- Free boundary problem of invasive behavior of one species
- Free boundary problem of invasive behavior with competition between two/three species
- Cell polarization and cell movement
- Free boundary Grad-Shafranov problem

- Front tracking methods and front fixing methods
- Fast local level set method
- Integration factor methods and ETD/ETDRK schemes
- CPU parallel cut-cell algorithm
- AMG accelerated embedded boundary method for PDEs in irregular domains

- Binary level set method
- GPU parallel computing for variational implicit-solvent models
- Monte Carlo simulations for protein folding/unfolding

- Programming Languages: C/C++, PETSc, Julia, Matlab, Maple.
- GPU/CPU Parallel Computing

- Free-boundary GS solver: A parallel PETSc-based cut cell free-boundary MHD equilibrium solver (primary developer)
- AMG Accelerated Cut Cell Algorithm: A universal AMG accelerated cut cell solver (one of the principle developers)