• 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