-
Research Areas
- Applied Mathematics
- Computational Mathematics
-
Research Interests
- Numerical Analysis
- Numerical solutions of deterministic and stochastic partial
differential equations:
finite element methods, discontinuous and spectral Galerkin methods,
multigrid methods, domain decomposition methods
- Nonlinear partial differential equations: Geometric evolution
PDEs and fully nonlinear PDEs
- Parallel computing
- Uncertainty quantification (UQ)
- Mathematical modeling
-
Application Areas
- Computer vision and image processing: PDE and variational methods for
imaging process
- Materials science: Phase transitions in the materials science and
related geometric problems of moving surfaces/curves, multiscale modeling and
simulations
- Fluid mechanics: porous media flow, reservoir
simulation and groundwater contaminant simulation, geostrophic flow,
viscoelastic fluids (liquid crystals, polymers)
- Solid mechanics: linear elasticity, plates and shells,
poroelasticity (gels, porous media)
- Wave propagation: acoustic waves, elastic waves, electromagnetic
waves, inverse scattering, fluid-solid interactions
- General relativity: numerical solutions of wave maps, mean
curvature and inverse mean curvature flow, and Einstein equations
- Mathematical biology: systems biology, gene regulatory network
identification and functional prediction