Visiting Chair Professor
Dr. Cai received the B.S. degree in 1981 and the M.S. degree in 1985 from University of Science and Technology of China. He obtained the Ph.D. degree in 1989 from Brown University. Since 1999, Dr. Cai has been a tenured full professor in mathematics at University of North Carolina at Charlotte, United States. He was awarded the Feng Kang Prize of scientific computing in 2005. Since 1990, his research has been supported by US National Science Foundation, US Air Force, Department of Energy, Army Research Office, and National Institutes of Health and so on. He has worked on multiple research fields, in particular, his work on computational electromagnetics, electrostatic interactions in computational biology, and quantum device transport etc. has been widely cited in literature and used in applications. He published over 100 papers in top international scientific journals.
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. Research topics include: Uncertainty quantifications and stochastic modeling of meta-materials and VLSI interconnect; Computational probability and Feynman-Kac representation of PDE solutions and electric and magnetic 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.
Current Research Projects
- US National Institute of Health (DMS/NIGMS), Fast Algorithms of Electrostatic Interactions for Biomolecular Simulations, (2007-2012)
- US Department of Energy Grant, Numerical Methods of Computational Electromagnetics for Complex Inhomogeneous Systems, (2005-2012)
- US National Science Foundation, Numerical Methods for Wave Propagations in Inhomogeneous Media, (2010-2013)
- US Army Research Office, Multiscale and Multiphysics Modeling of Transport in Mesoscopic System (2007-2014)
- US Army Research Office, Numerical Methods for Studying Optical Absorption of Random Media and Quantum Dots for Solar Cell Designs (2014-2017)
- US National Science Foundation, High Order and Efficient Numerical Methods for Simulating Electromagnetic Phenomena (2016-2019)
Computational Methods for Electromagnetic Phenomena:
electrostatics in solvations, scattering, and electron transport, Wei Cai, 464 page, Cambridge University Press, 2012 [amazon link] [toc]
Major Publications on Algorithms
- A computational stochastic methodology for the design of random meta-materials under geometric constraints, Ivi C Tsantili Min Hyung Cho Wei Cai George Em Karniadakis, submitted to SIAM J. on Scientific computing, 2017.
- High Order Hierarchical Divergence-free Constrained Transport H(div) Finite Element Method for Magnetic Induction Equation, W. Cai, J. Hu, and S.Y. Zhang, to appear in Numerical Mathematics: Theory, Methods and Applications, 2017.
- Computation of Local Time of Reflecting Brownian Motion and Probabilistic Representation of the Neumann Problem, Y.J. Zhou, W. Cai, E. Hsu, the Communications in Mathematical Sciences, Vol. 15, No. 1, pp. 237–259, 2017.
- Accurate and Efficient Nystrom Volume Integral Equation Method for the Maxwell equations for Multiple 3-D Scatterers, D. Chen, Wei Cai, B. Zinser, and M.H. Cho, Journal of Computational Physics, 321 (2016), 303-320.
- Quadrature Weights on Tensor-Product Nodes for Accurate Integration of Hypersingular Functions over Some Simple 3-D Geometric Shapes, B. Zinser, W. Cai, D. Chen, Communication in Computational Physics, Vol. 20, No. 5, pp. 1283-1312, 2016.
- A well-conditioned hypersingular boundary element method for electrostatic potentials in the presence of inhomogeneities within layered media, Brian Zinser, and Wei Cai, Communication in Computational Physics, Vol. 19, No. 4, pp. 970-997, 2016.
- Investigating the Selectivity of KcsA Channel by an Image Charge Solvation Method (ICSM) in Molecular Dynamics Simulations, K. Baker, D. Chen, W. Cai, Commun. Comput. Phys, Vol. 19, No. 4, pp.927-943, 2016.
- A device adaptive inflow boundary condition for Wigner equations of quantum transport, H.Y. Jiang, T. Lu, W. Cai, Journal of Computational Physics , 258 (2014) 773–786.
- Accuracy and efficiency in computing electrostatic potential for an ion channel model in layered dielectric/electrolyte media, H.M. Lin, W. Cai, and H. Z. Tang, Journal of Computational Physics 259 (2014) 488–512.
- Feature-Scale Simulations of Particulate Slurry Flows in Chemical Mechanical Polishing by Smoothed Particle Hydrodynamics, D. Wang, S. Shao, C. Yan, W. Cai, X. Zeng, Commun. Comput. Phys, Volume 16 / (2014), pp 1389-1418.
- Fast Integral Equation Solver for Maxwell’s Equations in Layered Media with FMM for Bessel Functions, M.H. Cho and W. Cai, Science China, December 2013, Vol. 56 No. 12: 2561–257.
- Divergence-free H(div)-conforming hierarchical bases for Magnetohydrodynamics (MHD), Wei Cai, Jian Wu and Jianguo Xin, Communications in Mathematics and Statistics (2013) 1:19-35.
- Linear scaling discontinuous Galerkin density matrix minimization method with local orbital enriched finite element basis: 1-D lattice model system, T. Lu, W. Cai, J.G. Xin, Y. L. Guo, Communication in computational physics, vol. 14, No. 2, (2013), pp. 276-300.
- A parallel method for solving Laplace equations with Dirichlet data using local boundary integral equations and random walks, C.H. Yan, W. Cai, X. Zeng, SIAM J. Scientific computing (2013), vol. 35, No. 4, pp. B868-B889.
- A parallel fast algorithm for computing the Helmholtz integral operator in 3-D layered media, M. H. Cho, W. Cai, Journal of computational physics, 231 (2012) 5910–5925.
- Accuracy of the Frensley inflow boundary condition for Wigner equations in simulating resonant tunneling diodes, H.Y. Jiang, W. Cai, R. Tsu, Journal of Computational Physics, 230 (2011) 2031-2044. Journal of scientific computing, J Sci Comput (2012) 50:446–461.
- Image Approximations to Electrostatic Potentials in Layered Electrolytes/Dielectrics and an Ion-Channel Model, H. M. Lin, Z. L. Xu, H.Z. Tang, and W. Cai, the Journal of Scientific computing, Online, 20 December 2011, DOI 10.1007/s10915-011-9567-2.
- A well-conditioned Hiearchical Basis for Triangular H(Curl)-conforming elements, J. G. Xin, W. Cai, Communication in Computational Physics, vol. 9, pp. 780-806, (2011).
- A wideband Fast multipole method for the two-dimensional complex Helmholtz equation, M.H. Cho, W. Cai, Computer Physics Communications, 181 (2010) 2086-2090.
- Adaptive conservative cell-averaged spectral element methods for transient Wigner equation for quantum transport, S. H. Shao, T. Lu, W. Cai, Communication in Computational Physics, vol. 9, pp. 711-739, 2011.
- Fast analytical methods for macroscopic electrostatic models in biomolecular simulations, Z. L. Xu, W. Cai, SIAM Rev. 53, pp. 683-720, 2011.
- An Image-based reaction field method for electrostatic interactions in molecular dynamics simulations of aqueous solutions, Yuchun Lin, Andriy Baumketner, Shaozhong Deng, Zhenli Xu, Donald Jacobs, Wei Cai, the Journal of Chemical Physics, 131, 154103 (2009).
- A new FFT-based algorithm to compute Born radii in the generalized Born theory of biomolecule solvation, Wei Cai, Zhenli Xu, A. Baumketner, the Journal of Computational Physics, 227 (2008) 10162-10177.
- A Schwarz Generalized Eigen-oscillation Spectral Element Method (GeSEM) for 2-D High Frequency Electromagnetic Scattering in Dispersive Inhomogeneous Media, W. Cai, X. Ji, J.G. Sun, S.H. Shao, the Journal of Computational Physics, 227 (2008) 9933-9954.
- Boundary Treatments in the Nonequilibrium Green’s functions (NEGF) methods for transport in Nano-MOSFETs, H. Y. Jiang, S.H. Shao, W. Cai, P.W. Zhang, the Journal of Computational Physics, 227, (2008), pp. 6553.
- A Generalized Discontinuous Galerkin Method (GDG) for Schrodinger Equations with Nonsmooth Solutions, Kai Fan, Wei Cai, Xia Ji, the Journal of Computational Physics, 227 (2008), pp. 2387-2410.
- Extending the Fast Multipole Method to Charges Inside or Outside a Dielectric Sphere, W. Cai, S. Z. Deng, D. Jacobs, the Journal of Computational Physics, 223 (2007), pp. 846-864.
- Extending the fast multipole method for charges inside a dielectric sphere in an ionic solvent: high order image approximations for reaction fields, S.Z. Deng, W. Cai, the Journal of Computational Physics, 227 (2007), 1246-1266.
- Discontinuous Galerkin Methods for Dispersive and Lossy Maxwell’s Equations and PML Boundary Conditions, T. Lu, P.W. Zhang, W. Cai, Journal of Computational Physics, 200 (2004), pp. 549-580.
- High Order mixed RWG basis functions for electromagnetic applications, IEEE transaction on Microwave Theory and Technology, Vol. 49, No. 7, pp. 1295-1303, July 2001.
- Fast calculation of dyadic Green’s functions for electromagnetic scattering in a multi-layered medium, (with Tiejun Yu), Journal ofComputational Physics, 165, 1-21, 2000.
- Adaptive Wavelet Collocation Method for the Initial Value Boundary Problem of Nonlinear PDE’s, (with J.Z. Wang), SIAM Journal of Numerical Analysis, Volume 33, Number 3, pp. 937-970, June 1996.