# All Journal Publications in Categories

I.     Computational Algorithms and Methodologies

II.    Combustion System

III.  Electromagnetic Scattering in Microwave devices

IV.  Circuit Simulation and Model Reductions

V.   Meta-Materials, Photonics, and Plasmon Systems

VI.   Quantum Transport in Nano-devices

VII.  Electrostatics and MD simulations for Biomolecules and Ion-Channels

IX.  Stochastic methods and simulations

* * *

I. Computational Algorithms and Methodologies

1. Convergence of two nonconforming finite elements, in Journal of Computational Mathematics, Academia Sinica, 2, pp. 63-74, 1986.
2. The limit problem of the Ziekiewicz finite element, in Journal of Computational Mathematics, Academia Sinica, 4, pp. 345-353, 1986.
3. 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.
4. 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, September1992.
5. 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.
6. 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.
7. Coupling of Spectral Methods and H-P Version Finite Element Methods for PDE’s on Nonsmooth Domains, (with H.C. Lee and H. -S. Oh), in Journal of Computational Physics, vol. 108, No. 2, pp. 314-326, October 1993.
8. Domain decomposition and Computation of 2-D Detonation Waves, Contemporary Mathematics, Vol. 180, pp. 459-464, 1994.
9. Adaptive Multiresolution 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.
10. Higher order mixed current basis functions for electromagnetic scattering of curved surfaces, Journal of Scientific Computing, Vol. 14, No. 1, pp. 73-105, 1999.
11. 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.
12. High Order Current Basis Functions for Electromagnetic Scattering of Curved Surfaces, Discontinous Galerkin Methods, 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.
13. Inverse Matrix Evaluation for Linear Systems, (with Mohsen Tadi), Inverse Problems 17, pp. 247-260, 2001.
14.  Level Set-Boundary Element Method for Simulation of Dynamic Powder Consolidation of metels, (with Zhilin Li) Lecture Notes in Computer Science 1988, Edited by L. Vulkov, J. Wasniewski, and P. Yalamov, pp. 527-534, Springer-verlag, 2001.
15. An Inverse Method for Parabolic Equations Based on Quasi-Reversibility, (with Mohsen Tadi, Michael Klibanov), COMPUTERS & MATHEMATICS WITH APPLICATIONS  43 (8-9): 927-941, APR-MAY 2002.
16. Singularity Treatment and High Order RWG Basis Functions for Integral Equations of Electromagnetic Scattering, International Journal for Numerical Methods in Engineering, Vol. 53, No. 1, January  2002.
17. Algorithmic Issues for Computational Electromagnetic Scattering in Layered Media: Green’s Function, Basis Function and Fast Solver, Special Issue of Advances in Computational Mathematics: Modeling and Computation of Optics and Electromagnetics, 16: 157-174, 2002.
18. An Upwinding Embedded Boundary Methods for Maxwell equations, (with S.  Deng) Journal of Computational Phyiscs, 190, 2003.
19. An Exact Absorbing Boundary Condition for Exterior Helmholtz Equation in Layered Media (with H.T. Yang), in Advances in Computation: Theory and Practice, Science Press, NY, p97, 2004
20. 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.
21. 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.
22. Analysis and Application of an Orthogonal Nodal Basis on Triangles for Discontinuous Spectral Element Methods, Applied Numerical Analysis and Computational Mathematics, 2(3):311-330, 2005
23. FIFA –  Fast Interpolation and Filtering Algorithm for Calculating Dyadic Green’s Function in the Electromagnetic Scattering of Multi-layered Structures,   the Communication in Computational Physics, Vol. 1, No. 2, pp. 228-258, 2006.
24. 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.
25.  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.
26. 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.
27.  Image Methods for Electrostatics Potentials, advances in Mathematics and Its Application, USTC Press, 2008.
28. 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.
29. Transmission and Dispersion Characteristic of a Discontinuous Galerkin Method for Maxwell’s Equations in Dispersive Inhomogeneuos Media, X. Ji, W. Cai, P.W. Zhang,  Journal of Computational Mathematics, 26, (2008), pp. 347-364.
30. 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.
31. 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.
32. 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
33. 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.
34. A Sixth-order Image Approximation to the Ionic Solvent Induced Reaction Field, M. Xiang, S. Z. Deng, W. Cai,   the Journal of Scientific computing, Published online: 17 June 2009.
35. A wideband Fast multipole method for the two-dimensional complex Helmholtz equation, M.H. Cho, W. Cai, Computer Physics Communications, 181 (2010) 2086-2090.
36. 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).
37. 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
38. Well-conditioned orthonormal hierarchical L2  bases on R^n simplicial elements, J. Xin, W. Cai,  J Sci Comput (2012) 50:446–461.
39. 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.
40. 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.
41.  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.
42. 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.
43.    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.
44.   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, Vol. 16, No. 5, pp. 1389-1418 November 2014.
45.    Accurate and Efficient Nystrom 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.
46.  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, the Communication in Computational Physics, Vol. 20, No. 5, pp. 1283-1312, 2016.
47. 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.
48.   Accurate and Efficient Nystrom Volume  Integral Equation Method for Electromagnetic Scattering of 3-D Meta-materials in Layered Media, ,  Duan Chen Min Hyung Cho Wei Cai, SIAM J. on Scientific computing, Vol. 40, No. 1, pp. B259–B282, 2018.
49. 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.
50. Wenzhong Zhang, Bo Wang, Wei Cai, Exponential Convergence For Multipole Expansion And Translation To Local Expansions For Sources In Layered Media: 2-D Acoustic Wave, Arxiv manuscript, September, 2018.
51. A Hierarchical Random Compression Method For Kernel Matrices, Duan Chen, Wei Cai, submitted in revision to SIAM J. on Scientific Computing,  2018.                                                    II. Combustion System
52. High-order Numerical Methods for the Computation of Cellular Structure of 2-D Detonation Waves, AIAA Journal, Vol. 33, No. 7, PP 1248-1255, (July, 1995).
53. Direct numerical calculation of neutral stability curve for one-dimensional detonations, (with W.H. Oh, Y.L. Zhu), SIAM Journal of Scientific Computing, Volume 17, Number 4, pp. 814-829, July 1996.
54. An Adaptive Spline Wavelet ADI (SW-ADI) Method for two-dimensional Reaction Diffusion Equations, (with Wu Zhang), Journal of Computational Physics, Vol. 139, pp. 92-126 (1998).                                                                                                                                                                                                                III.  Electromagnetic Scattering in Microwave devices
55. 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.
56. High Order Window Functions and Fast Algorithms for Calculating Dyadic Electromagnetic Green?s Functions in Multilayered Media, (with Tiejun Yu), Radio Science, July, 2001.
57. 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.                                                                                                                                                                                                                           IV.  Circuit Simulation and Model Reductions
58. A fast wavelet collocation method for high speed circuit simulation (with Dian Zhou), IEEE transaction on circuits and systems, Vol. 46, No. 8, pp. 920-930, 1999.
59. An adaptive wavelet method for nonlinear circuit simulation (with Dian Zhou and W, Zhang), IEEE transaction on circuits and systems, Vol. 46, No. 8, pp. 931-938, 1999.
60. An efficient DC-gain matched balanced truncation realization for VLSI interconnect circuit order reduction, Microelectronic Engineering, Vol. 60, issue 1-2, p. 3-15, 2002.
61. 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).
62. 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.
63. 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.
64.  G.L. Chen, H.L. Zhu, Tao Cui, Z.M. Chen, X. Zeng, and W. Cai, ParAFEMCap: A Parallel Adaptive Finite Element Method for 3-D VLSI Interconnect Capacitance Extraction , IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 2, FEBRUARY 2012.                                                                                                                                                           V. Meta-Materials, Photonics, and Plasmon Systems
65. Numerical Study of Light Propagation via Whispering Gallery Modes in Microcylinder Coupled Resonator Optical Waveguides,   Optics Express, 12, 6468-6480 (2004).
66. 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.
67. 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.
68. Optical Coupling at a distance between detuned spherical cavities, A. Kanaev, V. Astratov, W. Cai,  Applied Physics Letter, 88, 111111 (2006).
69. 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.
70. 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, In Press, July, 2006.
71. 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.
72. 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.
73. 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. Scientific computing, 2017.                                                                                                                        VI. Quantum Transport in Nano-devices
74. 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.
75. 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.
76. 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.
77. 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).
78. 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).
79. 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.
80. 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)                                                                                                             VII. Electrostatics and MD simulations for Biomolecules and Ion-Channels
81. 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.
82. 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.
83.  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
84. 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)
85. 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).
86. Fast analytical methods for macroscopic electrostatic models in biomolecular simulations, Z. L. Xu, W. Cai, Z. L. Xu, W. Cai,  SIAM Rev. 53, pp. 683-720.
87. 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).
88. 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.
89. 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).
90. Effect of the Reaction Field onMolecular 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.
91. 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,Volume 184, Issue 1, January 2013, Pages 19–26.
92. 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, in press, Journal of Computational Physics, 2013.
93. 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.
94. 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.
95. 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.
96. 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).                                                                                                                                                                                                                                                               VIII. Mask Simulation in Lithography
97. 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.
98. 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)                                                                                                                                            IX. Stochastic methods and simulations
99. 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.
100. 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.
101. A modified nested sparse grid based adaptive stochastic collocation method for statistical state timing analysis, the IEICE TRANS. Fundamentals, vol. E92-A, No. 12, pp. 3024-3034, (2009).
102. 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).
103. A fundamental model proposed for material removal in chemical mechanical polishing,   S. Xin, W. Cai, and J. Tichy, Wear 268 (2010), 837-844.
104. 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.
105. 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.
106. 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).
107. Anna Lischke, Guofei Pang, Mamikon Gulian, Fangying Song, Christian Glusa, Xiaoning Zheng,Zhiping Mao, Wei Cai, Mark M. Meerschaert, Mark Ainsworth, George Em Karniadakis, What Is the Fractional Laplacian? Submitted to Journal of Computational Physics, 1/2018.
108. Pang G, Perdikaris P, Cai W, Karniadakis GE. Discovering variable fractional orders of advection-dispersion equations from field data using multi-fidelity Bayesian optimization. Journal of Computational Physics. 2017 Nov 1;348(C):694-714.