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

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

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.

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 in Mathematical Sciences, Vol. 15, No. 1, pp. 237–259, 2017.

19. Xuan Zhao,, Xiaozhe Hu, Wei Cai, George Em Karniadakise, Adaptive finite element method for fractional differential equations using hierarchical matrices, Comput. Methods Appl. Mech. Engrg. 325 (2017) 56–76

20. A high-order time domain discontinuous Galerkin method with orthogonal tetrahedral basis for electromagnetic simulations in 3-D heterogeneous conductive media, Jun Yang, Wei Cai, Xiaoping Wang, Communications in Computational Physics, Volume 21, Issue 4 April 2017 , pp. 1065- 1089.

21. Efficient and accurate computation of electric field dyadic Green's function in layered media, M.H. Cho, W. Cai, Journal of Scientific Computing, 71 (2017), pp. 1319-1350.

22. 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, the Journal of Computational Physics, 321 (2016), 303-320.

23. 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.

24. 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.

25. Equilibrium clusters in suspensions of colloids interacting via potentials with a local minimum, A. Baumketner, and W. Cai, Cond. Matt. Phys. 19, 13605 (2016)

26. Softness and non-spherical shape define the phase behavior and the structural properties of lysozyme in aqueous solutions, A. Baumketner,, R. Melnyk, M. F. Holovko, W. Cai, D. Costa and C. Caccamo, J. Chem. Phys. 144, 015103 (2016);.

27. Investigating the Selectivity of KcsA Channel by an Image Charge Solvation Method (ICSM) in Molecular Dynamics Simulations, K. Baker, D. Chen, W. Cai,, Communications in Computational Physics, Vol. 19, No. 4, pp.927-943, (2016).

28. Numerical Solution of the Robin Problem of Laplace Equations with a Feynman-Kac Formula and Reflecting Brownian Motions, Yijing Zhou, Wei Cai, Journal of Scientific Computing, (2016) 69(1), 107-121.

29. Feature-scale Simulations of Particulate Slurry Flows in Chemical Mechanical Polishing by Smoothed Particle Hydrodynamics, Dong Wang, Sihong Shao, Changhao Yan,Wei Cai and Xuan Zeng, Communication in Computational Physics, 16.5 (2014): 1389-1418.

30. 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.

31. 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.

32. 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.

33. 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.

34. On the construction of well-conditioned hierarchical bases for H(div)-conforming R^n simplicial elements, J Xin, W. Cai, and N.L. Guo, Communications in computational physics, Vol. 14, No.3, (2013), pp. 621-638. .

35. A parallel method for solving Poisson equations with Dirichlet data using local boundary integral equations and random walks, SIAM J. Scientific computing, C.H. Yan, W. Cai, X. Zeng, (2013), vol. 35, No. 4, pp. B868-B889.

36. 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.

37. Generalized image charge solvation model for electrostatic interactions in molecular dynamics simulations of aqueous solutions, S.Z. Deng, C.F. Xue, A. Baumketner, D. Jacobs, W. Cai, Journal of Computational Physics, Volume 245, (2013), Pages 84-106. .

38. ICSM: An order N method for calculating electrostatic interactions added to TINKER, K. Baker, A. Baumketner, Y.C. Lin, S.Z. Deng, D.Jacobs, W. Cai, Computer Physics Communication, ,Vol. 184, Issue 1, January 2013, Pages 19–26.

39. Effect of the Reaction Field on Molecular Forces and Torques Revealed by an Image-Charge Solvation Model, W. Song, Y.C. Lin, A. Baumketner, S.Z. Deng,W. Cai and D. J. Jacobs, Commun. Comput. Phys, Vol. 13, No. 1, pp. 129-149, 2013.

40. 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.

41. Well-conditioned orthonormal hierarchical L^2 bases on R^n simplicial elements, J. Xin, W. Cai, J. of Scientific Computing (2012) 50:446–461.

42. ParAFEMCap: A Parallel Adaptive Finite Element Method for 3-D VLSI Interconnect Capacitance Extraction, G.L. Chen, H.L. Zhu, Tao Cui, Z.M. Chen, X. Zeng, and W. Cai , IEEE Transactions on Microwave Theory and Techniques, VOL. 60, NO. 2, FEBRUARY 2012.

43. Fast analytical methods for macroscopic electrostatic models in biomolecular simulations, Z. L. Xu, W. Cai, SIAM Review 53, pp. 683-720, 2012.

44. 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.

45. 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). 46. Accurate simulation of 2-D phase shift masks with a generalized discontinuous Galerkin method, X. Ji, W. Cai, Discrete and Continuous Dynamical Systems Series B, Volume 15, Number 2, pp. 401-415, (2011)

47. On the construction of well-conditioned hierarchical bases for tetrahedral H(curl)-conforming Nedelec elements, J. Xin, N. Guo and W. Cai, Journal of Computational Mathematics, v29 (2011), No.5, pp.526-542

48. A well-conditioned Hierarchical Basis for Triangular H(Curl)-conforming elements, J. G. Xin, W. Cai, Communication in Computational Physics, vol. 9, pp. 780-806, (2011).

49. Ionic solvation studied by image-charge reaction field method, Y. C. Lin, A. Baumketner, W. Song, S. Deng, D. Jacobs, W. Cai, the Journal of Chemical Physics, 134, 044105 (2011).

50. 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.

51. Improved rigorous coupled-wave analysis for polar magnetic gratings, Min Hyung Cho, Haiyu Zheng, Yuehui Lu, YoungPak Lee and Wei Cai, Computer Physics Communications, 182 (2011) 360-365.

52. Image Charge Method for Reaction Fields in a Hybrid Ion-Channel Model, Z. L. Xu, W. Cai and X. L. Cheng, Communications in Computational Physics, vol. 9, pp. 1056-1070 (2011).

53. A wideband Fast multipole method for the two-dimensional complex Helmholtz equation, M.H. Cho, W. Cai, Computer Physics Communications, 181 (2010) 2086-2090.

54. A fundamental model proposed for material removal in chemical mechanical polishing, S. Xin, W. Cai, and J. Tichy, Wear 268 (2010), 837-844.

55. Effect of Boundary Treatment on Quantum Transport Current in the Green's Function and Wigner Distribution Methods for a Nano-scale DG-MOSFET, H. Y. Jiang, W. Cai, the Journal of Computational Physics, 229, pp. 4461-4475, (2010).

56. A modified nested sparse grid based adaptive stochastic collocation method for statistical state timing analysis, X. Luo, H. L. Zhu, W. Cai, the IEICE Trans. Fundamentals, vol. E92-A, No. 12, pp. 3024-3034, (2009).

57. Generalized stochastic collocation method for variation-aware capacitance extraction of interconnects considering arbitrary random probability, H. L. Zhu, X. Zeng, X. Luo, W. Cai, the IEICE Trans. Electron, p. 508, vol. E92.C, 2009.

58. A contact mechanics based model for general rough pads in chemical mechanical polishing processes, C. Y. Feng, X. Zeng, Changhao Yan , Jun Tao ,W. Cai, the Journal of The Electrochemical Society, pp. H601-H611, vol. 156, (2009).

59. A Sixth-order Image Approximation to the Ionic Solvent Induced Reaction Field, M. Xiang, S. Z. Deng, W. Cai, the Journal of Scientific computing, 2009 December 1; 41(3): 411–435.

60. Image charge methods for a three-dielectric-layer hybrid solvation model of biomolecules, P.H. Qin, Z.L. Xu, W. Cai and D. Jacobs, the Communications in Computational Physics, Vol. 6, No. 5, (2009) pp. 955-977.

61. Fast Spectral Collocation Method for Surface Integral Equations of Potential Problems in a Spheroid, Zhenli Xu, W. Cai, the Communications in Computational Physics, 6 (2009), pp. 625-638 9

62. 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 Jour of Chemical Physics, 131, 154103 (2009).

63. Image Charge Approximations of Reaction Fields in Solvation with Arbitrary Ionic Strength, Zhenli Xu, Shaozhong Deng, submitted to the Journal of Computational Physics, 228, pp. 2092- 2099, (2009)

64. 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 65. Adaptive stochastic collocation method for parameterized statistical timing analysis with quadratic delay model, Y. Wang, X. Zeng, J. Tao, H.L. Zhu and W. Cai, IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences Vol.E91-A No.12 pp.3465-3473, 2008.

66. Image Methods for Electrostatics Potentials, W. Cai, Advances in Mathematics and Its Application, USTC Press, 2008.

67. Highly Parallel Rigorous Simulation of Phase Shift Masks with a Generalized Eigen-oscillation Spectral Element Method (GeSEM), K. Zong, X. Zeng, X. Ji and W. Cai, the Journal of Micro/Nanolithography, MEMS, and MOEMS, special issue on Computational Lithography, October, 2008.

68. 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.

69. Transmission and Dispersion Characteristic of a Discontinuous Galerkin Method for Maxwell's Equations in Dispersive Inhomogeneous Media, X. Ji, W. Cai, P.W. Zhang, Journal of Computational Mathematics, 26, (2008), pp. 347-364.

70. A Fourier Spectral-Discontinuous Galerkin Methods for Time Dependent 3-D Schrodinger- Poission Equations with Discontinuous Potentials, T. Lu, W. Cai, the Journal of Computational and Applied Mathematics, 220, (2008), 558-614.

71. 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.

72. 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

73. A Full Vectorial Generalized Discontinuous Galerkin Beam Propagatiom Method (GDG-BPM) for Inhomogeneous Optical Waveguide, K. Fan, W. Cai, X. Ji, the Journal of Computational Physics, 227 (2008), p.7178.

74. A sparse grid based spectral stochastic collocation method for variations-Aware capacitance extraction of interconnects under nanometer process technology, H.L. Zhu, X. Zeng, W. Cai, J.T. Xue, D. Zhou, IEEE/ACM DATE 2007.

75. 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.

76. 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.

77. Discrete Image Approximations of Ionic Solvent Induced Reaction Field to Charges, S.Z. Deng, W. Cai, the Communications in Computational Physics, 2 (2007), p.1007-1026.

78. A Comparable study of image approximations to the reaction fields, Shaozhong Deng, Wei Cai, Donald Jacobs, Computer Physics Communications, Vol. 177, 9, Nov. (2007), pp. 689-699.

79. FIFA - Fast Interpolation and Filtering Algorithm for Calculating Dyadic Green's Function in the Electromagnetic Scattering of Multi-layered Structures, T.J. Yu, W. Cai, the Communication in Computational Physics, Vol. 1, No. 2, pp. 228-258, 2006.

80. A Fourth-Order Upwinding Embedded Boundary Method (UEBM) for Maxwell's Equations in Media with Material Interfaces: Part I, S. Deng, W. Cai, the Communication in Computational Physics, Volume 1, Number 4, June 2006, pp. 744-764.

81. Analog behavioral modeling by multi-companding and wavelet collocation method, J. Tao, X. Zeng, W. Cai, D. Zhou, C. Chiang, Analogue Integrated Circuits and Signal Processing, An International Journal, vol. 49, pp 291-297, Sept, 2006.

82. High Order DGTD Methods for Dispersive Maxwell's Equations and Modelling of Silver Nanowire Coupling, X. Ji, W. Cai, P. Zhang, the International Journal of Numerical Methods in Engineering, July, 2006.

83. A Boundary Integral Equation Method for Photonic Crystal Fiber, M. Cho, W. Cai, T. Her, the Journal of Scientific Computing, vol. 28, No. 2-3, Sept. 2006, pp. 263-278.

84. Optical Coupling at a distance between detuned spherical cavities, A. Kanaev, V. Astratov, W. Cai, Applied Physics Letter, 88, 111111 (2006).

85. Accurate Calculation of Green's Functions of Schrodinger Equations in Block Layered Potentials, S. H. Shao, W. Cai, H. Z. Tang, the Journal of Computational Physics, 216 (2006), pp. 733- 748.

86. Conservative Local Discontinuous Galerkin Methods for Time Dependent Schroedinger Equation, T. Lu, W. Cai, and P.W. Zhang, International Journal of Numerical Analysis and Modeling, Vo. 1, 45-65, 2005.

87. Discontinuous Galerkin Time Domain (DGTD) Methods for the Study of Waveguide Coupled Microring Resonators, X. Ji, T. Lu, W. Cai, and P.W. Zhang, the Journal of Lightwave Technology, VOL. 23, NO. 11, pp. 3864-3874, NOVEMBER 2005.

88. Discontinuous Spectral Element Methods for Optical Transfer by Whispering Gallery Modes in a Photonic Waveguide of Coupled Microcylinders, S. Deng, W. Cai, Journal of Optical Society of America, A, Vol. 22, No. 5/May 2005.

89. Analysis and Application of an Orthogonal Nodal Basis on Triangles for Discontinuous Spectral Element Methods, S.Z. Deng, W. Cai, Applied Numerical Analysis and Computational Mathematics, 2(3):311-330, 2005

90. Discontinuous Galerkin Time Domain Methods for GPR Simulation in Dispersive Media, T. Lu, W. Cai, Pingwen Zhang, IEEE Transaction GRS, Volume: 43 , Issue: 1 , Pages:72 - 80, Jan. 2005.

91. Numerical Methods for Maxwell's Equations in Inhomogeneous Media with Material Interfaces, W. Cai, Journal of Computational Mathematics, Vol. 22, No. 2, pp. 156-167, 2004.

92. 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.

93. Numerical Study of Light Propagation via Whispering Gallery Modes in Microcylinder Coupled Resonator Optical Waveguides, S. Z. Deng, W. Cai, V. Astratov, Optics Express, 12, 6468-6480 (2004).

94. An Exact Absorbing Boundary Condition for Exterior Helmholtz Equation in Layered Media, W. Cai, H.T. Yang, in Advances in Computation: Theory and Practice, Science Press, NY, p97, 2004.

95. Behavioral modeling for analog system-level simulation by wavelet collocation method, X. Li, X. Zeng, D. Zhou, X. Ling, W. Cai, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, Vol. 50, Issue: 6, 299-314, (2003).

96. An Upwinding Embedded Boundary Methods for Maxwell equations, W. Cai S. Deng, Journal of Computational Physics, 190, 2003.

97. Singularity Treatment and High Order RWG Basis Functions for Integral Equations of Electromagnetic Scattering, Y. J. Yu, W. Cai, X. C. Yuan, International Journal for Numerical Methods in Engineering, Vol. 53, No. 1, January 2002.

98. An efficient DC-gain matched balanced truncation realization for VLSI interconnect circuit order reduction, X. Zeng, D. Zhou, W. Cai, Microelectronic Engineering, Vol. 60, issue 1-2, p. 3-15, 2002.

99. Algorithmic Issues for Computational Electromagnetic Scattering in Layered Media: Green's Function, Basis Function and Fast Solver, W. Cai, Special Issue of Advances in Computational Mathematics: Modeling and Computation of Optics and Electromagnetics, 16: 157-174, 2002.

100. An Inverse Method for Parabolic Equations Based on Quasi-Reversibility, Mohsen Tadi, W. Cai, Michael Klibanov, Computers & Mathematics with Applications 43 (8-9): 927-941, APR- MAY 2002.

101. High Order Window Functions and Fast Algorithms for Calculating Dyadic Electromagnetic Green’s Functions in Multilayered Media, Tiejun Yu, W. Cai, Radio Science, July, 2001.

102. High Order mixed RWG basis functions for electromagnetic applications, IEEE transaction on Microwave Theory and Technology, W. Cai, T. J. Yu, H. Wang, Y. J. Yu, Vol. 49, No. 7, pp. 1295-1303, July 2001. 13

103. Inverse Matrix Evaluation for Linear Systems, Mohsen Tadi, W. Cai, Inverse Problems 17, pp. 247-260, 2001.

104. Level Set-Boundary Element Method for Simulation of Dynamic Powder Consolidation of metels, W. Cai, Zhilin Li, Lecture Notes in Computer Science 1988, Edited by L. Vulkov, J. Wasniewski, and P. Yalamov, pp. 527-534, Springer-verlag, 2001.

105. Fast calculation of dyadic Green's functions for electromagnetic scattering in a multi-layered medium, W. Cai, Tiejun Yu, Journal of Computational Physics, 165, 1-21, 2000.

106. High Order Current Basis Functions for Electromagnetic Scattering of Curved Surfaces, Discontinuous Galerkin Methods, W. Cai, Lecture Notes in Computational Science and Engineering, No. 11, Edited by B. Cockburn, G.E. Karniadakis, and C. W. Shu, pp. 271-276, Springer-Verlag, 2000.

107. Higher order mixed current basis functions for electromagnetic scattering of curved surfaces, W. Cai, Journal of Scientific Computing, Vol. 14, No. 1, pp. 73-105, 1999.

108. An adaptive wavelet method for nonlinear circuit simulation, Dian Zhou, W. Cai, W, Zhang, IEEE transaction on circuits and systems, Vol. 46, No. 8, pp. 931-938, 1999.

109. A fast wavelet collocation method for high speed circuit simulation, Dian Zhou, W. Cai, IEEE transaction on circuits and systems, Vol. 46, No. 8, pp. 920-930, 1999.

110. An Adaptive Spline Wavelet ADI (SW-ADI) Method for two-dimensional Reaction Diffusion Equations, W. Cai, Wu Zhang, Journal of Computational Physics, Vol. 139, pp. 92-126 (1998).

111. Adaptive Multiresolution Collocation Method for the Initial Value Boundary Problem of Nonlinear PDE's, W. Cai, J.Z. Wang, SIAM Journal of Numerical Analysis, Volume 33, Number 3, pp. 937-970, June 1996.

112. Direct numerical calculation of neutral stability curve for one-dimensional detonations, W. Cai, W.H. Oh, Y.L. Zhu, SIAM Journal of Scientific Computing, Volume 17, Number 4, pp. 814-829, July 1996.

113. High-order Numerical Methods for the Computation of Cellular Structure of 2-D Detonation Waves, W. Cai, AIAA Journal, Vol. 33, No. 7, PP 1248-1255, (July, 1995)

114. Domain decomposition and Computation of 2-D Detonation Waves, W. Cai, Contemporary Mathematics, Vol. 180, pp. 459-464, 1994.

115. Uniform High Order Spectral Methods for One and Two Dimensional Euler Equations, W. Cai, C.W. Shu, Journal of Computational Physics, vol. 104, No. 2, pp. 427-443, 1993.

116. Coupling of Spectral Methods and H-P Version Finite Element Methods for PDE's on Nonsmooth Domains, W. Cai, H.C. Lee and H. -S. Oh, in Journal of Computational Physics, vol. 108, No. 2, pp. 314-326, October 1993.

117. On One-sided Filters for Spectral Fourier Approximations of Discontinuous Functions, W. Cai, C.W. Shu and D. Gottlieb, SIAM Numerical Analysis, Vol. 29, No. 4, pp. 905-916, August 1992.

118. Cell averaging Chebychev Method for Hyperbolic Problems, W. Cai, D. Gottlieb and A. Harten, Computers and Mathematics with Applications, vol. 24, No. 516, pp. 37-49, September 1992.

119. Essentially Non-oscillatory Spectral Method for Shock Wave Calculations, W. Cai, D. Gottlieb and C. W. Shu, Mathematics of Computation, 52, (1989) pp.389-410.

120. The limit problem of the Ziekiewicz finite element, W. Cai, Math. Numer. Sinica 8, pp. 345- 353, 1986.

121. Convergence of two nonconforming finite elements, W. Cai, in Journal of Computational Mathematics, Academia Sinica, 2, pp. 63-74, 1986.

Invited talks and Presentations

1. Essentially nonoscillatory spectral methods for Euler Equations, 1990 SIAM Annual Meeting, Chicago. 2. High order methods for the computation of Cellular Structure of 2-D detonation waves, 4th International Conference on Combustion, St. Petersburg, Florida, December 1991. 3. Recent results on spectral methods for singular solutions, 2nd International ICOSAHOM conference, mini-symposium talks, Montpellier, France, June 22-26, 1992. 4. Spectral methods for PDE's with singular solutions, Invited talks at International IMACS Conference on Scientific Computing and Modeling, December 1992, Banglore, India. 15

5. Adaptive wavelet collocation methods for Initial value boundary problem for time dependent PDE's, presenter and organizer of Minisymposium on High Order method for shock wave computation, SIAM Annual Meeting, 1993, Philadelphia. 6. High order Hybrid method for 2-D detonation waves, SIAM Annual meeting, 1993, Philadelphia. 7. Hybrid Numerical Methods for the computation of Cellular Structure of 2-D detonation waves, 5th International Conference on Combustion, Garmish- Partenkirchen, Germany, September 29, 1993. 8. Multi-domain Techniques and Computation of 2-D Detonation Waves, 7th International Conference on Domain Decomposition, Penn. State University, October 1993. 9. Adaptive wavelet collocation methods and wave propagation, Invited talk at 129th meeting of Acoustical Society of America, 31 May - 2 June 1995, Washington D.C. 10. Adaptive wavelet time dependent calculations of laminar flames, The Third International Congress on Industrial and Applied Mathematics (ICIAM 95), 3-7 July 1995, Hamburg, Germany. 11. An adaptive Wavelet ADI method for two-dimensional flame propagation, the 17th biennial conference on numerical analysis, June 24 - 27, 1997, Dundee, Scotland 12. Present a week of Invited Lectures on Numerical Methods for Detonations and Electromagnetics at Institute of Applied and Computational Physics, June 25 - July 1, 1997, Beijing, China. 13. Adaptive Wavelet ADI methods for Combustion, the 3rd ICOSAHOM, June 22 -26, 1998, Herzliya, Israel, 1998. 14. Invited Mini-symposium Speaker, Adaptive Wavelet Methods and Applications in Combustions, SIAM Eighth International Conference on Numerical Combustion, March 5-8, 2000, Orlando, FL. 15. Invited Mini-symposium Organizer, High Order Methods in Computational Electromagnetics, p and finite element methods: Mathematics and Engineering, May 31-June 2, 2000, St. Louis. 16. Invited Mini-symposium Organizer, Computational Electromagnetics and Applications, SIAM First Conference on Computational Science and Engineering (CSE00), September 21-23, 2000, Washington, D. C. 17. Invited talk at Courant Institute, April, 2002 18. Invited talk at Dept. of Math., Pen. State University, May, 2002 19. Invited talk at Brown University, April, 2002 20. Invited talk at Michigan State University, May, 2002. 21. Invited Talk at 3rd International Conference on Scientific Computation and Applications, January 6-9, 2003, City University of Hong Kong. 22. Invited Talk at the 6th International Conference on Spectral and High order 16

Methods, June 21-25, 2004, Brown University, RI 23. Speaker and Co-organizer at a two-Session mini-symposium at the 2004 SIAM Conference on Material Science, LA, May 23-26, 2004. 24. Invited Talk at the International Conference on Multiscale Modeling and Scientific Computing, in honor of Bjorn Engquist’s 60th birthday, June 10-12, 2005, Beijing, China. 25. Invited talk at DOE annual Applied Mathematic Meeting, LLNL, May, 2007 26. Mini-symposium talk at ICOSAHOM, Beijing, June 18-23, 2007, Beijing 27. Invited talk at Dept. of Math, UNC Chapel Hill, September 2007. 28. Invited talk at Mechanical Engineering, Stanford, March 2008 29. Invited talk at Dept. of Math, U. South Carolina, 10/23, 2008. 30. Invited talk at the 4th SCPDE international Conference, Hong Kong, 12/8/2008. 31. Mini-symposium talk at the AMS regional meeting, NCSU, April 4-5, 2009 32. Two mini-symposium talks at ICOSAHOM 2009, June 22-26, 2009, Trondheim, Norway 33. Invited talk at the International Conference on Engineering and Computational Math (ECM2009) May 27-29, 2009, Hong Kong. 34. Invited talk at Meta-material workshop at IPAM, UCLA, Jan. 2010. 35. Invited talk at Dept of Math, University of Texas at Austin, February 2010. 36. Invited talk at workshop on Quantum-Classical Modeling of Chemical Phenomena, CSCAMM, University of Maryland, March, 2010. 37. Invited talk at Dept of Math, University of Alabamba, March, 2010. 38. Invited talk at DOE applied mathematics meeting, LBNL, UC Berkeley, May, 2010. 39. Invited talk at Workshop on Modeling and computation of biomolecular structure and dynamics, Ohio State University, MBI, April 25-29, 2011 40. Invited talk The 11th International Workshop on Finite Elements for Microwave Engineering FEM2012, June 4, 2012 - Wednesday, June 6, 2012, Estes Park, Colorado. 41. Invited talk at 4th International conference on scientific computing, Nanking, June 22-26, 2012. 42. Invited talk at the 6th International Conference of Chinese Mathematicians, July 13- 19, 2013, Taipei. 43. Invited mini-symposium talk at ICIAM 2015, August 8-13, 2015, Beijing, China 44. Invited talk at Modeling and Computation of Transmembrane Transport, Mathematical Biosciences Institute, Columbus, Ohio, 11/16-20, 2015 45. Invited talk at 13th Workshop on Finite Elements (FEM2016), Florence, Italy, May 15-19, 2016. 46. Invited talk at the Mathematics in Action: modeling and analysis in molecular 17

biology and electrophysiology, Suzhou, June 16-18, 2016. 47. Invited talk at Mathematical Analysis of Metamaterials and Applications Workshop” at Tsinghua Sanya International Mathematics Forum (TSIMF) from December 5-9, 2016. 48. Invited talk at international workshop on Soft Matter Sciences, Shanghai Jiao Tong University (SJTU) in December 12-14, 2016.

49. Invited talk Dept of Math, Duke University, March 21, 2017.

50. Invited talk Dept of Math, Wayne State University, November 19, 2017.

51. Invited talk International Conference on Recent Advances in Computational and Applied Mathematics, Wuhan, University, China, December 14-17, 2017.

52. Invited talk at SIAM Conference on Uncertainty Quantification (UQ18), April 16-19, 2018, Garden Grove, CA.

53. Invited talk at Invited talk at Dept of Physics, Yale University, May 8-9, 2018.

54. Invited talk at 2018 SIAM Annual Meeting (AN18), July 9 - 13, 2018, Oregon

Convention Center (OCC) | Portland, Oregon, USA.

55. Invited talk at Dept of Math, Stanford University, April 23, 2019

56. Invited talk Dept of Math., UC Berkeley, April 25, 2019.

57. Invited talk at Advanced Numerical Methods for Scientific Computation, June 15-17, 2019, Shenzhen, China

58. Invited talk at SIAM Southwest sectional meeting, Nov. 1-3, 2019, SMU, Dallas.

Graduate Courses Taught

Stochastic Finite Element Methods Computational Electromagnetics and Photonics Computational Quantum Methods for Submicron and Nanodevices Computational Stochastic Methods and uncertainty quantifications Computational Fluid Dynamics Multigrid Methods Adaptive Wavelet Methods for PDEs and Circuits Spectral Methods for CFD

PhD Student Supervision (13 with Ph.D. degree awarded, 4 on-going)

Kathy Baker (CPCC), H. Min Cho (U. Mass Lowell), Kai Fan (Infinite financial, China), Nailong Guo (John Smith University), Haiyang Jiang (Beijing Institute of Technology, China), Xia Ji (Chinese Academy of Sciences, China), Tiao Lu (Peking Univ.) , Shihong Shao (Peking Univ.), Patrick Wu (Wells Fargo), Ming Xiang (Bank of America), Yijun Yu (CPCC), Yijing Zhou (Wells Fargo), Brian Zinser (LANL). Cayle Retz, Yetong Zhou, (on going) Wenzhong Zhang, Lizhuo Liu.

Postdoctoral Supervision (15)

Drs. ShaoZhong Deng (UNCC), Xia, Ji (CAS, China), Haiyan Jiang (BIT, China), Xiaoguang Li, Yuchun Lin (Berkeley), Tiao Lu (Peking U.), Moshe Tadi (Univ. of Denver), Han Wang (Bank of America), Steve Xin (Bank of America), Zhenli Xu (SJTU, China), H.T. Yang (UNLV), Tiejun Yu (Cadence), Ivi Tsantili (CSRC, China), Guofei Pang, Bo Wang, Xuan Zhao

Synergistic Activities

• Public Release of a molecular dynamics simulation code: This code named ICSM, from our previous DMS/NIGMS grant (2007-2012), is an all-atom simulation package free for academic and non-profit use that can handle accurately and efficiently a multi-component solution representing the cellular environmet.The code can be downloaded from the PI’s website: http://www.math.uncc.edu/~wcai/TINKER-icsm/.

• Referees of scientific papers on regular basis for various journals including Journal of Computational Physics, SIAM Journals (Numerical Analysis, Applied Math, Scientific computing), Communications in Computational Physics, Mathematics of Computations, IEEE MTT, Journal of Scientific computing.

• Reviewer for NSF, AFOSR, ARO, NIH NSF Career Panelist, Computational Mathematics,2001, 2005, 2011

Professional Services

Conference Organization

• Organizer of a workshop on Spectral Methods at NCSU, 1994 • Mini-symposium Organizer, Computational Electromagnetics and Applications, SIAM First Conference on Computational Science and Engineering (CSE00), Sept. 21-23, 2000. • Mini-symposium Organizer, High Order Methods in Computational Electromagnetics, p and finite element methods: Mathematics and Engineering,

5/30-6/2, 2000, St. Louis. Organizer at a two-Session mini-symposium at the 2004 SIAM Conference on Material Science, LA, May 23-26, 2004. • Organizer of International Conference on the Research Trend for PDE Modeling and Computation, in honor of David Gottlieb 60th birthday, November 7-8, 2004, Brown University • Mini-symposium Organizer, Molecular Biosciences: Ion Channels and their Roles in Cell Biology, SIAM Conference on Life science, 2014, Charlotte, NC

• A workshop on Monte Carlo Methods and Applications, June 27-July 2, 2016, Beijing, China

• International Conference on Algorithms and Applications of Excited State Electronic Structure theories, August 8-10, 2016, Beijing, China