- Mathematical molecular biosciences; Mathematical biophysics; Variational multiscale models; Ion channel transport; Proton transport; PDE modeling of biomolecular surfaces; Virus capsid modeling.
- Bioimaging; Geometric flow approaches to images and surfaces; PDE transform; Image edge analysis by coupled PDEs; Bioluminescence tomography.
- High order interface methods; Matched interface and boundary (MIB); Multidomain interface problems.
- Modeling and computation of nano-electronic devices; Nanofluidic systems; Nano-bio sensors.
- Quantum kinetic theory; Transport theory; Quantum Boltzmann equation.
- Wavelet and local spectral methods for PDEs; Computational electromagnetics; Computational fluid dynamics; Richtmyer-Meshkov instability; Structural analysis.
- Dynamical systems; Controlling chaos ; Controlling turbulence; Controlling pattern formation.
Z. Ren and G. Zhu, "Integrated System Identification and Control design for an IC engine variable valve timing system," ASME Journal of DSMC (2011, DOI: 10.1115/1.4003263).
Sigal Gottlieb, Guo-Wei Wei, and Shan Zhao, A unified discontinuous Galerkin framework for time integration (46 pages). (2012)
Kelin Xia, Meng Zhan, and Guo-Wei Wei, Three-dimensional MIB Galerkin for elliptic interface problems. (2012)
Langhua Hu, Duan Chen and Guo-Wei Wei, Geometric and phonon effects on nano transistors. (2012)