Research Interests
My research primarily focuses on the development and analysis of efficient, 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 representative examples of my recent work include:
- Fast spectral methods for Boltzmann-type collision operators
- Asymptotic-preserving and positivity-preserving schemes for multiscale hyperbolic and kinetic equations
- Energy/entropy-dissipative schemes for Fokker-Planck type equations
- Uncertainty quantification for kinetic equations
- Dynamical low-rank methods for high-dimensional kinetic equations
- Structure-preserving particle methods for kinetic equations