Research Interests & Publications:

Developing advanced fast machine learning, stochastic, and deterministic numerical methods for data science and scientific computing applications, and understanding complex physical phenomena with a special focus on quantum phenomena, electromagnetic processes, and wave scattering in random media and stochastic controls.

  • Deep neural network machine learning algorithms for scientific computing,  wideband and multiscale spectral-bias-free learning for high dimensional quantum systems, high frequency wave scattering in random media,  and fluid dynamics, stochastic controls.
  • Fast multipole methods for wave source interactions in layered media
  • Hierarchical random compression methods for kernel matrices
  • Stochastic computing methods; Computational probability and Feynman-Kac representation of PDE solutions and E&M polarizability tensors of particle of complicated shapes
  • Computational biology, solvation, fast algorithms for electrostatics
  • Computational electromagnetics for wave scattering of meta-materials
  • Quantum transport   (Wigner transport and Non-equilibrium Green’s function methods)
  • Adaptive wavelet/multiscale methods
  • Monte Carlo and stochastic methods, Spectral methods, integral equation methods, discontinuous Galerkin methods   

Selected Journal Publications  

google scholar

Book Publication

Computational Methods for Electromagnetic Phenomena:  – electrostatics in solvation, scattering, and electron transport

Education

  • Brown University, 1989, Ph.D. in Applied Mathematics
  • University of Science and Technology of China, 1983, BS in Math, 1985, MS in Applied Math.

Professional Experience

  •  Southern Methodist University, Clements Chair,                                                               Dept. of Mathematics,   8/2017-present
  • University of North Carolina at Charlotte,   8/1989 – 7/2017,                                    Assistant,  Associate (1994) and full professor (1999),                                                Dept of Mathematics
  • University of California at Santa Barbara, 1/95-9/96                                            Assistant Professor, 1/1995-8/1996,  Associate Professor , 9/1996, Department of Mathematics.

Go to Math. Dept. Page

Go to SMU Page