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


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