Publications

Books

 
Numerical Methods in Applied Sciences edited by W. Cai, Z.C. Shi, C.W. Shu and J.C. Xu, Science Press, New York, pp 39-59, 1996
 

Journal Articles

 
  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, (with D. Gottlieb and C. W. Shu, Mathematics of Computation, 52, (1989) pp.389-410.                                                                                                                                                                                                                                                              
  4. Cell averaging Chebychev Method for Hyperbolic Problems, (with D. Gottlieb and A. Harten), Computers and Mathematics with Applications, vol. 24, No. 516, pp. 37-49, September 1992.                                                                                                                                                                                                                                                                                                                               
  5. Uniform High Order Spectral Methods for One and Two Dimensional Euler Equations, (with 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, (with 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. 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).

  10. 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.

  11. 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.

  12. 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).

  13. 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.

  14. 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.

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

  16. 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.

  17. Adaptive Wavelet ADI Method: Application and Parallelization, (jointly with Xianhe Sun), Proceeding of 2000 International Conference on Parallel Processing (ICPP), August 2000, Toronto, Canada.

  18. 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.

  19. 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.

  20. High Order Window Functions and Fast Algorithms for Calculating Dyadic Electromagnetic Green?s Functions in Multilayered Media, (with Tiejun Yu), Radio Science, July, 2001.

  21. Inverse Matrix Evaluation for Linear Systems, (with Mohsen Tadi), Inverse Problems 17, pp. 247-260, 2001.

  22. 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.

  23. 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.

  24. 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.

  25. 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.                                                                                                                                                                                                                                                                                                                 
  26. 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.

  27. An Upwinding Embedded Boundary Methods for Maxwell equations, (with S.  Deng)  Journal of Computational Phyiscs, 190, 2003.                                                                                                                                                                                                                                                                                                
  28. 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)

  29. 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

  30. 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.

  31. 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.

  32. 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.

  33. 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.

  34. 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.

  35. Numerical Study of Light Propagation via Whispering Gallery Modes in Microcylinder Coupled Resonator Optical Waveguides,   Optics Express, 12, 6468-6480 (2004).

  36. 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.

  37. 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.

  38. 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.

  39. 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

  40. 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

  41. FIFA - “ Fast Interpolation and Filtering Algorithm for Calculating Dyadic Green's Function in the Electromagnetic Scattering of Multi-layered Structures,   Communication in Computational Physics, Vol. 1, No. 2, pp. 228-258, 2006.

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

  43. 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.

  44. Super Structure Photonic Crystal Fiber, Min Hyung Cho, W. Cai, Tsinghua Her, Preprint

  45. A Fourier Spectral-Discontinuous Galerkin Methods for Time Dependent 3-D Schrodinger-Poission Equations with Discontinuous Potentials, T. Lu, W. Cai, to appear in  the Journal of Computational and Applied Mathematics, 2007.                                                                                                                                                                                                                                                                                                                                                                             
  46. Transmission and Dispersion Characteristic of a Discontinuous Galerkin Method for Maxwell's Equations in Dispersive Inhomogeneuos Media, X. Ji, W. Cai, P.W. Zhang, submitted to Journal of Computational Mathematics, October, 2007.                                                                                                                                                                                                                                                              
  47. 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.                                                                                                                                                                                                                                                                                                                                                                 
  48.  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.                                                                                                                                                                                                                                                                                                                                                
  49. A Sparse Grid based Spectral Stochastic Collocation Method for Variations-Aware the Capacitance Extraction of Interconnects under Nanometer Process Technology,  H. L. Zhu, X. Zeng, W. Cai, J. T. Xue, D. Zhou, submitted to IEEE Trans. 2007.                                                                                                                                                                                                                                                                                                                               
  50. 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.                                                                                                                                                                                                                                                                                                                                                                                                                                    
  51. A Full Vectorial Generalized Discontinuous Galerkin Beam Propagatiom Method (GDG-BPM) for Inhomogeneous Optical Waveguide, K. Fan, W. Cai, X. Ji, submitted to the Journal of Computational Physics, November, 2007.                                                                                                                                                                                                                                                                                                                                                                                                                        
  52. 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.                                                                                                                                                                                                                                                                                                                                                                                                                                                            
  53. 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.                                                                                                                                                                                                                                                                                                                                                                                                     
  54. 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, submitted to the Journal of Computational Physics, November, 2007.                                                                                                                                                                                                                                                                                                                                                                                   
  55. Image Methods for Electrostatics Potentials, to appear in Advances in mathematics and applications, 2008.                                                                                                                                                                                                                                                                                                                                           
  56. A Fast Algorithm to Evaluate Generalized Born Radii for Implicit Solvation Models of Biomolecules, Wei Cai, Zhenli Xu, submitted to the Journal of Computational Physics,  Jan.  2008.                                                        
                                                                                                                                                                             
  57. Image Charge Approximations of Reaction Fields in Solvation with Arbitrary Ionic Strength,  Zhenli Xu, Shaozhong Deng, submitted to the Journal of Computational Physics, Jan. 2008.     
             
  58. 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, submitted to Journal of Computational Physics, April, 2008.