
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, fluidsolid 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