Prof. Wei Cai's Home Page




Research Interest & Publications:

Developing advanced stochastic and deterministic numerical methods to understand complex physical phenomena with a special focus on electromagnetic processes
arising from complex biological systems, quantum dynamics and transport, and meta-materials and nano-photonics, and scattering in random media
.  

  • Stochastic computing methods for meta-materials and VLSI interconnect 
  • Computational probability and Feynman-Kac representation of PDE solutions and E&M polarizability tensors of nano-particle of complicated shapes
  • Computational biology, solvation, fast algorithms for electrostatics
  • Computational electromagnetics for meta-materials, random scattering, nano-photonic, and plasmonic devices
  • Quantum transport in nano-devices (Wigner transport and Non-equilibrium Green’s function methods)
  • Adaptive wavelet/multiscale methods for numerical combustion and circuit System
  • Monte Carlo and stochastic methods, Spectral methods, integral equation methods, discontinuous Galerkin methods
  • Fast integral solvers for wave scattering in layered media
  Publications                           

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

  Recent Research Projects:

  • DOE, Numerical Methods of Compuational Electromagnetics in Complex Inhomogenuous Systems, (2005-2013)
  • DMS/NIGMS Math Biology Initiative (NIH), Fast Algorithms of Electrostatic Interactions for Biomolecular Simulations, (2007-2013)
  • ARO, Numerical Methods for Studying Optical Absorption of Random Media and Quantum Dots for Solar Cell Designs (2014-2017)
  • NSF, High Order and Efficient Numerical Methods for Simulating Electromagnetic Phenomena, (2016-2019)
  • ARO, Efficient Numerical Methods for Stochastical Modeling for Optical Absorption in Solar Cells (2017-2020)
  • NSF, Path Integral Monte Carlo Methods for Computing Polarizability Tensors of Nano-materials and Electrical Impedance Tomography, (2017-2020)

Contact Information:

Education:

Professional Experience:

           Clements Chair of Applied Mathematics, Department of Mathematics, 8/2017-present

Assistant Professor, Department of Mathematics, 8/89-7/94
Associate Professor, Department of Mathematics, 7/94-7/99
Professor, Department of Mathematics, 7/99-present
Assistant Professor V (off-scale), Department of Mathematics, 1/95-5/96
Associate Professor II (off-scale), Department of Mathematics, 5/96-9/96

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