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
Computational Methods for Electromagnetic Phenomena: – electrostatics in solvation, scattering, and electron transport
- CUP, 461 pages, 2013 (Table of Content) (Amazon link) (errata)
- Book review by OpticsPhotonicsNews
- Book review by Contemporary Physics
- Brown University, 1989, Ph.D. in Applied Mathematics
- University of Science and Technology of China, 1983, BS in Math, 1985, MS in Applied Math.
- 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.