Research Interests

My research areas are computational and applied mathematics with an emphasis on numerical methods for partial differential equations. Some specific interests include

  1. •High-order discontinuous Galerkin methods

  2. •Numerical methods for hyperbolic conservation laws with shocks and discontinuities

  3. •Curved mesh generation and adaptation

  4. •Numerical optimization and numerical linear algebra

Publications

Journal Papers

  1. 1.(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]

  2. 2.(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]

  3. 3.(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]

    4. Conference Papers

  4. 4.(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]

    5. Book Chapters

  5. 5.(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]

Welcome

Research

Teaching

Other