Research Interests

My research areas are computational and applied mathematics with an emphasis on numerical methods for partial differential equations. Some specific areas I work on or have worked on include

  1. •Mean field games

  2. •High-order discontinuous Galerkin methods

  3. •Curved mesh generation and adaptation

  4. •Numerical optimization and numerical linear algebra

Publications

Journal Papers

  1. 1.(with Mathieu Lauriere)
    Newton Methods for Finite-Difference Discretizations of Mean Field Games: A Numerical Study
    to be submitted to the Journal of Scientific Computing.
    [pdf] [code]

  2. 2.(with Zhongyuan Cao, Mathieu Lauriere, and Jiefei Yang)
    Linear-Quadratic Extended Mean Field Control Games
    to be submitted to the IEEE Transactions on Automatic Control.
    [pdf] [code]

  3. 3.(with Per-Olof Persson)
    Local element operations for curved simplex meshes
    International Journal for Numerical Methods in Engineering, Volume 125, Issue 2, 2024.
    [pdf] [doi] [arXiv:2307.07707]

  4. 4.(with Per-Olof Persson and Matthew J. Zahr)
    Implicit shock tracking for unsteady flows by the method of lines
    Journal of Computational Physics, Volume 454, 2022.
    [pdf] [doi] [arXiv:2101.08913]

  5. 5.(with Per-Olof Persson and Matthew J. Zahr)
    Implicit shock tracking using an optimization-based high-order discontinuous Galerkin method
    Journal of Computational Physics, Volume 410, 2020.
    [pdf] [doi] [arXiv:1912.11207]

    6. Conference Papers

  6. 6.(with Per-Olof Persson and Matthew J. Zahr)
    An Optimization-Based Discontinuous Galerkin approach for high-order accurate shock tracking with guaranteed mesh quality
    Proceedings of the AIAA Science and Technology Forum and Exposition (SciTech), 2019.
    [pdf] [doi]

    7. Book Chapters

  7. 7.(with Per-Olof Persson and Matthew J. Zahr)
    High-Order Implicit Shock Tracking (HOIST)
    SEMA-SIMAI Springer Series, Volume 30, "Mesh Generation and Adaptation: Cutting-Edge Techniques", special volume in honor of the 60th birthday of Oubay Hassan.
    [pdf] [doi]

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