My research is primarily focused on the development and analysis of efficient and structure-preserving numerical methods for kinetic equations - a mesoscopic description of interacting particle systems with the nonlinear Boltzmann equation as a prominent example - and related problems arising in multiscale modeling and simulation.
Some of my recent representative work includes:
- Fast spectral methods for Boltzmann type collisional kinetic equations
- Asymptotic-preserving and positivity-preserving schemes for multiscale hyperbolic and kinetic equations
- Energy/entropy dissipative schemes for Fokker-Planck type equations
- Dynamical low rank methods for high dimensional kinetic equations
- Uncertainty quantification for kinetic equations