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Curriculum Vitae Wei Cai, Clements Chair of Applied Mathematics Curriculum Vitae Wei Cai, Clements Chair of Applied Mathematics Department of Mathematics, Southern Methodist University Dallas, TX 75275 Phone: 214-768-3320, E-mail: [email protected] Homepage: https://people.smu.edu/cai/ Research Interest 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. Deep Neural network for wideband learning and PDE solutions 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 Fast integral solvers for wave scattering in layered media 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 Education Brown University, 1985-1989, Ph.D. in Applied Mathematics, Thesis Advisor, Prof. David Gottlieb University of Science and Technology, China, 1983-1985, M.S. in Applied Mathematics University of Science and Technology, China, 1978-1982, B.S. in Mathematics Professional Experience Southern Methodist University Clements Chair, Dept. of Mathematics, 8/2017-present University of North Carolina at Charlotte, 8/1989 – 7/2017 1 Assistant Professor, Department of Mathematics, 8/89-7/94 Associate Professor, Department of Mathematics, 7/94-7/99 Professor, Department of Mathematics, 7/99-7/2017 University of California at Santa Barbara, 1/95-9/96 Assistant Professor V (off-scale), Department of Mathematics, 1/95-8/96 Associate Professor II (off-scale), Department of Mathematics, 9/96 Honor and Award Winner of 2005 Feng Kang Prize for Scientific Computing (awarded by Chinese Academy of Sciences every two years) Editorial Board & Committee Associate Editor in the Communications in Computational Physics, 2005-present Associate Editor in the Journal of Computational Mathematics, 2009-present Associate Editor in Communications in Mathematics and Statistics, 2012-present Associate Editor in Communications on Applied Mathematics and Computation, 2018-present SIAM Gene Golub Summer School Committee, 1/1/2019 to 12/31/2022 Research Grants Finished Projects 1. National Science Foundation, Advanced Scientific Computation (PI $144,000, 1990-1994) 2. Air Force Grant, Wavelet Methods for Combustion (PI $230,000, 1994-99) 3. Advanced Research Project Agency Grant, Numerical Techniques for Efficient Evaluation and Physical Design of Mixed Signal Modules (PI $362,000, 1996-99) 4. National Science Foundation Grant, Adaptive Wavelet Element Methods for Highly Parallel Computations (PI $322,384, 1999-2002) 5. National Science Foundation Grant, Development of Fast and Accurate Numerical Algorithms for Embedded 3-D RF Components (Co-PI $381,000, 2000-03). 6. National Science Foundation Grant, Efficient and Performance Guaranteed Methods for Order Reduction, (Co-PI $160,274, 6/15/2001-5/31/2004) 7. National Science Foundation Grant, Fast Algorithms for Wave Scattering in Layered Media with Application in Electronics and Geophysical Exploration, (PI $54,000, 6/2001 – 7/2004). 8. Air Force Grant, International Conference on the Research Trend for PDE modeling and 2 Computation, (PI $14,000, 5/2004-5/2005) 9. Army Research Office Grant, International Conference on the Research Trend for PDE modeling and Computation, (PI $10,000, 5/2004-5/2005) 10. National Science Foundation Grant, Numerical Methods for Solving Maxwell Equations in Inhomogeneous Dispersive Media, (PI $231,000, 8/2004-7/2007). 11. National Science Foundation, High Order Numerical Methods for Light Propagation in Micro- Photonics, (PI $180,000, 8/2005-8/2009). 12. National Science Foundation, Stochastic Modeling of Interconnects in Nano-VLSI design, (PI, $70,000, 2007-2011). 13. National Institute of Health, Fast Algorithms of Electrostatic Interactions for Biomolecular Simulations, (PI/Director, $1.4 millions, 2007-2012). 14. Department of Energy, Numerical Methods of Computational Electromagnetics for Complex Inhomogeneous Systems, (sole PI $1.2 million, 6/2005-8/2013). 15. Army Research Office, Multiscale and Multiphysics Modeling of Transport in Mesoscopic System, (sole PI, $567,000, 2007-2014). 16. National Science Foundation Grant, Numerical Methods for Wave Propagations in Inhomogeneous Media, (sole PI $200,000, 8/2010-7/2014). 17. National Science Foundation Grant, A parallel Poisson/Helmholtz solver using local boundary integral equation and random walk methods, (sole PI $140,000, 9/2013-8/2015). 18. Army Research Office, Numerical Methods for Studying Optical Absorption of Random Media and Quantum Dots for Solar Cell Designs (sole PI $496, 000, 6/2014-5/2017). 19. National Science Foundation, High Order and Efficient Numerical Methods for Simulating Electromagnetic Phenomena (PI $170,000, 9/1/2016-8/30/2019). Current Projects 20. Army Research Office, Efficient Numerical Methods for Stochastic Modeling of Optical Absorption in Solar Cells under Uncertainty, (Sole PI, $419,811, 2017-2020). 21. National Science Foundation, Path Integral Monte Carlo Methods for Computing Polarizability Tensors of Nano-materials and Electrical Impedance Tomography, (Sole PI, $182,516, 2017-2020). Publications Book: Computational Methods for Electromagnetic Phenomena: electrostatics in solvation, scattering and electron transport, W. Cai, Cambridge University Press, 461 pages, 2013. 3 Journal Articles (120+ items) 1. Fast multipole method for 3-D Laplace equation in layered media, B Wang, WZ Zhang, W Cai, arXiv preprint arXiv:1908.10863, submitted to Computer Physics Communications, 11/2019. 2. Exponential convergence for multipole expansion and translation to local expansions for sources in layered media: 2-d acoustic wave, W Zhang, B Wang, W Cai, arXiv preprint arXiv:1809.07716, submitted in revision to SIAM Numerical Analysis, 12/2019. 3. A phase shift deep neural network for high frequency approximation and wave problems , Wei Cai, Xiaoguang Li, Lizuo Liu, arXiv:1909.11759, submitted to SIAM Numerical Analysis, 12/2019. 4. Multi-scale Deep Neural Networks for Solving High Dimensional PDEs, Wei Cai, Zhiqin John Xu, arXiv:1910.11710 , 10/2019. 5. Taylor Expansion based Fast Multipole Methods for 3-D Helmholtz equations in Layered Media, Bo Wang, Bo Zhang, Min Hyung Cho, Wenzhong Zhang, W. Cai, Journal of Computational Physics, 2020 Jan 15;401:109008. 6. Fast Multipole Methods for 3-D Helmholtz equations in Layered Media, Bo Wang, Wenzhong Zhang, W. Cai, SIAM J. on Scientific computing, 41(6), A3954–A3981, (2019). 7. Attraction between Like-Charged Macroions Mediated by Specific Counterion Configurations, A Stelmakh, W Cai, A Baumketner, The Journal of Physical Chemistry B 123 (46), 9971-9983, (2019) 8. An O (NlogN) hierarchical random compression method for kernel matrices by sampling partial matrix entries, Duan Chen, Wei Cai, Journal of Computational Physics, 2019 Nov 15;397:108828. 9. What Is the Fractional Laplacian? A comparative review with new results, Anna Lischke, Guofei Pang, Mamikon Gulian, Fangying Song, Christian Glusa, Xiaoning Zheng,Zhiping Mao, Wei Cai, Mark M. Meerschaert, Mark Ainsworth, George Em Karniadakis, Submitted in revision to Journal of Computational Physics, 404 (2020) 109009. 10. A high order efficient numerical method for 4-D Wigner equation of quantum double-slit interferences, Zhenzhu Chen, Sihong Shao, Wei Cai, Journal of Computational Physics, 396 (2019) 54-71. 4 11. Clusters of lysozyme in aqueous solutions, A Baumketner, W Cai, Physical Review E 98 (3), 032419, (2018). 12. A Heterogeneous FMM for Layered Media Helmholtz Equation I: Two Layers in R^2, M.H. Cho, J.F. Huang, D. Chen, W. Cai, Journal of Computational Physics, 369 (2018) 237–251. 13. Accurate and efficient Nystrom volume integral equation method for electromagnetic scattering of 3-D meta-materials in layered media, D. Chen, Wei Cai,, and M.H. Cho, SIAM J. on Scientific computing, Vol. 40, No. 1, pp. B259–B282, 2018. 14. 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, SIAM J. Scientific computing, Vol. 40, No. 2, pp. B353-B378, 2018. 15. Cluster crystals stabilized by hydrophobic and electrostatic interactions , A. Baumketner, A. Stelmakh and W. Cai, J. Phys. Chem. B 122, 2669 (2018) 16. Discovering variable fractional orders of advection-dispersion equations from field data using multi- fidelity Bayesian optimization. Pang G, Perdikaris P, Cai W, Karniadakis GE. Journal of Computational Physics. 2017 Nov 1;348(C):694-714. 17. High Order Hierarchical Divergence-free Constrained Transport H(div) Finite Element Method for Magnetic Induction Equation, W. Cai, J. Hu, S.Y. Zhang, Numerical Mathematics: Theory, Methods and Applications, Volume 10, Issue 2 May 2017 , pp. 243-254. 18. Y.J. Zhou, W. Cai, E. Hsu, Computation of Local Time of Reflecting Brownian Motion and Probabilistic Representation of the Neumann Problem, Communications
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