station (USA), September 2023 - May 2024.

    Teaching

  • Spring semester 2024 - Texas A&M University:

    •              1st year of Bachelor's degree in engineering
                 Course : Explorations in Mathematics
                 Instructor: give lectures, correct exercises, organize exams