Numerical methods in general settings:

  • Low rank structure of hyperbolic systems
    Sparse+Low-energy decomposition for viscous conservation laws
    with Thomas Y. Hou and Hayden Schaeffer, submitted

  • Elliptic equation with high dimensional randomness
    Local decomposition for elliptic equations with random rough coefficients
    with Thomas Y. Hou and Pengchuan Zhang, preprint

Multiscale analysis

Thesis:

Modeling and Computational Methods for Multi-scale Quantum Dynamics and Kinetic Equations